TSTP Solution File: KRS098+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS098+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 : Sun Jul 17 03:18:42 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 114 ( 28 unt; 1 def)
% Number of atoms : 373 ( 56 equ)
% Maximal formula atoms : 70 ( 3 avg)
% Number of connectives : 460 ( 201 ~; 189 |; 56 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-1 aty)
% Number of variables : 176 ( 8 sgn 97 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rr3(X,Y)
& ? [Z] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z2,Z3] :
( ( rtt(Y,Z2)
& rtt(Y,Z3) )
=> Z2 = Z3 ) )
& ? [Y] :
( rr2(X,Y)
& ! [Z2,Z3] :
( ( rtt(Y,Z2)
& rtt(Y,Z3) )
=> Z2 = Z3 )
& ? [Z] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y2,Y3] :
( rr(X,Y2)
& rr(X,Y3)
& Y2 != Y3 )
& ? [Y] :
( rr1(X,Y)
& ! [Z2,Z3] :
( ( rtt(Y,Z2)
& rtt(Y,Z3) )
=> Z2 = Z3 )
& ? [Z] :
( rt1(Y,Z)
& cc(Z) ) ) ) ) ).
fof(axiom_4,axiom,
cUnsatisfiable(i2003_11_14_17_20_25524) ).
fof(axiom_6,axiom,
! [X] :
~ ( ce(X)
& cc(X) ) ).
fof(axiom_8,axiom,
! [X,Y] :
( rr1(X,Y)
=> rr(X,Y) ) ).
fof(axiom_9,axiom,
! [X,Y] :
( rr2(X,Y)
=> rr(X,Y) ) ).
fof(axiom_10,axiom,
! [X,Y] :
( rt1(X,Y)
=> rtt(X,Y) ) ).
fof(axiom_12,axiom,
! [X,Y] :
( rr3(X,Y)
=> rr(X,Y) ) ).
fof(axiom_13,axiom,
! [X,Y] :
( rt3(X,Y)
=> rtt(X,Y) ) ).
fof(definition_0,definition,
! [Y,Z2,Z3] :
( definitionFOFtoCNF_0(Y,Z2,Z3)
<=> ( ~ rtt(Y,Z2)
| ~ rtt(Y,Z3)
| Z2 = Z3 ) ) ).
fof(normalize_0_0,plain,
cUnsatisfiable(i2003_11_14_17_20_25524),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y2,Y3] :
( Y2 != Y3
& rr(X,Y2)
& rr(X,Y3) )
| ! [Y] :
( ~ rr1(X,Y)
| ? [Z2,Z3] :
( Z2 != Z3
& rtt(Y,Z2)
& rtt(Y,Z3) )
| ! [Z] :
( ~ cc(Z)
| ~ rt1(Y,Z) ) )
| ! [Y] :
( ~ rr2(X,Y)
| ? [Z2,Z3] :
( Z2 != Z3
& rtt(Y,Z2)
& rtt(Y,Z3) )
| ! [Z] :
( ~ cd(Z)
| ~ rt2(Y,Z) ) )
| ! [Y] :
( ~ rr3(X,Y)
| ? [Z2,Z3] :
( Z2 != Z3
& rtt(Y,Z2)
& rtt(Y,Z3) )
| ! [Z] :
( ~ ce(Z)
| ~ rt3(Y,Z) ) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y2,Y3] :
( Y2 != Y3
& rr(X,Y2)
& rr(X,Y3) )
| ! [Y] :
( ~ rr1(X,Y)
| ? [Z2,Z3] :
( Z2 != Z3
& rtt(Y,Z2)
& rtt(Y,Z3) )
| ! [Z] :
( ~ cc(Z)
| ~ rt1(Y,Z) ) )
| ! [Y] :
( ~ rr2(X,Y)
| ? [Z2,Z3] :
( Z2 != Z3
& rtt(Y,Z2)
& rtt(Y,Z3) )
| ! [Z] :
( ~ cd(Z)
| ~ rt2(Y,Z) ) )
| ! [Y] :
( ~ rr3(X,Y)
| ? [Z2,Z3] :
( Z2 != Z3
& rtt(Y,Z2)
& rtt(Y,Z3) )
| ! [Z] :
( ~ ce(Z)
| ~ rt3(Y,Z) ) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y,Z2,Z3] :
( ~ definitionFOFtoCNF_0(Y,Z2,Z3)
<=> ( Z2 != Z3
& rtt(Y,Z2)
& rtt(Y,Z3) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ? [Y2,Y3] :
( Y2 != Y3
& rr(X,Y2)
& rr(X,Y3) )
| ! [Y] :
( ~ rr1(X,Y)
| ? [Z2,Z3] : ~ definitionFOFtoCNF_0(Y,Z2,Z3)
| ! [Z] :
( ~ cc(Z)
| ~ rt1(Y,Z) ) )
| ! [Y] :
( ~ rr2(X,Y)
| ? [Z2,Z3] : ~ definitionFOFtoCNF_0(Y,Z2,Z3)
| ! [Z] :
( ~ cd(Z)
| ~ rt2(Y,Z) ) )
| ! [Y] :
( ~ rr3(X,Y)
| ? [Z2,Z3] : ~ definitionFOFtoCNF_0(Y,Z2,Z3)
| ! [Z] :
( ~ ce(Z)
| ~ rt3(Y,Z) ) ) ) ),
inference(simplify,[],[normalize_0_2,normalize_0_3,normalize_0_3,normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y,Y0,Y1,Y2,Y3,Z,Z0,Z1,Z2,Z3] :
( ( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Z_2(X)) )
& ( ~ cUnsatisfiable(X)
| cd(skolemFOFtoCNF_Z_1(X)) )
& ( ~ cUnsatisfiable(X)
| ce(skolemFOFtoCNF_Z(X)) )
& ( ~ cUnsatisfiable(X)
| definitionFOFtoCNF_0(skolemFOFtoCNF_Y(X),Z2,Z3) )
& ( ~ cUnsatisfiable(X)
| definitionFOFtoCNF_0(skolemFOFtoCNF_Y_1(X),Z2,Z3) )
& ( ~ cUnsatisfiable(X)
| definitionFOFtoCNF_0(skolemFOFtoCNF_Y_2(X),Z2,Z3) )
& ( ~ cUnsatisfiable(X)
| rr1(X,skolemFOFtoCNF_Y_2(X)) )
& ( ~ cUnsatisfiable(X)
| rr2(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| rr3(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rt1(skolemFOFtoCNF_Y_2(X),skolemFOFtoCNF_Z_2(X)) )
& ( ~ cUnsatisfiable(X)
| rt2(skolemFOFtoCNF_Y_1(X),skolemFOFtoCNF_Z_1(X)) )
& ( ~ cUnsatisfiable(X)
| rt3(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rr(X,Y2)
| ~ rr(X,Y3)
| Y2 = Y3 )
& ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
| ~ cc(Z)
| ~ cd(Z0)
| ~ ce(Z1)
| ~ definitionFOFtoCNF_0(Y,skolemFOFtoCNF_Z0(Y),skolemFOFtoCNF_Z1(Y))
| ~ definitionFOFtoCNF_0(Y0,skolemFOFtoCNF_Z0_1(Y0),skolemFOFtoCNF_Z1_1(Y0))
| ~ definitionFOFtoCNF_0(Y1,skolemFOFtoCNF_Z0_2(Y1),skolemFOFtoCNF_Z1_2(Y1))
| ~ rr1(X,Y)
| ~ rr2(X,Y0)
| ~ rr3(X,Y1)
| ~ rt1(Y,Z)
| ~ rt2(Y0,Z0)
| ~ rt3(Y1,Z1)
| cUnsatisfiable(X) )
& ( ~ cc(Z)
| ~ cd(Z0)
| ~ ce(Z1)
| ~ definitionFOFtoCNF_0(Y,skolemFOFtoCNF_Z0(Y),skolemFOFtoCNF_Z1(Y))
| ~ definitionFOFtoCNF_0(Y0,skolemFOFtoCNF_Z0_1(Y0),skolemFOFtoCNF_Z1_1(Y0))
| ~ definitionFOFtoCNF_0(Y1,skolemFOFtoCNF_Z0_2(Y1),skolemFOFtoCNF_Z1_2(Y1))
| ~ rr1(X,Y)
| ~ rr2(X,Y0)
| ~ rr3(X,Y1)
| ~ rt1(Y,Z)
| ~ rt2(Y0,Z0)
| ~ rt3(Y1,Z1)
| cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ cc(Z)
| ~ cd(Z0)
| ~ ce(Z1)
| ~ definitionFOFtoCNF_0(Y,skolemFOFtoCNF_Z0(Y),skolemFOFtoCNF_Z1(Y))
| ~ definitionFOFtoCNF_0(Y0,skolemFOFtoCNF_Z0_1(Y0),skolemFOFtoCNF_Z1_1(Y0))
| ~ definitionFOFtoCNF_0(Y1,skolemFOFtoCNF_Z0_2(Y1),skolemFOFtoCNF_Z1_2(Y1))
| ~ rr1(X,Y)
| ~ rr2(X,Y0)
| ~ rr3(X,Y1)
| ~ rt1(Y,Z)
| ~ rt2(Y0,Z0)
| ~ rt3(Y1,Z1)
| cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y1(X)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Z_2(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rt1(skolemFOFtoCNF_Y_2(X),skolemFOFtoCNF_Z_2(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ rt1(X,Y)
| rtt(X,Y) ),
inference(canonicalize,[],[axiom_10]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ rt1(X,Y)
| rtt(X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr1(X,skolemFOFtoCNF_Y_2(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr2(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y2,Y3] :
( ~ cUnsatisfiable(X)
| ~ rr(X,Y2)
| ~ rr(X,Y3)
| Y2 = Y3 ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr3(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[axiom_12]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rt3(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ~ rt3(X,Y)
| rtt(X,Y) ),
inference(canonicalize,[],[axiom_13]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ~ rt3(X,Y)
| rtt(X,Y) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X,Z2,Z3] :
( ~ cUnsatisfiable(X)
| definitionFOFtoCNF_0(skolemFOFtoCNF_Y(X),Z2,Z3) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_24,plain,
! [Y,Z2,Z3] :
( ( Z2 != Z3
| definitionFOFtoCNF_0(Y,Z2,Z3) )
& ( definitionFOFtoCNF_0(Y,Z2,Z3)
| rtt(Y,Z2) )
& ( definitionFOFtoCNF_0(Y,Z2,Z3)
| rtt(Y,Z3) )
& ( ~ definitionFOFtoCNF_0(Y,Z2,Z3)
| ~ rtt(Y,Z2)
| ~ rtt(Y,Z3)
| Z2 = Z3 ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_25,plain,
! [Y,Z2,Z3] :
( ~ definitionFOFtoCNF_0(Y,Z2,Z3)
| ~ rtt(Y,Z2)
| ~ rtt(Y,Z3)
| Z2 = Z3 ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X] :
( ~ cc(X)
| ~ ce(X) ),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_0_27,plain,
! [X] :
( ~ cc(X)
| ~ ce(X) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ce(skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
cUnsatisfiable(i2003_11_14_17_20_25524),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(X)
| cc(skolemFOFtoCNF_Z_2(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| cc(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_3,plain,
cc(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(X)
| rt1(skolemFOFtoCNF_Y_2(X),skolemFOFtoCNF_Z_2(X)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| rt1(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_6,plain,
rt1(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ rt1(X,Y)
| rtt(X,Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( ~ rt1(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524))
| rtt(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524))),bind(Y,$fot(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_9,plain,
rtt(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( rt1(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ cUnsatisfiable(X)
| rr1(X,skolemFOFtoCNF_Y_2(X)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| rr1(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_12,plain,
rr1(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
( ~ rr1(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(i2003_11_14_17_20_25524)),bind(Y,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_15,plain,
rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( rr1(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ cUnsatisfiable(X)
| rr2(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| rr2(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_18,plain,
rr2(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_20,plain,
( ~ rr2(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(i2003_11_14_17_20_25524)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_21,plain,
rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( rr2(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524)) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ cUnsatisfiable(X)
| ~ rr(X,Y2)
| ~ rr(X,Y3)
| Y2 = Y3 ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_23,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ rr(i2003_11_14_17_20_25524,X_56)
| ~ rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) = X_56 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(i2003_11_14_17_20_25524)),bind(Y2,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524))),bind(Y3,$fot(X_56))]]) ).
cnf(refute_0_24,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ rr(i2003_11_14_17_20_25524,X_56)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) = X_56 ),
inference(resolve,[$cnf( rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524)) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ rr(i2003_11_14_17_20_25524,X_56)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) = X_56 ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524) ),
inference(subst,[],[refute_0_25:[bind(X_56,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),
inference(resolve,[$cnf( rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)) )],[refute_0_15,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ cUnsatisfiable(X)
| rr3(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_29,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| rr3(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_28:[bind(X,$fot(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_30,plain,
rr3(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_32,plain,
( ~ rr3(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(i2003_11_14_17_20_25524)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_33,plain,
rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( rr3(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)) )],[refute_0_30,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y(i2003_11_14_17_20_25524) ),
inference(subst,[],[refute_0_25:[bind(X_56,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_35,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),
inference(resolve,[$cnf( rr(i2003_11_14_17_20_25524,skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) != skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) != skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)
| skolemFOFtoCNF_Y(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524),skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_37,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524) != skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)
| skolemFOFtoCNF_Y(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524),skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
skolemFOFtoCNF_Y(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_25524),skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)) )],[refute_0_27,refute_0_37]) ).
cnf(refute_0_39,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_40,plain,
( X0 != X0
| X0 != Y4
| Y4 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y4)]]) ).
cnf(refute_0_41,plain,
( X0 != Y4
| Y4 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( skolemFOFtoCNF_Y(i2003_11_14_17_20_25524) != skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)
| skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y(i2003_11_14_17_20_25524) ),
inference(subst,[],[refute_0_41:[bind(X0,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524))),bind(Y4,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_43,plain,
skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524)) )],[refute_0_38,refute_0_42]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524) != skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)
| ~ rtt(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524))
| rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) ),
introduced(tautology,[equality,[$cnf( rtt(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_45,plain,
( ~ rtt(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524))
| rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Y(i2003_11_14_17_20_25524)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( rtt(skolemFOFtoCNF_Y_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) )],[refute_0_9,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ cUnsatisfiable(X)
| rt3(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_48,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| rt3(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_47:[bind(X,$fot(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_49,plain,
rt3(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ rt3(X,Y)
| rtt(X,Y) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_51,plain,
( ~ rt3(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524))
| rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524))),bind(Y,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_52,plain,
rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( rt3(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ cUnsatisfiable(X)
| definitionFOFtoCNF_0(skolemFOFtoCNF_Y(X),Z2,Z3) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_54,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| definitionFOFtoCNF_0(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_40,X_41) ),
inference(subst,[],[refute_0_53:[bind(X,$fot(i2003_11_14_17_20_25524)),bind(Z2,$fot(X_40)),bind(Z3,$fot(X_41))]]) ).
cnf(refute_0_55,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_40,X_41),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_54]) ).
cnf(refute_0_56,plain,
definitionFOFtoCNF_0(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_60,X_61),
inference(subst,[],[refute_0_55:[bind(X_40,$fot(X_60)),bind(X_41,$fot(X_61))]]) ).
cnf(refute_0_57,plain,
( ~ definitionFOFtoCNF_0(Y,Z2,Z3)
| ~ rtt(Y,Z2)
| ~ rtt(Y,Z3)
| Z2 = Z3 ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_58,plain,
( ~ definitionFOFtoCNF_0(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_60,X_61)
| ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_60)
| ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_61)
| X_60 = X_61 ),
inference(subst,[],[refute_0_57:[bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524))),bind(Z2,$fot(X_60)),bind(Z3,$fot(X_61))]]) ).
cnf(refute_0_59,plain,
( ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_60)
| ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_61)
| X_60 = X_61 ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_60,X_61) )],[refute_0_56,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_63)
| ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524))
| skolemFOFtoCNF_Z(i2003_11_14_17_20_25524) = X_63 ),
inference(subst,[],[refute_0_59:[bind(X_60,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524))),bind(X_61,$fot(X_63))]]) ).
cnf(refute_0_61,plain,
( ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),X_63)
| skolemFOFtoCNF_Z(i2003_11_14_17_20_25524) = X_63 ),
inference(resolve,[$cnf( rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) )],[refute_0_52,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524))
| skolemFOFtoCNF_Z(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524) ),
inference(subst,[],[refute_0_61:[bind(X_63,$fot(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_63,plain,
skolemFOFtoCNF_Z(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524),
inference(resolve,[$cnf( rtt(skolemFOFtoCNF_Y(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) )],[refute_0_46,refute_0_62]) ).
cnf(refute_0_64,plain,
( skolemFOFtoCNF_Z(i2003_11_14_17_20_25524) != skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)
| skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Z(i2003_11_14_17_20_25524) ),
inference(subst,[],[refute_0_41:[bind(X0,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524))),bind(Y4,$fot(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_65,plain,
skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524) = skolemFOFtoCNF_Z(i2003_11_14_17_20_25524),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524) != skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)
| ~ cc(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524))
| cc(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) ),
introduced(tautology,[equality,[$cnf( cc(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) ),[0],$fot(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_67,plain,
( ~ cc(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524))
| cc(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524),skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
cc(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cc(skolemFOFtoCNF_Z_2(i2003_11_14_17_20_25524)) )],[refute_0_3,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ cc(X)
| ~ ce(X) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_70,plain,
( ~ cc(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524))
| ~ ce(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_69:[bind(X,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)))]]) ).
cnf(refute_0_71,plain,
( ~ cUnsatisfiable(X)
| ce(skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_72,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ce(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) ),
inference(subst,[],[refute_0_71:[bind(X,$fot(i2003_11_14_17_20_25524))]]) ).
cnf(refute_0_73,plain,
ce(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_25524) )],[refute_0_0,refute_0_72]) ).
cnf(refute_0_74,plain,
~ cc(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)),
inference(resolve,[$cnf( ce(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) )],[refute_0_73,refute_0_70]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( cc(skolemFOFtoCNF_Z(i2003_11_14_17_20_25524)) )],[refute_0_68,refute_0_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS098+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 : Tue Jun 7 20:12:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------