%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS069+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 03:18:35 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 16 unt; 0 def)
% Number of atoms : 163 ( 27 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 180 ( 84 ~; 76 |; 13 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 75 ( 0 sgn 48 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rf1(X,Y)
& cp1(Y) )
& ? [Y] :
( rf2(X,Y)
& ~ cp1(Y) )
& ? [Y] :
( rf3(X,Y)
& cp2(Y) ) ) ) ).
fof(axiom_3,axiom,
! [X,Y,Z] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> Y = Z ) ).
fof(axiom_4,axiom,
! [X,Y,Z] :
( ( rf2(X,Y)
& rf2(X,Z) )
=> Y = Z ) ).
fof(axiom_6,axiom,
cUnsatisfiable(i2003_11_14_17_18_2750) ).
fof(axiom_7,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf1(X,Y) ) ).
fof(axiom_8,axiom,
! [X,Y] :
( rf3(X,Y)
=> rf2(X,Y) ) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf3(X,Y) )
| ! [Y] :
( ~ rf2(X,Y)
| cp1(Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ! [Y] :
( ~ cp1(Y)
| ~ rf1(X,Y) )
| ! [Y] :
( ~ cp2(Y)
| ~ rf3(X,Y) )
| ! [Y] :
( ~ rf2(X,Y)
| cp1(Y) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Y0,Y1] :
( ( ~ cUnsatisfiable(X)
| ~ cp1(skolemFOFtoCNF_Y_2(X)) )
& ( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| cp2(skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rf1(X,skolemFOFtoCNF_Y_1(X)) )
& ( ~ cUnsatisfiable(X)
| rf2(X,skolemFOFtoCNF_Y_2(X)) )
& ( ~ cUnsatisfiable(X)
| rf3(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cp1(Y)
| ~ cp2(Y0)
| ~ rf1(X,Y)
| ~ rf2(X,Y1)
| ~ rf3(X,Y0)
| cUnsatisfiable(X)
| cp1(Y1) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ~ cp1(skolemFOFtoCNF_Y_2(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
cUnsatisfiable(i2003_11_14_17_18_2750),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rf2(X,skolemFOFtoCNF_Y_2(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rf3(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ rf3(X,Y)
| rf2(X,Y) ),
inference(canonicalize,[],[axiom_8]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ rf3(X,Y)
| rf2(X,Y) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ rf2(X,Y)
| ~ rf2(X,Z)
| Y = Z ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ rf2(X,Y)
| ~ rf2(X,Z)
| Y = Z ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ rf3(X,Y)
| rf1(X,Y) ),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ rf3(X,Y)
| rf1(X,Y) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rf1(X,skolemFOFtoCNF_Y_1(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ rf1(X,Y)
| ~ rf1(X,Z)
| Y = Z ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ rf1(X,Y)
| ~ rf1(X,Z)
| Y = Z ),
inference(specialize,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
( ~ cUnsatisfiable(X)
| ~ cp1(skolemFOFtoCNF_Y_2(X)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_2750)
| ~ cp1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_18_2750))]]) ).
cnf(refute_0_2,plain,
cUnsatisfiable(i2003_11_14_17_18_2750),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ cUnsatisfiable(X)
| rf2(X,skolemFOFtoCNF_Y_2(X)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_2750)
| rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(i2003_11_14_17_18_2750))]]) ).
cnf(refute_0_5,plain,
rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_2750) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(X)
| rf3(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_2750)
| rf3(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(i2003_11_14_17_18_2750))]]) ).
cnf(refute_0_8,plain,
rf3(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_2750) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ rf3(X,Y)
| rf2(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
( ~ rf3(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))
| rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(i2003_11_14_17_18_2750)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)))]]) ).
cnf(refute_0_11,plain,
rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( rf3(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ rf2(X,Y)
| ~ rf2(X,Z)
| Y = Z ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_13,plain,
( ~ rf2(i2003_11_14_17_18_2750,X_21)
| ~ rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))
| skolemFOFtoCNF_Y(i2003_11_14_17_18_2750) = X_21 ),
inference(subst,[],[refute_0_12:[bind(X,$fot(i2003_11_14_17_18_2750)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_14,plain,
( ~ rf2(i2003_11_14_17_18_2750,X_21)
| skolemFOFtoCNF_Y(i2003_11_14_17_18_2750) = X_21 ),
inference(resolve,[$cnf( rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750))
| skolemFOFtoCNF_Y(i2003_11_14_17_18_2750) = skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750) ),
inference(subst,[],[refute_0_14:[bind(X_21,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)))]]) ).
cnf(refute_0_16,plain,
skolemFOFtoCNF_Y(i2003_11_14_17_18_2750) = skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750),
inference(resolve,[$cnf( rf2(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) )],[refute_0_5,refute_0_15]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y2
| Y2 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y2)]]) ).
cnf(refute_0_19,plain,
( X0 != Y2
| Y2 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_Y(i2003_11_14_17_18_2750) != skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)
| skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750) = skolemFOFtoCNF_Y(i2003_11_14_17_18_2750) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))),bind(Y2,$fot(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)))]]) ).
cnf(refute_0_21,plain,
skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750) = skolemFOFtoCNF_Y(i2003_11_14_17_18_2750),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750),skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750) != skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)
| ~ cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))
| cp1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) ),
introduced(tautology,[equality,[$cnf( ~ cp1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))]]) ).
cnf(refute_0_23,plain,
( ~ cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))
| cp1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750),skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_2750)
| ~ cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) ),
inference(resolve,[$cnf( cp1(skolemFOFtoCNF_Y_2(i2003_11_14_17_18_2750)) )],[refute_0_23,refute_0_1]) ).
cnf(refute_0_25,plain,
~ cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_2750) )],[refute_0_2,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_27,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_2750)
| cp1(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750)) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(i2003_11_14_17_18_2750))]]) ).
cnf(refute_0_28,plain,
cp1(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_2750) )],[refute_0_2,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ rf3(X,Y)
| rf1(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_30,plain,
( ~ rf3(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))
| rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(i2003_11_14_17_18_2750)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)))]]) ).
cnf(refute_0_31,plain,
rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( rf3(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) )],[refute_0_8,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ cUnsatisfiable(X)
| rf1(X,skolemFOFtoCNF_Y_1(X)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_33,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_2750)
| rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(i2003_11_14_17_18_2750))]]) ).
cnf(refute_0_34,plain,
rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_2750) )],[refute_0_2,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ rf1(X,Y)
| ~ rf1(X,Z)
| Y = Z ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_36,plain,
( ~ rf1(i2003_11_14_17_18_2750,X_16)
| ~ rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750) = X_16 ),
inference(subst,[],[refute_0_35:[bind(X,$fot(i2003_11_14_17_18_2750)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750))),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_37,plain,
( ~ rf1(i2003_11_14_17_18_2750,X_16)
| skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750) = X_16 ),
inference(resolve,[$cnf( rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750)) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))
| skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750) = skolemFOFtoCNF_Y(i2003_11_14_17_18_2750) ),
inference(subst,[],[refute_0_37:[bind(X_16,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)))]]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750) = skolemFOFtoCNF_Y(i2003_11_14_17_18_2750),
inference(resolve,[$cnf( rf1(i2003_11_14_17_18_2750,skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) )],[refute_0_31,refute_0_38]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750) != skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)
| ~ cp1(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750))
| cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) ),
introduced(tautology,[equality,[$cnf( cp1(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750)) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750))]]) ).
cnf(refute_0_41,plain,
( ~ cp1(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750))
| cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750),skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)),
inference(resolve,[$cnf( cp1(skolemFOFtoCNF_Y_1(i2003_11_14_17_18_2750)) )],[refute_0_28,refute_0_41]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( cp1(skolemFOFtoCNF_Y(i2003_11_14_17_18_2750)) )],[refute_0_42,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS069+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 15:05:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------