%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS073+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 03:18:36 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 14 unt; 0 def)
% Number of atoms : 185 ( 18 equ)
% Maximal formula atoms : 35 ( 2 avg)
% Number of connectives : 216 ( 96 ~; 88 |; 19 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 87 ( 0 sgn 54 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rf(X,Y)
& ! [Z] :
( rinvS(Y,Z)
=> cp(Z) )
& ! [Z] :
( rinvF(Y,Z)
=> ? [W] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) ) ).
fof(axiom_3,axiom,
! [X,Y,Z] :
( ( rf(X,Y)
& rf(X,Z) )
=> Y = Z ) ).
fof(axiom_5,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ) ).
fof(axiom_7,axiom,
! [X,Y] :
( rinvS(X,Y)
<=> rs(Y,X) ) ).
fof(axiom_9,axiom,
cUnsatisfiable(i2003_11_14_17_18_54369) ).
fof(axiom_11,axiom,
! [X,Y] :
( rs(X,Y)
=> rf(X,Y) ) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( cp(X)
| ! [Y] :
( ~ rf(X,Y)
| ? [Z] :
( ~ cp(Z)
& rinvS(Y,Z) )
| ? [Z] :
( rinvF(Y,Z)
& ! [W] :
( ~ cp(W)
| ~ rs(Z,W) ) ) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( cp(X)
| ! [Y] :
( ~ rf(X,Y)
| ? [Z] :
( ~ cp(Z)
& rinvS(Y,Z) )
| ? [Z] :
( rinvF(Y,Z)
& ! [W] :
( ~ cp(W)
| ~ rs(Z,W) ) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W,X,Y,Z] :
( ( ~ cUnsatisfiable(X)
| ~ cp(X) )
& ( ~ cUnsatisfiable(X)
| rf(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| ~ rinvF(skolemFOFtoCNF_Y(X),Z)
| cp(skolemFOFtoCNF_W(Z)) )
& ( ~ cUnsatisfiable(X)
| ~ rinvF(skolemFOFtoCNF_Y(X),Z)
| rs(Z,skolemFOFtoCNF_W(Z)) )
& ( ~ cUnsatisfiable(X)
| ~ rinvS(skolemFOFtoCNF_Y(X),Z)
| cp(Z) )
& ( ~ cp(skolemFOFtoCNF_Z(Y))
| ~ rf(X,Y)
| cUnsatisfiable(X)
| cp(X)
| rinvF(Y,skolemFOFtoCNF_Z_1(Y)) )
& ( ~ rf(X,Y)
| cUnsatisfiable(X)
| cp(X)
| rinvF(Y,skolemFOFtoCNF_Z_1(Y))
| rinvS(Y,skolemFOFtoCNF_Z(Y)) )
& ( ~ cp(W)
| ~ cp(skolemFOFtoCNF_Z(Y))
| ~ rf(X,Y)
| ~ rs(skolemFOFtoCNF_Z_1(Y),W)
| cUnsatisfiable(X)
| cp(X) )
& ( ~ cp(W)
| ~ rf(X,Y)
| ~ rs(skolemFOFtoCNF_Z_1(Y),W)
| cUnsatisfiable(X)
| cp(X)
| rinvS(Y,skolemFOFtoCNF_Z(Y)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ~ cp(X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ rinvS(X,Y)
<=> ~ rs(Y,X) ),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ rinvS(X,Y)
<=> ~ rs(Y,X) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ( ~ rinvS(X,Y)
| rs(Y,X) )
& ( ~ rs(Y,X)
| rinvS(X,Y) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ rs(Y,X)
| rinvS(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
cUnsatisfiable(i2003_11_14_17_18_54369),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rf(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ rf(Y,X)
<=> ~ rinvF(X,Y) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ rf(Y,X)
<=> ~ rinvF(X,Y) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( ~ rinvF(X,Y)
| rf(Y,X) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ rf(Y,X)
| rinvF(X,Y) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Z] :
( ~ cUnsatisfiable(X)
| ~ rinvF(skolemFOFtoCNF_Y(X),Z)
| rs(Z,skolemFOFtoCNF_W(Z)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_15,plain,
! [X,Z] :
( ~ cUnsatisfiable(X)
| ~ rinvS(skolemFOFtoCNF_Y(X),Z)
| cp(Z) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(canonicalize,[],[axiom_11]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y,Z] :
( ~ rf(X,Y)
| ~ rf(X,Z)
| Y = Z ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_19,plain,
! [X,Y,Z] :
( ~ rf(X,Y)
| ~ rf(X,Z)
| Y = Z ),
inference(specialize,[],[normalize_0_18]) ).
cnf(refute_0_0,plain,
( ~ cUnsatisfiable(X)
| ~ cp(X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ cp(i2003_11_14_17_18_54369) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_2,plain,
( ~ rs(Y,X)
| rinvS(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ rs(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369))
| rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_W(i2003_11_14_17_18_54369))),bind(Y,$fot(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_4,plain,
cUnsatisfiable(i2003_11_14_17_18_54369),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ cUnsatisfiable(X)
| rf(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_7,plain,
rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_54369) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ rf(Y,X)
| rinvF(X,Y) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_Y(i2003_11_14_17_18_54369))
| rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369))),bind(Y,$fot(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_10,plain,
rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(resolve,[$cnf( rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ cUnsatisfiable(X)
| ~ rinvF(skolemFOFtoCNF_Y(X),Z)
| rs(Z,skolemFOFtoCNF_W(Z)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| rs(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(i2003_11_14_17_18_54369)),bind(Z,$fot(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_13,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| rs(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)) ),
inference(resolve,[$cnf( rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
rs(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_54369) )],[refute_0_4,refute_0_13]) ).
cnf(refute_0_15,plain,
rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(resolve,[$cnf( rs(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)) )],[refute_0_14,refute_0_3]) ).
cnf(refute_0_16,plain,
( ~ cUnsatisfiable(X)
| ~ rinvS(skolemFOFtoCNF_Y(X),Z)
| cp(Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_17,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),Z)
| cp(Z) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_18,plain,
( ~ rs(X,Y)
| rf(X,Y) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_19,plain,
( ~ rs(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369))
| rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(i2003_11_14_17_18_54369)),bind(Y,$fot(skolemFOFtoCNF_W(i2003_11_14_17_18_54369)))]]) ).
cnf(refute_0_20,plain,
rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)),
inference(resolve,[$cnf( rs(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rf(X,Y)
| ~ rf(X,Z)
| Y = Z ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_22,plain,
( ~ rf(i2003_11_14_17_18_54369,X_30)
| ~ rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369))
| skolemFOFtoCNF_W(i2003_11_14_17_18_54369) = X_30 ),
inference(subst,[],[refute_0_21:[bind(X,$fot(i2003_11_14_17_18_54369)),bind(Y,$fot(skolemFOFtoCNF_W(i2003_11_14_17_18_54369))),bind(Z,$fot(X_30))]]) ).
cnf(refute_0_23,plain,
( ~ rf(i2003_11_14_17_18_54369,X_30)
| skolemFOFtoCNF_W(i2003_11_14_17_18_54369) = X_30 ),
inference(resolve,[$cnf( rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_W(i2003_11_14_17_18_54369)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_Y(i2003_11_14_17_18_54369))
| skolemFOFtoCNF_W(i2003_11_14_17_18_54369) = skolemFOFtoCNF_Y(i2003_11_14_17_18_54369) ),
inference(subst,[],[refute_0_23:[bind(X_30,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)))]]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_W(i2003_11_14_17_18_54369) = skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),
inference(resolve,[$cnf( rf(i2003_11_14_17_18_54369,skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)) )],[refute_0_7,refute_0_24]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_28,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_W(i2003_11_14_17_18_54369) != skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)
| skolemFOFtoCNF_Y(i2003_11_14_17_18_54369) = skolemFOFtoCNF_W(i2003_11_14_17_18_54369) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(skolemFOFtoCNF_W(i2003_11_14_17_18_54369))),bind(Y0,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)))]]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_Y(i2003_11_14_17_18_54369) = skolemFOFtoCNF_W(i2003_11_14_17_18_54369),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),skolemFOFtoCNF_Y(i2003_11_14_17_18_54369)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_Y(i2003_11_14_17_18_54369) != skolemFOFtoCNF_W(i2003_11_14_17_18_54369)
| ~ rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),Z)
| rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),Z) ),
introduced(tautology,[equality,[$cnf( ~ rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),Z) ),[0],$fot(skolemFOFtoCNF_W(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_32,plain,
( ~ rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),Z)
| rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),Z) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),skolemFOFtoCNF_W(i2003_11_14_17_18_54369)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),Z)
| cp(Z) ),
inference(resolve,[$cnf( rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_18_54369),Z) )],[refute_0_32,refute_0_17]) ).
cnf(refute_0_34,plain,
( ~ rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),Z)
| cp(Z) ),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_54369) )],[refute_0_4,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369) ),
inference(subst,[],[refute_0_34:[bind(Z,$fot(i2003_11_14_17_18_54369))]]) ).
cnf(refute_0_36,plain,
cp(i2003_11_14_17_18_54369),
inference(resolve,[$cnf( rinvS(skolemFOFtoCNF_W(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) )],[refute_0_15,refute_0_35]) ).
cnf(refute_0_37,plain,
~ cUnsatisfiable(i2003_11_14_17_18_54369),
inference(resolve,[$cnf( cp(i2003_11_14_17_18_54369) )],[refute_0_36,refute_0_1]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_54369) )],[refute_0_4,refute_0_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS073+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % 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 12:06:15 EDT 2022
% 0.12/0.33 % 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
%------------------------------------------------------------------------------