TSTP Solution File: KRS086+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS086+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:18:39 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 120 ( 10 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 136 ( 64 ~; 51 |; 13 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 58 ( 0 sgn 44 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
! [X] :
( cowlThing(X)
& ~ cowlNothing(X) ) ).
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ? [Y] :
( rf(X,Y)
& ? [Z] :
( rinvF(Y,Z)
& ? [W] :
( rf(Z,W)
& ~ cp1(W) ) )
& cp1(Y) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cowlThing(X)
=> ! [Y0,Y1] :
( ( rf(X,Y0)
& rf(X,Y1) )
=> Y0 = Y1 ) ) ).
fof(axiom_4,axiom,
! [X,Y] :
( rinvF(X,Y)
<=> rf(Y,X) ) ).
fof(axiom_7,axiom,
cUnsatisfiable(i2003_11_14_17_19_42328) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ! [Y] :
( ~ cp1(Y)
| ~ rf(X,Y)
| ! [Z] :
( ~ rinvF(Y,Z)
| ! [W] :
( ~ rf(Z,W)
| cp1(W) ) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ! [Y] :
( ~ cp1(Y)
| ~ rf(X,Y)
| ! [Z] :
( ~ rinvF(Y,Z)
| ! [W] :
( ~ rf(Z,W)
| cp1(W) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W,X,Y,Z] :
( ( ~ cUnsatisfiable(X)
| ~ cp1(skolemFOFtoCNF_W(X)) )
& ( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rf(X,skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| rf(skolemFOFtoCNF_Z(X),skolemFOFtoCNF_W(X)) )
& ( ~ cUnsatisfiable(X)
| rinvF(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) )
& ( ~ cp1(Y)
| ~ rf(X,Y)
| ~ rf(Z,W)
| ~ rinvF(Y,Z)
| cUnsatisfiable(X)
| cp1(W) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ~ cp1(skolemFOFtoCNF_W(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
cUnsatisfiable(i2003_11_14_17_19_42328),
inference(canonicalize,[],[axiom_7]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rf(skolemFOFtoCNF_Z(X),skolemFOFtoCNF_W(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rinvF(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ rf(Y,X)
<=> ~ rinvF(X,Y) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ rf(Y,X)
<=> ~ rinvF(X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ rf(Y,X)
| rinvF(X,Y) )
& ( ~ rinvF(X,Y)
| rf(Y,X) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ rinvF(X,Y)
| rf(Y,X) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ cowlThing(X)
| ! [Y0,Y1] :
( ~ rf(X,Y0)
| ~ rf(X,Y1)
| Y0 = Y1 ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_13,plain,
( ! [X] : ~ cowlNothing(X)
& ! [X] : cowlThing(X) ),
inference(canonicalize,[],[axiom_0]) ).
fof(normalize_0_14,plain,
! [X] : cowlThing(X),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X] : cowlThing(X),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y0,Y1] :
( ~ rf(X,Y0)
| ~ rf(X,Y1)
| Y0 = Y1 ),
inference(simplify,[],[normalize_0_12,normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y0,Y1] :
( ~ rf(X,Y0)
| ~ rf(X,Y1)
| Y0 = Y1 ),
inference(specialize,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
( ~ cUnsatisfiable(X)
| ~ cp1(skolemFOFtoCNF_W(X)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_42328)
| ~ cp1(skolemFOFtoCNF_W(i2003_11_14_17_19_42328)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_19_42328))]]) ).
cnf(refute_0_2,plain,
cUnsatisfiable(i2003_11_14_17_19_42328),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ cUnsatisfiable(X)
| cp1(skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_42328)
| cp1(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(i2003_11_14_17_19_42328))]]) ).
cnf(refute_0_5,plain,
cp1(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_42328) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ cUnsatisfiable(X)
| rf(skolemFOFtoCNF_Z(X),skolemFOFtoCNF_W(X)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_42328)
| rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_W(i2003_11_14_17_19_42328)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(i2003_11_14_17_19_42328))]]) ).
cnf(refute_0_8,plain,
rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_W(i2003_11_14_17_19_42328)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_42328) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ cUnsatisfiable(X)
| rinvF(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_10,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_42328)
| rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328),skolemFOFtoCNF_Z(i2003_11_14_17_19_42328)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(i2003_11_14_17_19_42328))]]) ).
cnf(refute_0_11,plain,
rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328),skolemFOFtoCNF_Z(i2003_11_14_17_19_42328)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_42328) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ rinvF(X,Y)
| rf(Y,X) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( ~ rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328),skolemFOFtoCNF_Z(i2003_11_14_17_19_42328))
| rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_Y(i2003_11_14_17_19_42328)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328))),bind(Y,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328)))]]) ).
cnf(refute_0_14,plain,
rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_Y(i2003_11_14_17_19_42328)),
inference(resolve,[$cnf( rinvF(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328),skolemFOFtoCNF_Z(i2003_11_14_17_19_42328)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ rf(X,Y0)
| ~ rf(X,Y1)
| Y0 = Y1 ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
( ~ rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),X_19)
| ~ rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_Y(i2003_11_14_17_19_42328))
| skolemFOFtoCNF_Y(i2003_11_14_17_19_42328) = X_19 ),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328))),bind(Y0,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328))),bind(Y1,$fot(X_19))]]) ).
cnf(refute_0_17,plain,
( ~ rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),X_19)
| skolemFOFtoCNF_Y(i2003_11_14_17_19_42328) = X_19 ),
inference(resolve,[$cnf( rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_Y(i2003_11_14_17_19_42328)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_W(i2003_11_14_17_19_42328))
| skolemFOFtoCNF_Y(i2003_11_14_17_19_42328) = skolemFOFtoCNF_W(i2003_11_14_17_19_42328) ),
inference(subst,[],[refute_0_17:[bind(X_19,$fot(skolemFOFtoCNF_W(i2003_11_14_17_19_42328)))]]) ).
cnf(refute_0_19,plain,
skolemFOFtoCNF_Y(i2003_11_14_17_19_42328) = skolemFOFtoCNF_W(i2003_11_14_17_19_42328),
inference(resolve,[$cnf( rf(skolemFOFtoCNF_Z(i2003_11_14_17_19_42328),skolemFOFtoCNF_W(i2003_11_14_17_19_42328)) )],[refute_0_8,refute_0_18]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_Y(i2003_11_14_17_19_42328) != skolemFOFtoCNF_W(i2003_11_14_17_19_42328)
| ~ cp1(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328))
| cp1(skolemFOFtoCNF_W(i2003_11_14_17_19_42328)) ),
introduced(tautology,[equality,[$cnf( cp1(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328)) ),[0],$fot(skolemFOFtoCNF_W(i2003_11_14_17_19_42328))]]) ).
cnf(refute_0_21,plain,
( ~ cp1(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328))
| cp1(skolemFOFtoCNF_W(i2003_11_14_17_19_42328)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328),skolemFOFtoCNF_W(i2003_11_14_17_19_42328)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
cp1(skolemFOFtoCNF_W(i2003_11_14_17_19_42328)),
inference(resolve,[$cnf( cp1(skolemFOFtoCNF_Y(i2003_11_14_17_19_42328)) )],[refute_0_5,refute_0_21]) ).
cnf(refute_0_23,plain,
~ cUnsatisfiable(i2003_11_14_17_19_42328),
inference(resolve,[$cnf( cp1(skolemFOFtoCNF_W(i2003_11_14_17_19_42328)) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_42328) )],[refute_0_2,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS086+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 : n022.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 18:53:05 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
%------------------------------------------------------------------------------