TSTP Solution File: KRS119+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KRS119+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:18:47 EDT 2022
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 73 ( 14 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 208 ( 98 ~; 72 |; 18 &)
% ( 18 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 86 ( 1 sgn 61 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X] :
( cUnsatisfiable(X)
<=> ( ? [Y] :
( rr(X,Y)
& ca_Vx3(Y) )
& cp1(X) ) ) ).
fof(axiom_3,axiom,
! [X] :
( cp1(X)
<=> ~ ? [Y] : ra_Px1(X,Y) ) ).
fof(axiom_4,axiom,
! [X] :
( cp1xcomp(X)
<=> ? [Y0] : ra_Px1(X,Y0) ) ).
fof(axiom_5,axiom,
! [X] :
( ca_Ax2(X)
<=> ( cp1(X)
& ! [Y] :
( rinvR(X,Y)
=> cp1xcomp(Y) ) ) ) ).
fof(axiom_6,axiom,
! [X] :
( ca_Vx3(X)
<=> ? [Y] :
( rr(X,Y)
& ca_Ax2(Y) ) ) ).
fof(axiom_9,axiom,
! [X,Y] :
( rinvR(X,Y)
<=> rr(Y,X) ) ).
fof(axiom_10,axiom,
! [X,Y,Z] :
( ( rr(X,Y)
& rr(Y,Z) )
=> rr(X,Z) ) ).
fof(axiom_11,axiom,
cUnsatisfiable(i2003_11_14_17_21_44786) ).
fof(normalize_0_0,plain,
! [X] :
( ~ cp1(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ cp1(X)
<=> ? [Y] : ra_Px1(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ cp1(X)
| ~ ra_Px1(X,Y) )
& ( cp1(X)
| ra_Px1(X,skolemFOFtoCNF_Y_1(X)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ cp1(X)
| ~ ra_Px1(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ cp1xcomp(X)
<=> ! [Y0] : ~ ra_Px1(X,Y0) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ cp1xcomp(X)
<=> ! [Y0] : ~ ra_Px1(X,Y0) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y0] :
( ( ~ cp1xcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) )
& ( ~ ra_Px1(X,Y0)
| cp1xcomp(X) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ cp1xcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ ca_Ax2(X)
<=> ( ~ cp1(X)
| ? [Y] :
( ~ cp1xcomp(Y)
& rinvR(X,Y) ) ) ),
inference(canonicalize,[],[axiom_5]) ).
fof(normalize_0_9,plain,
! [X] :
( ~ ca_Ax2(X)
<=> ( ~ cp1(X)
| ? [Y] :
( ~ cp1xcomp(Y)
& rinvR(X,Y) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ ca_Ax2(X)
| cp1(X) )
& ( ~ ca_Ax2(X)
| ~ rinvR(X,Y)
| cp1xcomp(Y) )
& ( ~ cp1(X)
| ~ cp1xcomp(skolemFOFtoCNF_Y_2(X))
| ca_Ax2(X) )
& ( ~ cp1(X)
| ca_Ax2(X)
| rinvR(X,skolemFOFtoCNF_Y_2(X)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ ca_Ax2(X)
| ~ rinvR(X,Y)
| cp1xcomp(Y) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(canonicalize,[],[axiom_9]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ rinvR(X,Y)
<=> ~ rr(Y,X) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ( ~ rinvR(X,Y)
| rr(Y,X) )
& ( ~ rr(Y,X)
| rinvR(X,Y) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
cUnsatisfiable(i2003_11_14_17_21_44786),
inference(canonicalize,[],[axiom_11]) ).
fof(normalize_0_17,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) ) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_18,plain,
! [X] :
( ~ cUnsatisfiable(X)
<=> ( ~ cp1(X)
| ! [Y] :
( ~ ca_Vx3(Y)
| ~ rr(X,Y) ) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ( ~ cUnsatisfiable(X)
| ca_Vx3(skolemFOFtoCNF_Y(X)) )
& ( ~ cUnsatisfiable(X)
| cp1(X) )
& ( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) )
& ( ~ ca_Vx3(Y)
| ~ cp1(X)
| ~ rr(X,Y)
| cUnsatisfiable(X) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] :
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X] :
( ~ cUnsatisfiable(X)
| ca_Vx3(skolemFOFtoCNF_Y(X)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_22,plain,
! [X] :
( ~ ca_Vx3(X)
<=> ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ),
inference(canonicalize,[],[axiom_6]) ).
fof(normalize_0_23,plain,
! [X] :
( ~ ca_Vx3(X)
<=> ! [Y] :
( ~ ca_Ax2(Y)
| ~ rr(X,Y) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ( ~ ca_Vx3(X)
| ca_Ax2(skolemFOFtoCNF_Y_3(X)) )
& ( ~ ca_Vx3(X)
| rr(X,skolemFOFtoCNF_Y_3(X)) )
& ( ~ ca_Ax2(Y)
| ~ rr(X,Y)
| ca_Vx3(X) ) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X] :
( ~ ca_Vx3(X)
| rr(X,skolemFOFtoCNF_Y_3(X)) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X,Y,Z] :
( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ),
inference(canonicalize,[],[axiom_10]) ).
fof(normalize_0_27,plain,
! [X,Y,Z] :
( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X] :
( ~ ca_Vx3(X)
| ca_Ax2(skolemFOFtoCNF_Y_3(X)) ),
inference(conjunct,[],[normalize_0_24]) ).
fof(normalize_0_29,plain,
! [X] :
( ~ cUnsatisfiable(X)
| cp1(X) ),
inference(conjunct,[],[normalize_0_19]) ).
cnf(refute_0_0,plain,
( ~ cp1(X)
| ~ ra_Px1(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ cp1(i2003_11_14_17_21_44786)
| ~ ra_Px1(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y0(i2003_11_14_17_21_44786)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_21_44786)),bind(Y,$fot(skolemFOFtoCNF_Y0(i2003_11_14_17_21_44786)))]]) ).
cnf(refute_0_2,plain,
( ~ cp1xcomp(X)
| ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ cp1xcomp(i2003_11_14_17_21_44786)
| ra_Px1(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y0(i2003_11_14_17_21_44786)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(i2003_11_14_17_21_44786))]]) ).
cnf(refute_0_4,plain,
( ~ ca_Ax2(X)
| ~ rinvR(X,Y)
| cp1xcomp(Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ ca_Ax2(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))
| ~ rinvR(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)),i2003_11_14_17_21_44786)
| cp1xcomp(i2003_11_14_17_21_44786) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))),bind(Y,$fot(i2003_11_14_17_21_44786))]]) ).
cnf(refute_0_6,plain,
( ~ rr(Y,X)
| rinvR(X,Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
( ~ rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))
| rinvR(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)),i2003_11_14_17_21_44786) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))),bind(Y,$fot(i2003_11_14_17_21_44786))]]) ).
cnf(refute_0_8,plain,
cUnsatisfiable(i2003_11_14_17_21_44786),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( ~ cUnsatisfiable(X)
| rr(X,skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_10,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_44786)
| rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(i2003_11_14_17_21_44786))]]) ).
cnf(refute_0_11,plain,
rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_44786) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ cUnsatisfiable(X)
| ca_Vx3(skolemFOFtoCNF_Y(X)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_13,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_44786)
| ca_Vx3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(i2003_11_14_17_21_44786))]]) ).
cnf(refute_0_14,plain,
ca_Vx3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_44786) )],[refute_0_8,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ ca_Vx3(X)
| rr(X,skolemFOFtoCNF_Y_3(X)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_16,plain,
( ~ ca_Vx3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))
| rr(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))]]) ).
cnf(refute_0_17,plain,
rr(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))),
inference(resolve,[$cnf( ca_Vx3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ rr(X,Y)
| ~ rr(Y,Z)
| rr(X,Z) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_19,plain,
( ~ rr(X_38,skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))
| ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))
| rr(X_38,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_38)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))),bind(Z,$fot(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))))]]) ).
cnf(refute_0_20,plain,
( ~ rr(X_38,skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))
| rr(X_38,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) ),
inference(resolve,[$cnf( rr(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786),skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))
| rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) ),
inference(subst,[],[refute_0_20:[bind(X_38,$fot(i2003_11_14_17_21_44786))]]) ).
cnf(refute_0_22,plain,
rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))),
inference(resolve,[$cnf( rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)) )],[refute_0_11,refute_0_21]) ).
cnf(refute_0_23,plain,
rinvR(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)),i2003_11_14_17_21_44786),
inference(resolve,[$cnf( rr(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) )],[refute_0_22,refute_0_7]) ).
cnf(refute_0_24,plain,
( ~ ca_Ax2(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))
| cp1xcomp(i2003_11_14_17_21_44786) ),
inference(resolve,[$cnf( rinvR(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)),i2003_11_14_17_21_44786) )],[refute_0_23,refute_0_5]) ).
cnf(refute_0_25,plain,
( ~ ca_Vx3(X)
| ca_Ax2(skolemFOFtoCNF_Y_3(X)) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_26,plain,
( ~ ca_Vx3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))
| ca_Ax2(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)))]]) ).
cnf(refute_0_27,plain,
ca_Ax2(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))),
inference(resolve,[$cnf( ca_Vx3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786)) )],[refute_0_14,refute_0_26]) ).
cnf(refute_0_28,plain,
cp1xcomp(i2003_11_14_17_21_44786),
inference(resolve,[$cnf( ca_Ax2(skolemFOFtoCNF_Y_3(skolemFOFtoCNF_Y(i2003_11_14_17_21_44786))) )],[refute_0_27,refute_0_24]) ).
cnf(refute_0_29,plain,
ra_Px1(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y0(i2003_11_14_17_21_44786)),
inference(resolve,[$cnf( cp1xcomp(i2003_11_14_17_21_44786) )],[refute_0_28,refute_0_3]) ).
cnf(refute_0_30,plain,
~ cp1(i2003_11_14_17_21_44786),
inference(resolve,[$cnf( ra_Px1(i2003_11_14_17_21_44786,skolemFOFtoCNF_Y0(i2003_11_14_17_21_44786)) )],[refute_0_29,refute_0_1]) ).
cnf(refute_0_31,plain,
( ~ cUnsatisfiable(X)
| cp1(X) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_32,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_44786)
| cp1(i2003_11_14_17_21_44786) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(i2003_11_14_17_21_44786))]]) ).
cnf(refute_0_33,plain,
cp1(i2003_11_14_17_21_44786),
inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_21_44786) )],[refute_0_8,refute_0_32]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( cp1(i2003_11_14_17_21_44786) )],[refute_0_33,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : KRS119+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 7 08:44:20 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.40
%------------------------------------------------------------------------------