TSTP Solution File: SWV488+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV488+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 : Wed Jul 20 20:32:00 EDT 2022
% Result : Theorem 0.93s 1.09s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 22 unt; 0 def)
% Number of atoms : 200 ( 82 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 250 ( 106 ~; 95 |; 36 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 44 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(int_leq,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( int_less(I,J)
| I = J ) ) ).
fof(real_constants,axiom,
real_zero != real_one ).
fof(qil,hypothesis,
! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,n)
& int_leq(int_one,J)
& int_leq(J,n) )
=> ( ! [C] :
( ( int_less(int_zero,C)
& I = plus(J,C) )
=> ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,J) )
=> a(plus(K,C),K) = lu(plus(K,C),K) ) )
& ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,J) )
=> a(K,K) = real_one )
& ! [C] :
( ( int_less(int_zero,C)
& J = plus(I,C) )
=> ! [K] :
( ( int_leq(int_one,K)
& int_leq(K,I) )
=> a(K,plus(K,C)) = real_zero ) ) ) ) ).
fof(lti,conjecture,
! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,J)
& int_leq(J,n) )
=> ( I = J
=> a(I,J) != real_zero ) ) ).
fof(subgoal_0,plain,
! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,J)
& int_leq(J,n)
& I = J )
=> a(I,J) != real_zero ),
inference(strip,[],[lti]) ).
fof(negate_0_0,plain,
~ ! [I,J] :
( ( int_leq(int_one,I)
& int_leq(I,J)
& int_leq(J,n)
& I = J )
=> a(I,J) != real_zero ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [I,J] :
( I = J
& a(I,J) = real_zero
& int_leq(I,J)
& int_leq(J,n)
& int_leq(int_one,I) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) = real_zero
& skolemFOFtoCNF_I = skolemFOFtoCNF_J
& int_leq(int_one,skolemFOFtoCNF_I)
& int_leq(skolemFOFtoCNF_I,skolemFOFtoCNF_J)
& int_leq(skolemFOFtoCNF_J,n) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
int_leq(skolemFOFtoCNF_J,n),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
skolemFOFtoCNF_I = skolemFOFtoCNF_J,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [I,J] :
( ~ int_leq(I,n)
| ~ int_leq(J,n)
| ~ int_leq(int_one,I)
| ~ int_leq(int_one,J)
| ( ! [C] :
( I != plus(J,C)
| ~ int_less(int_zero,C)
| ! [K] :
( ~ int_leq(K,J)
| ~ int_leq(int_one,K)
| a(plus(K,C),K) = lu(plus(K,C),K) ) )
& ! [C] :
( J != plus(I,C)
| ~ int_less(int_zero,C)
| ! [K] :
( ~ int_leq(K,I)
| ~ int_leq(int_one,K)
| a(K,plus(K,C)) = real_zero ) )
& ! [K] :
( ~ int_leq(K,J)
| ~ int_leq(int_one,K)
| a(K,K) = real_one ) ) ),
inference(canonicalize,[],[qil]) ).
fof(normalize_0_5,plain,
! [I,J] :
( ~ int_leq(I,n)
| ~ int_leq(J,n)
| ~ int_leq(int_one,I)
| ~ int_leq(int_one,J)
| ( ! [C] :
( I != plus(J,C)
| ~ int_less(int_zero,C)
| ! [K] :
( ~ int_leq(K,J)
| ~ int_leq(int_one,K)
| a(plus(K,C),K) = lu(plus(K,C),K) ) )
& ! [C] :
( J != plus(I,C)
| ~ int_less(int_zero,C)
| ! [K] :
( ~ int_leq(K,I)
| ~ int_leq(int_one,K)
| a(K,plus(K,C)) = real_zero ) )
& ! [K] :
( ~ int_leq(K,J)
| ~ int_leq(int_one,K)
| a(K,K) = real_one ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [C,I,J,K] :
( ( ~ int_leq(I,n)
| ~ int_leq(J,n)
| ~ int_leq(K,J)
| ~ int_leq(int_one,I)
| ~ int_leq(int_one,J)
| ~ int_leq(int_one,K)
| a(K,K) = real_one )
& ( I != plus(J,C)
| ~ int_leq(I,n)
| ~ int_leq(J,n)
| ~ int_leq(K,J)
| ~ int_leq(int_one,I)
| ~ int_leq(int_one,J)
| ~ int_leq(int_one,K)
| ~ int_less(int_zero,C)
| a(plus(K,C),K) = lu(plus(K,C),K) )
& ( J != plus(I,C)
| ~ int_leq(I,n)
| ~ int_leq(J,n)
| ~ int_leq(K,I)
| ~ int_leq(int_one,I)
| ~ int_leq(int_one,J)
| ~ int_leq(int_one,K)
| ~ int_less(int_zero,C)
| a(K,plus(K,C)) = real_zero ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [I,J,K] :
( ~ int_leq(I,n)
| ~ int_leq(J,n)
| ~ int_leq(K,J)
| ~ int_leq(int_one,I)
| ~ int_leq(int_one,J)
| ~ int_leq(int_one,K)
| a(K,K) = real_one ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [I,J] :
( ~ int_leq(I,J)
<=> ( I != J
& ~ int_less(I,J) ) ),
inference(canonicalize,[],[int_leq]) ).
fof(normalize_0_9,plain,
! [I,J] :
( ~ int_leq(I,J)
<=> ( I != J
& ~ int_less(I,J) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [I,J] :
( ( I != J
| int_leq(I,J) )
& ( ~ int_less(I,J)
| int_leq(I,J) )
& ( ~ int_leq(I,J)
| I = J
| int_less(I,J) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [I,J] :
( I != J
| int_leq(I,J) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) = real_zero,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_13,plain,
int_leq(int_one,skolemFOFtoCNF_I),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,plain,
real_zero != real_one,
inference(canonicalize,[],[real_constants]) ).
cnf(refute_0_0,plain,
int_leq(skolemFOFtoCNF_J,n),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
skolemFOFtoCNF_I = skolemFOFtoCNF_J,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( skolemFOFtoCNF_I != skolemFOFtoCNF_J
| skolemFOFtoCNF_J = skolemFOFtoCNF_I ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_I)),bind(Y,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_J = skolemFOFtoCNF_I,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_I,skolemFOFtoCNF_J) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_J != skolemFOFtoCNF_I
| ~ int_leq(skolemFOFtoCNF_J,n)
| int_leq(skolemFOFtoCNF_I,n) ),
introduced(tautology,[equality,[$cnf( int_leq(skolemFOFtoCNF_J,n) ),[0],$fot(skolemFOFtoCNF_I)]]) ).
cnf(refute_0_8,plain,
( ~ int_leq(skolemFOFtoCNF_J,n)
| int_leq(skolemFOFtoCNF_I,n) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_J,skolemFOFtoCNF_I) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
int_leq(skolemFOFtoCNF_I,n),
inference(resolve,[$cnf( int_leq(skolemFOFtoCNF_J,n) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ int_leq(I,n)
| ~ int_leq(J,n)
| ~ int_leq(K,J)
| ~ int_leq(int_one,I)
| ~ int_leq(int_one,J)
| ~ int_leq(int_one,K)
| a(K,K) = real_one ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_11,plain,
( ~ int_leq(K,K)
| ~ int_leq(K,n)
| ~ int_leq(int_one,K)
| a(K,K) = real_one ),
inference(subst,[],[refute_0_10:[bind(I,$fot(K)),bind(J,$fot(K))]]) ).
cnf(refute_0_12,plain,
( I != J
| int_leq(I,J) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
( J != J
| int_leq(J,J) ),
inference(subst,[],[refute_0_12:[bind(I,$fot(J))]]) ).
cnf(refute_0_14,plain,
J = J,
introduced(tautology,[refl,[$fot(J)]]) ).
cnf(refute_0_15,plain,
int_leq(J,J),
inference(resolve,[$cnf( $equal(J,J) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
int_leq(K,K),
inference(subst,[],[refute_0_15:[bind(J,$fot(K))]]) ).
cnf(refute_0_17,plain,
( ~ int_leq(K,n)
| ~ int_leq(int_one,K)
| a(K,K) = real_one ),
inference(resolve,[$cnf( int_leq(K,K) )],[refute_0_16,refute_0_11]) ).
cnf(refute_0_18,plain,
( ~ int_leq(int_one,skolemFOFtoCNF_I)
| ~ int_leq(skolemFOFtoCNF_I,n)
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) = real_one ),
inference(subst,[],[refute_0_17:[bind(K,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_19,plain,
( ~ int_leq(int_one,skolemFOFtoCNF_I)
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) = real_one ),
inference(resolve,[$cnf( int_leq(skolemFOFtoCNF_I,n) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) = real_zero,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_21,plain,
a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) = a(skolemFOFtoCNF_I,skolemFOFtoCNF_J),
introduced(tautology,[refl,[$fot(a(skolemFOFtoCNF_I,skolemFOFtoCNF_J))]]) ).
cnf(refute_0_22,plain,
( a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) != a(skolemFOFtoCNF_I,skolemFOFtoCNF_J)
| skolemFOFtoCNF_J != skolemFOFtoCNF_I
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) = a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) ),
introduced(tautology,[equality,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_J),a(skolemFOFtoCNF_I,skolemFOFtoCNF_J)) ),[1,1],$fot(skolemFOFtoCNF_I)]]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_J != skolemFOFtoCNF_I
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) = a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) ),
inference(resolve,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_J),a(skolemFOFtoCNF_I,skolemFOFtoCNF_J)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) = a(skolemFOFtoCNF_I,skolemFOFtoCNF_I),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_J,skolemFOFtoCNF_I) )],[refute_0_6,refute_0_23]) ).
cnf(refute_0_25,plain,
( a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) != a(skolemFOFtoCNF_I,skolemFOFtoCNF_I)
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) != real_zero
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) = real_zero ),
introduced(tautology,[equality,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_J),real_zero) ),[0],$fot(a(skolemFOFtoCNF_I,skolemFOFtoCNF_I))]]) ).
cnf(refute_0_26,plain,
( a(skolemFOFtoCNF_I,skolemFOFtoCNF_J) != real_zero
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) = real_zero ),
inference(resolve,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_J),a(skolemFOFtoCNF_I,skolemFOFtoCNF_I)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) = real_zero,
inference(resolve,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_J),real_zero) )],[refute_0_20,refute_0_26]) ).
cnf(refute_0_28,plain,
( a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) != real_one
| a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) != real_zero
| real_zero = real_one ),
introduced(tautology,[equality,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_I),real_one) ),[0],$fot(real_zero)]]) ).
cnf(refute_0_29,plain,
( a(skolemFOFtoCNF_I,skolemFOFtoCNF_I) != real_one
| real_zero = real_one ),
inference(resolve,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_I),real_zero) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ int_leq(int_one,skolemFOFtoCNF_I)
| real_zero = real_one ),
inference(resolve,[$cnf( $equal(a(skolemFOFtoCNF_I,skolemFOFtoCNF_I),real_one) )],[refute_0_19,refute_0_29]) ).
cnf(refute_0_31,plain,
int_leq(int_one,skolemFOFtoCNF_I),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_32,plain,
real_zero = real_one,
inference(resolve,[$cnf( int_leq(int_one,skolemFOFtoCNF_I) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
real_zero != real_one,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_34,plain,
$false,
inference(resolve,[$cnf( $equal(real_zero,real_one) )],[refute_0_32,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV488+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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 : Wed Jun 15 15:18:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.93/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.93/1.09
% 0.93/1.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.93/1.09
%------------------------------------------------------------------------------