TSTP Solution File: ALG227+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% 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 : Thu Jul 14 17:39:40 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 18 unt; 0 def)
% Number of atoms : 185 ( 65 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 220 ( 90 ~; 84 |; 27 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 81 ( 0 sgn 43 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_closure3,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ) ) ).
fof(d3_closure3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( C = k1_closure3(A,B)
<=> C = a_2_0_closure3(A,B) ) ) ) ).
fof(fraenkel_a_2_0_closure3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& m1_pboole(C,B) )
=> ( r2_hidden(A,a_2_0_closure3(B,C))
<=> ? [D] :
( m1_subset_1(D,B)
& A = D
& k1_funct_1(C,D) != k1_xboole_0 ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( m1_subset_1(C,A)
& ~ r2_hidden(C,k1_closure3(A,B)) )
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ),
inference(strip,[],[t8_closure3]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( m1_subset_1(C,A)
& ~ r2_hidden(C,k1_closure3(A,B)) )
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ~ v1_xboole_0(A)
& ? [B] :
( m1_pboole(B,A)
& ? [C] :
( k1_funct_1(B,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(A,B))
& m1_subset_1(C,A) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ v1_xboole_0(skolemFOFtoCNF_A_7)
& ? [B] :
( m1_pboole(B,skolemFOFtoCNF_A_7)
& ? [C] :
( k1_funct_1(B,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(skolemFOFtoCNF_A_7,B))
& m1_subset_1(C,skolemFOFtoCNF_A_7) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B] :
( m1_pboole(B,skolemFOFtoCNF_A_7)
& ? [C] :
( k1_funct_1(B,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(skolemFOFtoCNF_A_7,B))
& m1_subset_1(C,skolemFOFtoCNF_A_7) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( m1_pboole(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_7)
& ? [C] :
( k1_funct_1(skolemFOFtoCNF_B_2,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2))
& m1_subset_1(C,skolemFOFtoCNF_A_7) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
m1_pboole(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_7),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [C] :
( k1_funct_1(skolemFOFtoCNF_B_2,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2))
& m1_subset_1(C,skolemFOFtoCNF_A_7) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
( k1_funct_1(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != k1_xboole_0
& ~ r2_hidden(skolemFOFtoCNF_C_1,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2))
& m1_subset_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A_7) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
m1_subset_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A_7),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ~ m1_pboole(C,B)
| v1_xboole_0(B)
| ( ~ r2_hidden(A,a_2_0_closure3(B,C))
<=> ! [D] :
( A != D
| ~ m1_subset_1(D,B)
| k1_funct_1(C,D) = k1_xboole_0 ) ) ),
inference(canonicalize,[],[fraenkel_a_2_0_closure3]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ~ m1_pboole(C,B)
| v1_xboole_0(B)
| ( ~ r2_hidden(A,a_2_0_closure3(B,C))
<=> ! [D] :
( A != D
| ~ m1_subset_1(D,B)
| k1_funct_1(C,D) = k1_xboole_0 ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ( k1_funct_1(C,skolemFOFtoCNF_D(A,B,C)) != k1_xboole_0
| ~ m1_pboole(C,B)
| ~ r2_hidden(A,a_2_0_closure3(B,C))
| v1_xboole_0(B) )
& ( ~ m1_pboole(C,B)
| ~ r2_hidden(A,a_2_0_closure3(B,C))
| A = skolemFOFtoCNF_D(A,B,C)
| v1_xboole_0(B) )
& ( ~ m1_pboole(C,B)
| ~ r2_hidden(A,a_2_0_closure3(B,C))
| m1_subset_1(skolemFOFtoCNF_D(A,B,C),B)
| v1_xboole_0(B) )
& ( A != D
| ~ m1_pboole(C,B)
| ~ m1_subset_1(D,B)
| k1_funct_1(C,D) = k1_xboole_0
| r2_hidden(A,a_2_0_closure3(B,C))
| v1_xboole_0(B) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( A != D
| ~ m1_pboole(C,B)
| ~ m1_subset_1(D,B)
| k1_funct_1(C,D) = k1_xboole_0
| r2_hidden(A,a_2_0_closure3(B,C))
| v1_xboole_0(B) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
~ v1_xboole_0(skolemFOFtoCNF_A_7),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_13,plain,
k1_funct_1(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != k1_xboole_0,
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_14,plain,
~ r2_hidden(skolemFOFtoCNF_C_1,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_15,plain,
! [A] :
( v1_xboole_0(A)
| ! [B] :
( ~ m1_pboole(B,A)
| ! [C] :
( C != a_2_0_closure3(A,B)
<=> C != k1_closure3(A,B) ) ) ),
inference(canonicalize,[],[d3_closure3]) ).
fof(normalize_0_16,plain,
! [A] :
( v1_xboole_0(A)
| ! [B] :
( ~ m1_pboole(B,A)
| ! [C] :
( C != a_2_0_closure3(A,B)
<=> C != k1_closure3(A,B) ) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C] :
( ( C != a_2_0_closure3(A,B)
| ~ m1_pboole(B,A)
| C = k1_closure3(A,B)
| v1_xboole_0(A) )
& ( C != k1_closure3(A,B)
| ~ m1_pboole(B,A)
| C = a_2_0_closure3(A,B)
| v1_xboole_0(A) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B,C] :
( C != a_2_0_closure3(A,B)
| ~ m1_pboole(B,A)
| C = k1_closure3(A,B)
| v1_xboole_0(A) ),
inference(conjunct,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
m1_pboole(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_7),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
m1_subset_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A_7),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( A != D
| ~ m1_pboole(C,B)
| ~ m1_subset_1(D,B)
| k1_funct_1(C,D) = k1_xboole_0
| r2_hidden(A,a_2_0_closure3(B,C))
| v1_xboole_0(B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_3,plain,
( D != D
| ~ m1_pboole(C,B)
| ~ m1_subset_1(D,B)
| k1_funct_1(C,D) = k1_xboole_0
| r2_hidden(D,a_2_0_closure3(B,C))
| v1_xboole_0(B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(D))]]) ).
cnf(refute_0_4,plain,
D = D,
introduced(tautology,[refl,[$fot(D)]]) ).
cnf(refute_0_5,plain,
( ~ m1_pboole(C,B)
| ~ m1_subset_1(D,B)
| k1_funct_1(C,D) = k1_xboole_0
| r2_hidden(D,a_2_0_closure3(B,C))
| v1_xboole_0(B) ),
inference(resolve,[$cnf( $equal(D,D) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ m1_pboole(X_78,skolemFOFtoCNF_A_7)
| ~ m1_subset_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A_7)
| k1_funct_1(X_78,skolemFOFtoCNF_C_1) = k1_xboole_0
| r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,X_78))
| v1_xboole_0(skolemFOFtoCNF_A_7) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(skolemFOFtoCNF_A_7)),bind(C,$fot(X_78)),bind(D,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_0_7,plain,
( ~ m1_pboole(X_78,skolemFOFtoCNF_A_7)
| k1_funct_1(X_78,skolemFOFtoCNF_C_1) = k1_xboole_0
| r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,X_78))
| v1_xboole_0(skolemFOFtoCNF_A_7) ),
inference(resolve,[$cnf( m1_subset_1(skolemFOFtoCNF_C_1,skolemFOFtoCNF_A_7) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
~ v1_xboole_0(skolemFOFtoCNF_A_7),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( ~ m1_pboole(X_78,skolemFOFtoCNF_A_7)
| k1_funct_1(X_78,skolemFOFtoCNF_C_1) = k1_xboole_0
| r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,X_78)) ),
inference(resolve,[$cnf( v1_xboole_0(skolemFOFtoCNF_A_7) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ m1_pboole(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_7)
| k1_funct_1(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) = k1_xboole_0
| r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) ),
inference(subst,[],[refute_0_9:[bind(X_78,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_11,plain,
( k1_funct_1(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) = k1_xboole_0
| r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) ),
inference(resolve,[$cnf( m1_pboole(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_7) )],[refute_0_0,refute_0_10]) ).
cnf(refute_0_12,plain,
k1_funct_1(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1) != k1_xboole_0,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( $equal(k1_funct_1(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_1),k1_xboole_0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
~ r2_hidden(skolemFOFtoCNF_C_1,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
( C != a_2_0_closure3(A,B)
| ~ m1_pboole(B,A)
| C = k1_closure3(A,B)
| v1_xboole_0(A) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_16,plain,
( a_2_0_closure3(A,B) != a_2_0_closure3(A,B)
| ~ m1_pboole(B,A)
| a_2_0_closure3(A,B) = k1_closure3(A,B)
| v1_xboole_0(A) ),
inference(subst,[],[refute_0_15:[bind(C,$fot(a_2_0_closure3(A,B)))]]) ).
cnf(refute_0_17,plain,
a_2_0_closure3(A,B) = a_2_0_closure3(A,B),
introduced(tautology,[refl,[$fot(a_2_0_closure3(A,B))]]) ).
cnf(refute_0_18,plain,
( ~ m1_pboole(B,A)
| a_2_0_closure3(A,B) = k1_closure3(A,B)
| v1_xboole_0(A) ),
inference(resolve,[$cnf( $equal(a_2_0_closure3(A,B),a_2_0_closure3(A,B)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( ~ m1_pboole(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_7)
| a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) = k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)
| v1_xboole_0(skolemFOFtoCNF_A_7) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_A_7)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_20,plain,
( a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) = k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)
| v1_xboole_0(skolemFOFtoCNF_A_7) ),
inference(resolve,[$cnf( m1_pboole(skolemFOFtoCNF_B_2,skolemFOFtoCNF_A_7) )],[refute_0_0,refute_0_19]) ).
cnf(refute_0_21,plain,
a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) = k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( v1_xboole_0(skolemFOFtoCNF_A_7) )],[refute_0_20,refute_0_8]) ).
cnf(refute_0_22,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_23,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) != k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)
| k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) = a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2))),bind(Y,$fot(k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)))]]) ).
cnf(refute_0_26,plain,
k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) = a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( $equal(a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2),k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2) != a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)
| ~ r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2))
| r2_hidden(skolemFOFtoCNF_C_1,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) ),
introduced(tautology,[equality,[$cnf( ~ r2_hidden(skolemFOFtoCNF_C_1,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) ),[1],$fot(a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2))]]) ).
cnf(refute_0_28,plain,
( ~ r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2))
| r2_hidden(skolemFOFtoCNF_C_1,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) ),
inference(resolve,[$cnf( $equal(k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2),a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
~ r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_C_1,k1_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) )],[refute_0_28,refute_0_14]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( r2_hidden(skolemFOFtoCNF_C_1,a_2_0_closure3(skolemFOFtoCNF_A_7,skolemFOFtoCNF_B_2)) )],[refute_0_13,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG227+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 8 09:13:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.40
%------------------------------------------------------------------------------