TSTP Solution File: SEU245+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 : Tue Jul 19 12:39:40 EDT 2022
% Result : Theorem 0.48s 0.69s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 128 ( 48 unt; 0 def)
% Number of atoms : 319 ( 98 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 325 ( 134 ~; 119 |; 49 &)
% ( 15 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 217 ( 7 sgn 93 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ) ).
fof(t16_wellord1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,C)
& in(A,cartesian_product2(B,B)) ) ) ) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( relation(C)
& in(A,relation_restriction(C,B)) )
=> in(A,C) ),
inference(strip,[],[t16_wellord1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( relation(C)
& in(A,relation_restriction(C,B))
& in(A,C) )
=> in(A,cartesian_product2(B,B)) ),
inference(strip,[],[t16_wellord1]) ).
fof(subgoal_2,plain,
! [A,B,C] :
( ( relation(C)
& in(A,C)
& in(A,cartesian_product2(B,B)) )
=> in(A,relation_restriction(C,B)) ),
inference(strip,[],[t16_wellord1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( relation(C)
& in(A,relation_restriction(C,B)) )
=> in(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( ~ in(A,C)
& in(A,relation_restriction(C,B))
& relation(C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ in(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C)
& in(skolemFOFtoCNF_A_5,relation_restriction(skolemFOFtoCNF_C,skolemFOFtoCNF_B_1))
& relation(skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in(skolemFOFtoCNF_A_5,relation_restriction(skolemFOFtoCNF_C,skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
relation(skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(canonicalize,[],[d6_wellord1]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ relation(A)
| relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ in(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_A_5,relation_restriction(skolemFOFtoCNF_C,skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(subst,[],[refute_0_1:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_3,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_0_4,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ in(D,set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57)))
| in(D,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(cartesian_product2(X_57,X_57)))]]) ).
cnf(refute_0_6,plain,
relation(skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( ~ relation(A)
| relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ relation(skolemFOFtoCNF_C)
| relation_restriction(skolemFOFtoCNF_C,X_53) = set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_53,X_53)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(X_53))]]) ).
cnf(refute_0_9,plain,
relation_restriction(skolemFOFtoCNF_C,X_53) = set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_53,X_53)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
relation_restriction(skolemFOFtoCNF_C,X_57) = set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57)),
inference(subst,[],[refute_0_9:[bind(X_53,$fot(X_57))]]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( relation_restriction(skolemFOFtoCNF_C,X_57) != set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57))
| set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57)) = relation_restriction(skolemFOFtoCNF_C,X_57) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(relation_restriction(skolemFOFtoCNF_C,X_57))),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57))))]]) ).
cnf(refute_0_15,plain,
set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57)) = relation_restriction(skolemFOFtoCNF_C,X_57),
inference(resolve,[$cnf( $equal(relation_restriction(skolemFOFtoCNF_C,X_57),set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57)) != relation_restriction(skolemFOFtoCNF_C,X_57)
| ~ in(D,relation_restriction(skolemFOFtoCNF_C,X_57))
| in(D,set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57))) ),
introduced(tautology,[equality,[$cnf( ~ in(D,set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57))) ),[1],$fot(relation_restriction(skolemFOFtoCNF_C,X_57))]]) ).
cnf(refute_0_17,plain,
( ~ in(D,relation_restriction(skolemFOFtoCNF_C,X_57))
| in(D,set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57))) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57)),relation_restriction(skolemFOFtoCNF_C,X_57)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ in(D,relation_restriction(skolemFOFtoCNF_C,X_57))
| in(D,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( in(D,set_intersection2(skolemFOFtoCNF_C,cartesian_product2(X_57,X_57))) )],[refute_0_17,refute_0_5]) ).
cnf(refute_0_19,plain,
( ~ in(skolemFOFtoCNF_A_5,relation_restriction(skolemFOFtoCNF_C,skolemFOFtoCNF_B_1))
| in(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_18:[bind(D,$fot(skolemFOFtoCNF_A_5)),bind(X_57,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_20,plain,
in(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_5,relation_restriction(skolemFOFtoCNF_C,skolemFOFtoCNF_B_1)) )],[refute_0_0,refute_0_19]) ).
cnf(refute_0_21,plain,
~ in(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_5,skolemFOFtoCNF_C) )],[refute_0_20,refute_0_21]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( relation(C)
& in(A,relation_restriction(C,B))
& in(A,C) )
=> in(A,cartesian_product2(B,B)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C] :
( ~ in(A,cartesian_product2(B,B))
& in(A,C)
& in(A,relation_restriction(C,B))
& relation(C) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ in(skolemFOFtoCNF_A_6,cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2))
& in(skolemFOFtoCNF_A_6,relation_restriction(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_2))
& in(skolemFOFtoCNF_A_6,skolemFOFtoCNF_C_1)
& relation(skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
in(skolemFOFtoCNF_A_6,relation_restriction(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_1_4,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_1_8,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
relation(skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_10,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(canonicalize,[],[d6_wellord1]) ).
fof(normalize_1_11,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A,B] :
( ~ relation(A)
| relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(clausify,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
~ in(skolemFOFtoCNF_A_6,cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
in(skolemFOFtoCNF_A_6,relation_restriction(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(subst,[],[refute_1_1:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_1_3,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_1_4,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
( ~ in(X_209,set_intersection2(X_207,X_208))
| in(X_209,X_207) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(X_207)),bind(B,$fot(X_208)),bind(D,$fot(X_209))]]) ).
cnf(refute_1_6,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_7,plain,
set_intersection2(X_208,X_207) = set_intersection2(X_207,X_208),
inference(subst,[],[refute_1_6:[bind(A,$fot(X_208)),bind(B,$fot(X_207))]]) ).
cnf(refute_1_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
( set_intersection2(X_208,X_207) != set_intersection2(X_207,X_208)
| set_intersection2(X_207,X_208) = set_intersection2(X_208,X_207) ),
inference(subst,[],[refute_1_10:[bind(X,$fot(set_intersection2(X_208,X_207))),bind(Y,$fot(set_intersection2(X_207,X_208)))]]) ).
cnf(refute_1_12,plain,
set_intersection2(X_207,X_208) = set_intersection2(X_208,X_207),
inference(resolve,[$cnf( $equal(set_intersection2(X_208,X_207),set_intersection2(X_207,X_208)) )],[refute_1_7,refute_1_11]) ).
cnf(refute_1_13,plain,
( set_intersection2(X_207,X_208) != set_intersection2(X_208,X_207)
| ~ in(X_209,set_intersection2(X_208,X_207))
| in(X_209,set_intersection2(X_207,X_208)) ),
introduced(tautology,[equality,[$cnf( ~ in(X_209,set_intersection2(X_207,X_208)) ),[1],$fot(set_intersection2(X_208,X_207))]]) ).
cnf(refute_1_14,plain,
( ~ in(X_209,set_intersection2(X_208,X_207))
| in(X_209,set_intersection2(X_207,X_208)) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_207,X_208),set_intersection2(X_208,X_207)) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( ~ in(X_209,set_intersection2(X_208,X_207))
| in(X_209,X_207) ),
inference(resolve,[$cnf( in(X_209,set_intersection2(X_207,X_208)) )],[refute_1_14,refute_1_5]) ).
cnf(refute_1_16,plain,
( ~ in(X_209,set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219)))
| in(X_209,cartesian_product2(X_219,X_219)) ),
inference(subst,[],[refute_1_15:[bind(X_207,$fot(cartesian_product2(X_219,X_219))),bind(X_208,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_17,plain,
relation(skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_18,plain,
( ~ relation(A)
| relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_19,plain,
( ~ relation(skolemFOFtoCNF_C_1)
| relation_restriction(skolemFOFtoCNF_C_1,X_216) = set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_216,X_216)) ),
inference(subst,[],[refute_1_18:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(X_216))]]) ).
cnf(refute_1_20,plain,
relation_restriction(skolemFOFtoCNF_C_1,X_216) = set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_216,X_216)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_1) )],[refute_1_17,refute_1_19]) ).
cnf(refute_1_21,plain,
relation_restriction(skolemFOFtoCNF_C_1,X_219) = set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219)),
inference(subst,[],[refute_1_20:[bind(X_216,$fot(X_219))]]) ).
cnf(refute_1_22,plain,
( relation_restriction(skolemFOFtoCNF_C_1,X_219) != set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219))
| set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219)) = relation_restriction(skolemFOFtoCNF_C_1,X_219) ),
inference(subst,[],[refute_1_10:[bind(X,$fot(relation_restriction(skolemFOFtoCNF_C_1,X_219))),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219))))]]) ).
cnf(refute_1_23,plain,
set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219)) = relation_restriction(skolemFOFtoCNF_C_1,X_219),
inference(resolve,[$cnf( $equal(relation_restriction(skolemFOFtoCNF_C_1,X_219),set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219))) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
( set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219)) != relation_restriction(skolemFOFtoCNF_C_1,X_219)
| ~ in(X_209,relation_restriction(skolemFOFtoCNF_C_1,X_219))
| in(X_209,set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219))) ),
introduced(tautology,[equality,[$cnf( ~ in(X_209,set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219))) ),[1],$fot(relation_restriction(skolemFOFtoCNF_C_1,X_219))]]) ).
cnf(refute_1_25,plain,
( ~ in(X_209,relation_restriction(skolemFOFtoCNF_C_1,X_219))
| in(X_209,set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219))) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219)),relation_restriction(skolemFOFtoCNF_C_1,X_219)) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
( ~ in(X_209,relation_restriction(skolemFOFtoCNF_C_1,X_219))
| in(X_209,cartesian_product2(X_219,X_219)) ),
inference(resolve,[$cnf( in(X_209,set_intersection2(skolemFOFtoCNF_C_1,cartesian_product2(X_219,X_219))) )],[refute_1_25,refute_1_16]) ).
cnf(refute_1_27,plain,
( ~ in(skolemFOFtoCNF_A_6,relation_restriction(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_2))
| in(skolemFOFtoCNF_A_6,cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2)) ),
inference(subst,[],[refute_1_26:[bind(X_209,$fot(skolemFOFtoCNF_A_6)),bind(X_219,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_28,plain,
in(skolemFOFtoCNF_A_6,cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_6,relation_restriction(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_2)) )],[refute_1_0,refute_1_27]) ).
cnf(refute_1_29,plain,
~ in(skolemFOFtoCNF_A_6,cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_30,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_6,cartesian_product2(skolemFOFtoCNF_B_2,skolemFOFtoCNF_B_2)) )],[refute_1_28,refute_1_29]) ).
fof(negate_2_0,plain,
~ ! [A,B,C] :
( ( relation(C)
& in(A,C)
& in(A,cartesian_product2(B,B)) )
=> in(A,relation_restriction(C,B)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A,B,C] :
( ~ in(A,relation_restriction(C,B))
& in(A,C)
& in(A,cartesian_product2(B,B))
& relation(C) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( ~ in(skolemFOFtoCNF_A_7,relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3))
& in(skolemFOFtoCNF_A_7,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))
& in(skolemFOFtoCNF_A_7,skolemFOFtoCNF_C_2)
& relation(skolemFOFtoCNF_C_2) ),
inference(skolemize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
in(skolemFOFtoCNF_A_7,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
in(skolemFOFtoCNF_A_7,skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_4,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_2_5,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_2_5]) ).
fof(normalize_2_7,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
relation(skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_2_1]) ).
fof(normalize_2_9,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(canonicalize,[],[d6_wellord1]) ).
fof(normalize_2_10,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(specialize,[],[normalize_2_9]) ).
fof(normalize_2_11,plain,
! [A,B] :
( ~ relation(A)
| relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(clausify,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
~ in(skolemFOFtoCNF_A_7,relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)),
inference(conjunct,[],[normalize_2_1]) ).
cnf(refute_2_0,plain,
in(skolemFOFtoCNF_A_7,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
in(skolemFOFtoCNF_A_7,skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_2,plain,
( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_3,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,set_intersection2(A,B)) ),
inference(subst,[],[refute_2_2:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_2_4,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_2_5,plain,
( ~ in(D,A)
| ~ in(D,B)
| in(D,set_intersection2(A,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_2_4,refute_2_3]) ).
cnf(refute_2_6,plain,
( ~ in(skolemFOFtoCNF_A_7,X_609)
| ~ in(skolemFOFtoCNF_A_7,skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,X_609)) ),
inference(subst,[],[refute_2_5:[bind(A,$fot(skolemFOFtoCNF_C_2)),bind(B,$fot(X_609)),bind(D,$fot(skolemFOFtoCNF_A_7))]]) ).
cnf(refute_2_7,plain,
( ~ in(skolemFOFtoCNF_A_7,X_609)
| in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,X_609)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_7,skolemFOFtoCNF_C_2) )],[refute_2_1,refute_2_6]) ).
cnf(refute_2_8,plain,
( ~ in(skolemFOFtoCNF_A_7,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))
| in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) ),
inference(subst,[],[refute_2_7:[bind(X_609,$fot(cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_2_9,plain,
in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_7,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) )],[refute_2_0,refute_2_8]) ).
cnf(refute_2_10,plain,
relation(skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_11,plain,
( ~ relation(A)
| relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_12,plain,
( ~ relation(skolemFOFtoCNF_C_2)
| relation_restriction(skolemFOFtoCNF_C_2,X_435) = set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(X_435,X_435)) ),
inference(subst,[],[refute_2_11:[bind(A,$fot(skolemFOFtoCNF_C_2)),bind(B,$fot(X_435))]]) ).
cnf(refute_2_13,plain,
relation_restriction(skolemFOFtoCNF_C_2,X_435) = set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(X_435,X_435)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_2) )],[refute_2_10,refute_2_12]) ).
cnf(refute_2_14,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_15,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_16,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_14,refute_2_15]) ).
cnf(refute_2_17,plain,
( relation_restriction(skolemFOFtoCNF_C_2,X_435) != set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(X_435,X_435))
| set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(X_435,X_435)) = relation_restriction(skolemFOFtoCNF_C_2,X_435) ),
inference(subst,[],[refute_2_16:[bind(X,$fot(relation_restriction(skolemFOFtoCNF_C_2,X_435))),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(X_435,X_435))))]]) ).
cnf(refute_2_18,plain,
set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(X_435,X_435)) = relation_restriction(skolemFOFtoCNF_C_2,X_435),
inference(resolve,[$cnf( $equal(relation_restriction(skolemFOFtoCNF_C_2,X_435),set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(X_435,X_435))) )],[refute_2_13,refute_2_17]) ).
cnf(refute_2_19,plain,
set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) = relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3),
inference(subst,[],[refute_2_18:[bind(X_435,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_20,plain,
( set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)) != relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)
| ~ in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))
| in(skolemFOFtoCNF_A_7,relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) ),[1],$fot(relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3))]]) ).
cnf(refute_2_21,plain,
( ~ in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)))
| in(skolemFOFtoCNF_A_7,relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3)),relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)) )],[refute_2_19,refute_2_20]) ).
cnf(refute_2_22,plain,
in(skolemFOFtoCNF_A_7,relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_7,set_intersection2(skolemFOFtoCNF_C_2,cartesian_product2(skolemFOFtoCNF_B_3,skolemFOFtoCNF_B_3))) )],[refute_2_9,refute_2_21]) ).
cnf(refute_2_23,plain,
~ in(skolemFOFtoCNF_A_7,relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)),
inference(canonicalize,[],[normalize_2_12]) ).
cnf(refute_2_24,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_7,relation_restriction(skolemFOFtoCNF_C_2,skolemFOFtoCNF_B_3)) )],[refute_2_22,refute_2_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU245+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 11:58:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.69
% 0.48/0.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.48/0.70
%------------------------------------------------------------------------------