TSTP Solution File: SEU180+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU180+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:39:05 EDT 2022
% Result : Theorem 4.78s 4.94s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 25
% Syntax : Number of formulae : 150 ( 49 unt; 0 def)
% Number of atoms : 385 ( 95 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 412 ( 177 ~; 166 |; 34 &)
% ( 22 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 220 ( 20 sgn 117 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ) ).
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t30_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(A,relation_field(C))
& in(B,relation_field(C)) ) ) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C) )
=> in(A,relation_field(C)) ),
inference(strip,[],[t30_relat_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C)
& in(A,relation_field(C)) )
=> in(B,relation_field(C)) ),
inference(strip,[],[t30_relat_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C) )
=> in(A,relation_field(C)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( empty(A)
| ! [B] : ~ empty(set_union2(A,B)) ),
inference(canonicalize,[],[fc2_xboole_0]) ).
fof(normalize_0_1,plain,
! [A] :
( empty(A)
| ! [B] : ~ empty(set_union2(A,B)) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [A,B,C] :
( ~ in(A,relation_field(C))
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ in(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2))
& in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2)
& relation(skolemFOFtoCNF_C_2) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
relation(skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(canonicalize,[],[d6_relat_1]) ).
fof(normalize_0_7,plain,
! [A] :
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(canonicalize,[],[t1_subset]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ in(A,B)
| element(A,B) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B,C,D] :
( ( C != set_union2(A,B)
| ~ in(D,A)
| in(D,C) )
& ( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C,D] :
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_19,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_dom(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(canonicalize,[],[d4_relat_1]) ).
fof(normalize_0_20,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_dom(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C,D] :
( ( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_2(A,C)),A) )
& ( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) )
& ( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),D),A)
| ~ in(skolemFOFtoCNF_C(A,B),B)
| ~ relation(A)
| B = relation_dom(A) )
& ( ~ relation(A)
| B = relation_dom(A)
| in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_D_1(A,B)),A)
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B,C,D] :
( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_24,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
~ in(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_26,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_0_27,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[t7_boole]) ).
fof(normalize_0_28,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_27]) ).
cnf(refute_0_0,plain,
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ empty(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)))
| empty(relation_dom(skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(relation_dom(skolemFOFtoCNF_C_2))),bind(B,$fot(relation_rng(skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_0_2,plain,
relation(skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ relation(skolemFOFtoCNF_C_2)
| relation_field(skolemFOFtoCNF_C_2) = set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_0_5,plain,
relation_field(skolemFOFtoCNF_C_2) = set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_2) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( relation_field(skolemFOFtoCNF_C_2) != set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))
| set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)) = relation_field(skolemFOFtoCNF_C_2) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(relation_field(skolemFOFtoCNF_C_2))),bind(Y,$fot(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))))]]) ).
cnf(refute_0_10,plain,
set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)) = relation_field(skolemFOFtoCNF_C_2),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_C_2),set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)) != relation_field(skolemFOFtoCNF_C_2)
| ~ empty(relation_field(skolemFOFtoCNF_C_2))
| empty(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))) ),
introduced(tautology,[equality,[$cnf( ~ empty(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))) ),[0],$fot(relation_field(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_0_12,plain,
( ~ empty(relation_field(skolemFOFtoCNF_C_2))
| empty(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)),relation_field(skolemFOFtoCNF_C_2)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ empty(relation_field(skolemFOFtoCNF_C_2))
| empty(relation_dom(skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( empty(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_15,plain,
( ~ empty(relation_field(skolemFOFtoCNF_C_2))
| relation_field(skolemFOFtoCNF_C_2) = empty_set ),
inference(subst,[],[refute_0_14:[bind(A,$fot(relation_field(skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_0_16,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_17,plain,
( ~ element(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2))
| empty(relation_field(skolemFOFtoCNF_C_2))
| in(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(relation_field(skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_0_18,plain,
( ~ in(A,B)
| element(A,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_19,plain,
( ~ in(skolemFOFtoCNF_A_3,set_union2(X_490,relation_dom(skolemFOFtoCNF_C_2)))
| element(skolemFOFtoCNF_A_3,set_union2(X_490,relation_dom(skolemFOFtoCNF_C_2))) ),
inference(subst,[],[refute_0_18:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(set_union2(X_490,relation_dom(skolemFOFtoCNF_C_2))))]]) ).
cnf(refute_0_20,plain,
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_21,plain,
( set_union2(A,B) != set_union2(A,B)
| ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(subst,[],[refute_0_20:[bind(C,$fot(set_union2(A,B)))]]) ).
cnf(refute_0_22,plain,
set_union2(A,B) = set_union2(A,B),
introduced(tautology,[refl,[$fot(set_union2(A,B))]]) ).
cnf(refute_0_23,plain,
( ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(A,B)) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
( ~ in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2))
| in(skolemFOFtoCNF_A_3,set_union2(A,relation_dom(skolemFOFtoCNF_C_2))) ),
inference(subst,[],[refute_0_23:[bind(B,$fot(relation_dom(skolemFOFtoCNF_C_2))),bind(D,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_0_25,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_26,plain,
( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_27,plain,
( relation_dom(A) != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,relation_dom(A)) ),
inference(subst,[],[refute_0_26:[bind(B,$fot(relation_dom(A)))]]) ).
cnf(refute_0_28,plain,
relation_dom(A) = relation_dom(A),
introduced(tautology,[refl,[$fot(relation_dom(A))]]) ).
cnf(refute_0_29,plain,
( ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,relation_dom(A)) ),
inference(resolve,[$cnf( $equal(relation_dom(A),relation_dom(A)) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2)
| ~ relation(skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(skolemFOFtoCNF_A_3)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_31,plain,
( ~ relation(skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_2) )],[refute_0_2,refute_0_31]) ).
cnf(refute_0_33,plain,
in(skolemFOFtoCNF_A_3,set_union2(A,relation_dom(skolemFOFtoCNF_C_2))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) )],[refute_0_32,refute_0_24]) ).
cnf(refute_0_34,plain,
in(skolemFOFtoCNF_A_3,set_union2(X_490,relation_dom(skolemFOFtoCNF_C_2))),
inference(subst,[],[refute_0_33:[bind(A,$fot(X_490))]]) ).
cnf(refute_0_35,plain,
element(skolemFOFtoCNF_A_3,set_union2(X_490,relation_dom(skolemFOFtoCNF_C_2))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,set_union2(X_490,relation_dom(skolemFOFtoCNF_C_2))) )],[refute_0_34,refute_0_19]) ).
cnf(refute_0_36,plain,
element(skolemFOFtoCNF_A_3,set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2))),
inference(subst,[],[refute_0_35:[bind(X_490,$fot(X_491))]]) ).
cnf(refute_0_37,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_38,plain,
set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491) = set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2)),
inference(subst,[],[refute_0_37:[bind(A,$fot(relation_dom(skolemFOFtoCNF_C_2))),bind(B,$fot(X_491))]]) ).
cnf(refute_0_39,plain,
( set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491) != set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2))
| set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2)) = set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491))),bind(Y,$fot(set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2))))]]) ).
cnf(refute_0_40,plain,
set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2)) = set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491),set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2)) != set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491)
| ~ element(skolemFOFtoCNF_A_3,set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2)))
| element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491)) ),
introduced(tautology,[equality,[$cnf( element(skolemFOFtoCNF_A_3,set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2))) ),[1],$fot(set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491))]]) ).
cnf(refute_0_42,plain,
( ~ element(skolemFOFtoCNF_A_3,set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2)))
| element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491)) ),
inference(resolve,[$cnf( $equal(set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2)),set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),X_491)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_A_3,set_union2(X_491,relation_dom(skolemFOFtoCNF_C_2))) )],[refute_0_36,refute_0_42]) ).
cnf(refute_0_44,plain,
element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))),
inference(subst,[],[refute_0_43:[bind(X_491,$fot(relation_rng(skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_0_45,plain,
( set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)) != relation_field(skolemFOFtoCNF_C_2)
| ~ element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)))
| element(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)) ),
introduced(tautology,[equality,[$cnf( element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))) ),[1],$fot(relation_field(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_0_46,plain,
( ~ element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)))
| element(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2)),relation_field(skolemFOFtoCNF_C_2)) )],[refute_0_10,refute_0_45]) ).
cnf(refute_0_47,plain,
element(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( element(skolemFOFtoCNF_A_3,set_union2(relation_dom(skolemFOFtoCNF_C_2),relation_rng(skolemFOFtoCNF_C_2))) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
( empty(relation_field(skolemFOFtoCNF_C_2))
| in(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)) )],[refute_0_47,refute_0_17]) ).
cnf(refute_0_49,plain,
~ in(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_50,plain,
empty(relation_field(skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,relation_field(skolemFOFtoCNF_C_2)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
relation_field(skolemFOFtoCNF_C_2) = empty_set,
inference(resolve,[$cnf( empty(relation_field(skolemFOFtoCNF_C_2)) )],[refute_0_50,refute_0_15]) ).
cnf(refute_0_52,plain,
( relation_field(skolemFOFtoCNF_C_2) != empty_set
| ~ empty(empty_set)
| empty(relation_field(skolemFOFtoCNF_C_2)) ),
introduced(tautology,[equality,[$cnf( ~ empty(relation_field(skolemFOFtoCNF_C_2)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_53,plain,
( ~ empty(empty_set)
| empty(relation_field(skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_C_2),empty_set) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ empty(empty_set)
| empty(relation_dom(skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( empty(relation_field(skolemFOFtoCNF_C_2)) )],[refute_0_53,refute_0_13]) ).
cnf(refute_0_55,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_56,plain,
empty(relation_dom(skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_58,plain,
( ~ empty(relation_dom(skolemFOFtoCNF_C_2))
| ~ in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_0_57:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(relation_dom(skolemFOFtoCNF_C_2)))]]) ).
cnf(refute_0_59,plain,
~ empty(relation_dom(skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) )],[refute_0_32,refute_0_58]) ).
cnf(refute_0_60,plain,
$false,
inference(resolve,[$cnf( empty(relation_dom(skolemFOFtoCNF_C_2)) )],[refute_0_56,refute_0_59]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C)
& in(A,relation_field(C)) )
=> in(B,relation_field(C)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(canonicalize,[],[d2_xboole_0]) ).
fof(normalize_1_1,plain,
! [A,B,C] :
( C != set_union2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B,C,D] :
( ( C != set_union2(A,B)
| ~ in(D,A)
| in(D,C) )
& ( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_union2(A,B) )
& ( C != set_union2(A,B)
| ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( C = set_union2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C,D] :
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B,C] :
( ~ in(B,relation_field(C))
& in(A,relation_field(C))
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ in(skolemFOFtoCNF_B_2,relation_field(skolemFOFtoCNF_C_3))
& in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)
& in(skolemFOFtoCNF_A_4,relation_field(skolemFOFtoCNF_C_3))
& relation(skolemFOFtoCNF_C_3) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_rng(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(canonicalize,[],[d5_relat_1]) ).
fof(normalize_1_8,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_rng(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B,C,D] :
( ( B != relation_rng(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(skolemFOFtoCNF_D_4(A,C),C),A) )
& ( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) )
& ( ~ in(ordered_pair(D,skolemFOFtoCNF_C_1(A,B)),A)
| ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ relation(A)
| B = relation_rng(A) )
& ( ~ relation(A)
| B = relation_rng(A)
| in(ordered_pair(skolemFOFtoCNF_D_3(A,B),skolemFOFtoCNF_C_1(A,B)),A)
| in(skolemFOFtoCNF_C_1(A,B),B) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C,D] :
( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
relation(skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_12,plain,
! [A] :
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(canonicalize,[],[d6_relat_1]) ).
fof(normalize_1_13,plain,
! [A] :
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
~ in(skolemFOFtoCNF_B_2,relation_field(skolemFOFtoCNF_C_3)),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( C != set_union2(A,B)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( set_union2(A,B) != set_union2(A,B)
| ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(subst,[],[refute_1_0:[bind(C,$fot(set_union2(A,B)))]]) ).
cnf(refute_1_2,plain,
set_union2(A,B) = set_union2(A,B),
introduced(tautology,[refl,[$fot(set_union2(A,B))]]) ).
cnf(refute_1_3,plain,
( ~ in(D,B)
| in(D,set_union2(A,B)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(A,B)) )],[refute_1_2,refute_1_1]) ).
cnf(refute_1_4,plain,
( ~ in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3))
| in(skolemFOFtoCNF_B_2,set_union2(A,relation_rng(skolemFOFtoCNF_C_3))) ),
inference(subst,[],[refute_1_3:[bind(B,$fot(relation_rng(skolemFOFtoCNF_C_3))),bind(D,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_5,plain,
in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_6,plain,
( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_7,plain,
( relation_rng(A) != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,relation_rng(A)) ),
inference(subst,[],[refute_1_6:[bind(B,$fot(relation_rng(A)))]]) ).
cnf(refute_1_8,plain,
relation_rng(A) = relation_rng(A),
introduced(tautology,[refl,[$fot(relation_rng(A))]]) ).
cnf(refute_1_9,plain,
( ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,relation_rng(A)) ),
inference(resolve,[$cnf( $equal(relation_rng(A),relation_rng(A)) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)
| ~ relation(skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)) ),
inference(subst,[],[refute_1_9:[bind(A,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_1_11,plain,
( ~ relation(skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) )],[refute_1_5,refute_1_10]) ).
cnf(refute_1_12,plain,
relation(skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_13,plain,
in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_3) )],[refute_1_12,refute_1_11]) ).
cnf(refute_1_14,plain,
in(skolemFOFtoCNF_B_2,set_union2(A,relation_rng(skolemFOFtoCNF_C_3))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)) )],[refute_1_13,refute_1_4]) ).
cnf(refute_1_15,plain,
in(skolemFOFtoCNF_B_2,set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3))),
inference(subst,[],[refute_1_14:[bind(A,$fot(relation_dom(skolemFOFtoCNF_C_3)))]]) ).
cnf(refute_1_16,plain,
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_17,plain,
( ~ relation(skolemFOFtoCNF_C_3)
| relation_field(skolemFOFtoCNF_C_3) = set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)) ),
inference(subst,[],[refute_1_16:[bind(A,$fot(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_1_18,plain,
relation_field(skolemFOFtoCNF_C_3) = set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_3) )],[refute_1_12,refute_1_17]) ).
cnf(refute_1_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
( relation_field(skolemFOFtoCNF_C_3) != set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3))
| set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)) = relation_field(skolemFOFtoCNF_C_3) ),
inference(subst,[],[refute_1_21:[bind(X,$fot(relation_field(skolemFOFtoCNF_C_3))),bind(Y,$fot(set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3))))]]) ).
cnf(refute_1_23,plain,
set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)) = relation_field(skolemFOFtoCNF_C_3),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_C_3),set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3))) )],[refute_1_18,refute_1_22]) ).
cnf(refute_1_24,plain,
( set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)) != relation_field(skolemFOFtoCNF_C_3)
| ~ in(skolemFOFtoCNF_B_2,set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)))
| in(skolemFOFtoCNF_B_2,relation_field(skolemFOFtoCNF_C_3)) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_B_2,set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3))) ),[1],$fot(relation_field(skolemFOFtoCNF_C_3))]]) ).
cnf(refute_1_25,plain,
( ~ in(skolemFOFtoCNF_B_2,set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)))
| in(skolemFOFtoCNF_B_2,relation_field(skolemFOFtoCNF_C_3)) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3)),relation_field(skolemFOFtoCNF_C_3)) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
in(skolemFOFtoCNF_B_2,relation_field(skolemFOFtoCNF_C_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,set_union2(relation_dom(skolemFOFtoCNF_C_3),relation_rng(skolemFOFtoCNF_C_3))) )],[refute_1_15,refute_1_25]) ).
cnf(refute_1_27,plain,
~ in(skolemFOFtoCNF_B_2,relation_field(skolemFOFtoCNF_C_3)),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_28,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,relation_field(skolemFOFtoCNF_C_3)) )],[refute_1_26,refute_1_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU180+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 05:22:03 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.78/4.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.78/4.94
% 4.78/4.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.78/4.95
%------------------------------------------------------------------------------