TSTP Solution File: SEU179+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU179+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 235.12s 235.32s
% Output : CNFRefutation 235.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 110 ( 22 unt; 0 def)
% Number of atoms : 326 ( 28 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 356 ( 140 ~; 140 |; 45 &)
% ( 17 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 183 ( 6 sgn 77 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,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(t25_relat_1,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_dom(A),relation_dom(B))
& subset(relation_rng(A),relation_rng(B)) ) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( relation(A)
=> ! [B] :
( ( relation(B)
& subset(A,B) )
=> subset(relation_dom(A),relation_dom(B)) ) ),
inference(strip,[],[t25_relat_1]) ).
fof(subgoal_1,plain,
! [A] :
( relation(A)
=> ! [B] :
( ( relation(B)
& subset(A,B)
& subset(relation_dom(A),relation_dom(B)) )
=> subset(relation_rng(A),relation_rng(B)) ) ),
inference(strip,[],[t25_relat_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( relation(A)
=> ! [B] :
( ( relation(B)
& subset(A,B) )
=> subset(relation_dom(A),relation_dom(B)) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,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_5,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_dom(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( ( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) )
& ( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) )
& ( ~ in(ordered_pair(skolemFOFtoCNF_C_1(A,B),D),A)
| ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ relation(A)
| B = relation_dom(A) )
& ( ~ relation(A)
| B = relation_dom(A)
| in(ordered_pair(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D(A,B)),A)
| in(skolemFOFtoCNF_C_1(A,B),B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C,D] :
( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [A] :
( relation(A)
& ? [B] :
( ~ subset(relation_dom(A),relation_dom(B))
& relation(B)
& subset(A,B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( relation(skolemFOFtoCNF_A_3)
& ? [B] :
( ~ subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(B))
& relation(B)
& subset(skolemFOFtoCNF_A_3,B) ) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [B] :
( ~ subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(B))
& relation(B)
& subset(skolemFOFtoCNF_A_3,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( ~ subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3))
& relation(skolemFOFtoCNF_B_3)
& subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_3) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_14,plain,
relation(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_15,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_16,plain,
! [A,B,C] :
( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_17,plain,
relation(skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_18,plain,
~ subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)),relation_dom(skolemFOFtoCNF_B_3))
| subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(relation_dom(skolemFOFtoCNF_A_3))),bind(B,$fot(relation_dom(skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_2,plain,
( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( relation_dom(A) != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,relation_dom(A)) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(relation_dom(A)))]]) ).
cnf(refute_0_4,plain,
relation_dom(A) = relation_dom(A),
introduced(tautology,[refl,[$fot(relation_dom(A))]]) ).
cnf(refute_0_5,plain,
( ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,relation_dom(A)) ),
inference(resolve,[$cnf( $equal(relation_dom(A),relation_dom(A)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340))),skolemFOFtoCNF_B_3)
| ~ relation(skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340),relation_dom(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340))),bind(D,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340))))]]) ).
cnf(refute_0_7,plain,
subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ in(X_100,skolemFOFtoCNF_A_3)
| ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_3)
| in(X_100,skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_3)),bind(C,$fot(X_100))]]) ).
cnf(refute_0_10,plain,
( ~ in(X_100,skolemFOFtoCNF_A_3)
| in(X_100,skolemFOFtoCNF_B_3) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_3) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326))),skolemFOFtoCNF_A_3)
| in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326))),skolemFOFtoCNF_B_3) ),
inference(subst,[],[refute_0_10:[bind(X_100,$fot(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326)))))]]) ).
cnf(refute_0_12,plain,
relation(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
( in(skolemFOFtoCNF_C(relation_dom(X_150),B),relation_dom(X_150))
| subset(relation_dom(X_150),B) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(relation_dom(X_150)))]]) ).
cnf(refute_0_15,plain,
( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_16,plain,
( relation_dom(A) != relation_dom(A)
| ~ in(C,relation_dom(A))
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(subst,[],[refute_0_15:[bind(B,$fot(relation_dom(A)))]]) ).
cnf(refute_0_17,plain,
( ~ in(C,relation_dom(A))
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
inference(resolve,[$cnf( $equal(relation_dom(A),relation_dom(A)) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ in(skolemFOFtoCNF_C(relation_dom(X_150),B),relation_dom(X_150))
| ~ relation(X_150)
| in(ordered_pair(skolemFOFtoCNF_C(relation_dom(X_150),B),skolemFOFtoCNF_D_1(X_150,skolemFOFtoCNF_C(relation_dom(X_150),B))),X_150) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_150)),bind(C,$fot(skolemFOFtoCNF_C(relation_dom(X_150),B)))]]) ).
cnf(refute_0_19,plain,
( ~ relation(X_150)
| in(ordered_pair(skolemFOFtoCNF_C(relation_dom(X_150),B),skolemFOFtoCNF_D_1(X_150,skolemFOFtoCNF_C(relation_dom(X_150),B))),X_150)
| subset(relation_dom(X_150),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(relation_dom(X_150),B),relation_dom(X_150)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ relation(skolemFOFtoCNF_A_3)
| in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_324),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_324))),skolemFOFtoCNF_A_3)
| subset(relation_dom(skolemFOFtoCNF_A_3),X_324) ),
inference(subst,[],[refute_0_19:[bind(B,$fot(X_324)),bind(X_150,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_0_21,plain,
( in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_324),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_324))),skolemFOFtoCNF_A_3)
| subset(relation_dom(skolemFOFtoCNF_A_3),X_324) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_3) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
( in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326))),skolemFOFtoCNF_A_3)
| subset(relation_dom(skolemFOFtoCNF_A_3),X_326) ),
inference(subst,[],[refute_0_21:[bind(X_324,$fot(X_326))]]) ).
cnf(refute_0_23,plain,
( in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326))),skolemFOFtoCNF_B_3)
| subset(relation_dom(skolemFOFtoCNF_A_3),X_326) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_326))),skolemFOFtoCNF_A_3) )],[refute_0_22,refute_0_11]) ).
cnf(refute_0_24,plain,
( in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340))),skolemFOFtoCNF_B_3)
| subset(relation_dom(skolemFOFtoCNF_A_3),X_340) ),
inference(subst,[],[refute_0_23:[bind(X_326,$fot(X_340))]]) ).
cnf(refute_0_25,plain,
( ~ relation(skolemFOFtoCNF_B_3)
| in(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340),relation_dom(skolemFOFtoCNF_B_3))
| subset(relation_dom(skolemFOFtoCNF_A_3),X_340) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340),skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340))),skolemFOFtoCNF_B_3) )],[refute_0_24,refute_0_6]) ).
cnf(refute_0_26,plain,
relation(skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_27,plain,
( in(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),X_340),relation_dom(skolemFOFtoCNF_B_3))
| subset(relation_dom(skolemFOFtoCNF_A_3),X_340) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_3) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
( in(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)),relation_dom(skolemFOFtoCNF_B_3))
| subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_27:[bind(X_340,$fot(relation_dom(skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_29,plain,
subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)),relation_dom(skolemFOFtoCNF_B_3)) )],[refute_0_28,refute_0_1]) ).
cnf(refute_0_30,plain,
~ subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( subset(relation_dom(skolemFOFtoCNF_A_3),relation_dom(skolemFOFtoCNF_B_3)) )],[refute_0_29,refute_0_30]) ).
fof(negate_1_0,plain,
~ ! [A] :
( relation(A)
=> ! [B] :
( ( relation(B)
& subset(A,B)
& subset(relation_dom(A),relation_dom(B)) )
=> subset(relation_rng(A),relation_rng(B)) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_1_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,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_5,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_rng(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( ( B != relation_rng(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(skolemFOFtoCNF_D_3(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_2(A,B)),A)
| ~ in(skolemFOFtoCNF_C_2(A,B),B)
| ~ relation(A)
| B = relation_rng(A) )
& ( ~ relation(A)
| B = relation_rng(A)
| in(ordered_pair(skolemFOFtoCNF_D_2(A,B),skolemFOFtoCNF_C_2(A,B)),A)
| in(skolemFOFtoCNF_C_2(A,B),B) ) ),
inference(clausify,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C,D] :
( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
? [A] :
( relation(A)
& ? [B] :
( ~ subset(relation_rng(A),relation_rng(B))
& relation(B)
& subset(A,B)
& subset(relation_dom(A),relation_dom(B)) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_9,plain,
( relation(skolemFOFtoCNF_A_4)
& ? [B] :
( ~ subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(B))
& relation(B)
& subset(relation_dom(skolemFOFtoCNF_A_4),relation_dom(B))
& subset(skolemFOFtoCNF_A_4,B) ) ),
inference(skolemize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
? [B] :
( ~ subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(B))
& relation(B)
& subset(relation_dom(skolemFOFtoCNF_A_4),relation_dom(B))
& subset(skolemFOFtoCNF_A_4,B) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
( ~ subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4))
& relation(skolemFOFtoCNF_B_4)
& subset(relation_dom(skolemFOFtoCNF_A_4),relation_dom(skolemFOFtoCNF_B_4))
& subset(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_4) ),
inference(skolemize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
subset(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_4),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_14,plain,
relation(skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_15,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_16,plain,
! [A,B,C] :
( B != relation_rng(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_17,plain,
relation(skolemFOFtoCNF_B_4),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_18,plain,
~ subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)),
inference(conjunct,[],[normalize_1_11]) ).
cnf(refute_1_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ in(skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)),relation_rng(skolemFOFtoCNF_B_4))
| subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(relation_rng(skolemFOFtoCNF_A_4))),bind(B,$fot(relation_rng(skolemFOFtoCNF_B_4)))]]) ).
cnf(refute_1_2,plain,
( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( relation_rng(A) != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,relation_rng(A)) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(relation_rng(A)))]]) ).
cnf(refute_1_4,plain,
relation_rng(A) = relation_rng(A),
introduced(tautology,[refl,[$fot(relation_rng(A))]]) ).
cnf(refute_1_5,plain,
( ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,relation_rng(A)) ),
inference(resolve,[$cnf( $equal(relation_rng(A),relation_rng(A)) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056)),skolemFOFtoCNF_B_4)
| ~ relation(skolemFOFtoCNF_B_4)
| in(skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056),relation_rng(skolemFOFtoCNF_B_4)) ),
inference(subst,[],[refute_1_5:[bind(A,$fot(skolemFOFtoCNF_B_4)),bind(C,$fot(skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056))),bind(D,$fot(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056))))]]) ).
cnf(refute_1_7,plain,
subset(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_4),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_8,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_9,plain,
( ~ in(X_440,skolemFOFtoCNF_A_4)
| ~ subset(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_4)
| in(X_440,skolemFOFtoCNF_B_4) ),
inference(subst,[],[refute_1_8:[bind(A,$fot(skolemFOFtoCNF_A_4)),bind(B,$fot(skolemFOFtoCNF_B_4)),bind(C,$fot(X_440))]]) ).
cnf(refute_1_10,plain,
( ~ in(X_440,skolemFOFtoCNF_A_4)
| in(X_440,skolemFOFtoCNF_B_4) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_4) )],[refute_1_7,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_A_4)
| in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_B_4) ),
inference(subst,[],[refute_1_10:[bind(X_440,$fot(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046))))]]) ).
cnf(refute_1_12,plain,
relation(skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_13,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_14,plain,
( in(skolemFOFtoCNF_C(relation_rng(X_504),B),relation_rng(X_504))
| subset(relation_rng(X_504),B) ),
inference(subst,[],[refute_1_13:[bind(A,$fot(relation_rng(X_504)))]]) ).
cnf(refute_1_15,plain,
( B != relation_rng(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_16,plain,
( relation_rng(A) != relation_rng(A)
| ~ in(C,relation_rng(A))
| ~ relation(A)
| in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
inference(subst,[],[refute_1_15:[bind(B,$fot(relation_rng(A)))]]) ).
cnf(refute_1_17,plain,
( ~ in(C,relation_rng(A))
| ~ relation(A)
| in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
inference(resolve,[$cnf( $equal(relation_rng(A),relation_rng(A)) )],[refute_1_4,refute_1_16]) ).
cnf(refute_1_18,plain,
( ~ in(skolemFOFtoCNF_C(relation_rng(X_504),B),relation_rng(X_504))
| ~ relation(X_504)
| in(ordered_pair(skolemFOFtoCNF_D_3(X_504,skolemFOFtoCNF_C(relation_rng(X_504),B)),skolemFOFtoCNF_C(relation_rng(X_504),B)),X_504) ),
inference(subst,[],[refute_1_17:[bind(A,$fot(X_504)),bind(C,$fot(skolemFOFtoCNF_C(relation_rng(X_504),B)))]]) ).
cnf(refute_1_19,plain,
( ~ relation(X_504)
| in(ordered_pair(skolemFOFtoCNF_D_3(X_504,skolemFOFtoCNF_C(relation_rng(X_504),B)),skolemFOFtoCNF_C(relation_rng(X_504),B)),X_504)
| subset(relation_rng(X_504),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(relation_rng(X_504),B),relation_rng(X_504)) )],[refute_1_14,refute_1_18]) ).
cnf(refute_1_20,plain,
( ~ relation(skolemFOFtoCNF_A_4)
| in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1044)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1044)),skolemFOFtoCNF_A_4)
| subset(relation_rng(skolemFOFtoCNF_A_4),X_1044) ),
inference(subst,[],[refute_1_19:[bind(B,$fot(X_1044)),bind(X_504,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_1_21,plain,
( in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1044)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1044)),skolemFOFtoCNF_A_4)
| subset(relation_rng(skolemFOFtoCNF_A_4),X_1044) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_4) )],[refute_1_12,refute_1_20]) ).
cnf(refute_1_22,plain,
( in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_A_4)
| subset(relation_rng(skolemFOFtoCNF_A_4),X_1046) ),
inference(subst,[],[refute_1_21:[bind(X_1044,$fot(X_1046))]]) ).
cnf(refute_1_23,plain,
( in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_B_4)
| subset(relation_rng(skolemFOFtoCNF_A_4),X_1046) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1046)),skolemFOFtoCNF_A_4) )],[refute_1_22,refute_1_11]) ).
cnf(refute_1_24,plain,
( in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056)),skolemFOFtoCNF_B_4)
| subset(relation_rng(skolemFOFtoCNF_A_4),X_1056) ),
inference(subst,[],[refute_1_23:[bind(X_1046,$fot(X_1056))]]) ).
cnf(refute_1_25,plain,
( ~ relation(skolemFOFtoCNF_B_4)
| in(skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056),relation_rng(skolemFOFtoCNF_B_4))
| subset(relation_rng(skolemFOFtoCNF_A_4),X_1056) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_D_3(skolemFOFtoCNF_A_4,skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056)),skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056)),skolemFOFtoCNF_B_4) )],[refute_1_24,refute_1_6]) ).
cnf(refute_1_26,plain,
relation(skolemFOFtoCNF_B_4),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_27,plain,
( in(skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),X_1056),relation_rng(skolemFOFtoCNF_B_4))
| subset(relation_rng(skolemFOFtoCNF_A_4),X_1056) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_4) )],[refute_1_26,refute_1_25]) ).
cnf(refute_1_28,plain,
( in(skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)),relation_rng(skolemFOFtoCNF_B_4))
| subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)) ),
inference(subst,[],[refute_1_27:[bind(X_1056,$fot(relation_rng(skolemFOFtoCNF_B_4)))]]) ).
cnf(refute_1_29,plain,
subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)),relation_rng(skolemFOFtoCNF_B_4)) )],[refute_1_28,refute_1_1]) ).
cnf(refute_1_30,plain,
~ subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_31,plain,
$false,
inference(resolve,[$cnf( subset(relation_rng(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_B_4)) )],[refute_1_29,refute_1_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU179+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sun Jun 19 03:22:47 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.09/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 235.12/235.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 235.12/235.32
% 235.12/235.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 235.12/235.32
%------------------------------------------------------------------------------