TSTP Solution File: SEU239+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU239+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 12:39:37 EDT 2022
% Result : Theorem 40.19s 40.35s
% Output : CNFRefutation 40.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 228 ( 99 ~; 79 |; 26 &)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 47 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ) ).
fof(l1_wellord1,conjecture,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ( relation(A)
& reflexive(A) )
=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ),
inference(strip,[],[l1_wellord1]) ).
fof(subgoal_1,plain,
! [A] :
( ( relation(A)
& ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) )
=> reflexive(A) ),
inference(strip,[],[l1_wellord1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( relation(A)
& reflexive(A) )
=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( reflexive(A)
& relation(A)
& ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( reflexive(skolemFOFtoCNF_A_5)
& relation(skolemFOFtoCNF_A_5)
& ? [B] :
( ~ in(ordered_pair(B,B),skolemFOFtoCNF_A_5)
& in(B,relation_field(skolemFOFtoCNF_A_5)) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [B] :
( ~ in(ordered_pair(B,B),skolemFOFtoCNF_A_5)
& in(B,relation_field(skolemFOFtoCNF_A_5)) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_5)
& in(skolemFOFtoCNF_B_1,relation_field(skolemFOFtoCNF_A_5)) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
in(skolemFOFtoCNF_B_1,relation_field(skolemFOFtoCNF_A_5)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
relation(skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(canonicalize,[],[d9_relat_2]) ).
fof(normalize_0_7,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) )
& ( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
reflexive(skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ is_reflexive_in(A,B)
<=> ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) ) ),
inference(canonicalize,[],[d1_relat_2]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ is_reflexive_in(A,B)
<=> ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_C(A,B)),A)
| ~ relation(A)
| is_reflexive_in(A,B) )
& ( ~ relation(A)
| in(skolemFOFtoCNF_C(A,B),B)
| is_reflexive_in(A,B) )
& ( ~ in(C,B)
| ~ is_reflexive_in(A,B)
| ~ relation(A)
| in(ordered_pair(C,C),A) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ~ in(C,B)
| ~ is_reflexive_in(A,B)
| ~ relation(A)
| in(ordered_pair(C,C),A) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_B_1,relation_field(skolemFOFtoCNF_A_5)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
relation(skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( ~ reflexive(skolemFOFtoCNF_A_5)
| ~ relation(skolemFOFtoCNF_A_5)
| is_reflexive_in(skolemFOFtoCNF_A_5,relation_field(skolemFOFtoCNF_A_5)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_5))]]) ).
cnf(refute_0_4,plain,
( ~ reflexive(skolemFOFtoCNF_A_5)
| is_reflexive_in(skolemFOFtoCNF_A_5,relation_field(skolemFOFtoCNF_A_5)) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_5) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
reflexive(skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
is_reflexive_in(skolemFOFtoCNF_A_5,relation_field(skolemFOFtoCNF_A_5)),
inference(resolve,[$cnf( reflexive(skolemFOFtoCNF_A_5) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ in(C,B)
| ~ is_reflexive_in(A,B)
| ~ relation(A)
| in(ordered_pair(C,C),A) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ in(X_201,relation_field(skolemFOFtoCNF_A_5))
| ~ is_reflexive_in(skolemFOFtoCNF_A_5,relation_field(skolemFOFtoCNF_A_5))
| ~ relation(skolemFOFtoCNF_A_5)
| in(ordered_pair(X_201,X_201),skolemFOFtoCNF_A_5) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_5)),bind(B,$fot(relation_field(skolemFOFtoCNF_A_5))),bind(C,$fot(X_201))]]) ).
cnf(refute_0_9,plain,
( ~ in(X_201,relation_field(skolemFOFtoCNF_A_5))
| ~ relation(skolemFOFtoCNF_A_5)
| in(ordered_pair(X_201,X_201),skolemFOFtoCNF_A_5) ),
inference(resolve,[$cnf( is_reflexive_in(skolemFOFtoCNF_A_5,relation_field(skolemFOFtoCNF_A_5)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ in(X_201,relation_field(skolemFOFtoCNF_A_5))
| in(ordered_pair(X_201,X_201),skolemFOFtoCNF_A_5) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_5) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_B_1,relation_field(skolemFOFtoCNF_A_5))
| in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_5) ),
inference(subst,[],[refute_0_10:[bind(X_201,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_12,plain,
in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_5),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,relation_field(skolemFOFtoCNF_A_5)) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
~ in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_5) )],[refute_0_12,refute_0_13]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( relation(A)
& ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) )
=> reflexive(A) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(canonicalize,[],[d9_relat_2]) ).
fof(normalize_1_1,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A] :
( ( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) )
& ( ~ reflexive(A)
| ~ relation(A)
| is_reflexive_in(A,relation_field(A)) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A] :
( ~ reflexive(A)
& relation(A)
& ! [B] :
( ~ in(B,relation_field(A))
| in(ordered_pair(B,B),A) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ reflexive(skolemFOFtoCNF_A_6)
& relation(skolemFOFtoCNF_A_6)
& ! [B] :
( ~ in(B,relation_field(skolemFOFtoCNF_A_6))
| in(ordered_pair(B,B),skolemFOFtoCNF_A_6) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [B] :
( ~ in(B,relation_field(skolemFOFtoCNF_A_6))
| in(ordered_pair(B,B),skolemFOFtoCNF_A_6) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [B] :
( ~ in(B,relation_field(skolemFOFtoCNF_A_6))
| in(ordered_pair(B,B),skolemFOFtoCNF_A_6) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
relation(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_9,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ is_reflexive_in(A,B)
<=> ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) ) ),
inference(canonicalize,[],[d1_relat_2]) ).
fof(normalize_1_10,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ is_reflexive_in(A,B)
<=> ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) ) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B,C] :
( ( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_C(A,B)),A)
| ~ relation(A)
| is_reflexive_in(A,B) )
& ( ~ relation(A)
| in(skolemFOFtoCNF_C(A,B),B)
| is_reflexive_in(A,B) )
& ( ~ in(C,B)
| ~ is_reflexive_in(A,B)
| ~ relation(A)
| in(ordered_pair(C,C),A) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A,B] :
( ~ relation(A)
| in(skolemFOFtoCNF_C(A,B),B)
| is_reflexive_in(A,B) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B] :
( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_C(A,B)),A)
| ~ relation(A)
| is_reflexive_in(A,B) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_14,plain,
~ reflexive(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ is_reflexive_in(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6))
| ~ relation(skolemFOFtoCNF_A_6)
| reflexive(skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_1_2,plain,
( ~ in(B,relation_field(skolemFOFtoCNF_A_6))
| in(ordered_pair(B,B),skolemFOFtoCNF_A_6) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),relation_field(skolemFOFtoCNF_A_6))
| in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6))),skolemFOFtoCNF_A_6) ),
inference(subst,[],[refute_1_2:[bind(B,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6))))]]) ).
cnf(refute_1_4,plain,
relation(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
( ~ relation(A)
| in(skolemFOFtoCNF_C(A,B),B)
| is_reflexive_in(A,B) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_6,plain,
( ~ relation(skolemFOFtoCNF_A_6)
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,X_276),X_276)
| is_reflexive_in(skolemFOFtoCNF_A_6,X_276) ),
inference(subst,[],[refute_1_5:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(X_276))]]) ).
cnf(refute_1_7,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,X_276),X_276)
| is_reflexive_in(skolemFOFtoCNF_A_6,X_276) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_6) )],[refute_1_4,refute_1_6]) ).
cnf(refute_1_8,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),relation_field(skolemFOFtoCNF_A_6))
| is_reflexive_in(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_1_7:[bind(X_276,$fot(relation_field(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_1_9,plain,
( in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6))),skolemFOFtoCNF_A_6)
| is_reflexive_in(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),relation_field(skolemFOFtoCNF_A_6)) )],[refute_1_8,refute_1_3]) ).
cnf(refute_1_10,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_C(A,B)),A)
| ~ relation(A)
| is_reflexive_in(A,B) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_11,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6))),skolemFOFtoCNF_A_6)
| ~ relation(skolemFOFtoCNF_A_6)
| is_reflexive_in(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)) ),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(relation_field(skolemFOFtoCNF_A_6)))]]) ).
cnf(refute_1_12,plain,
( ~ relation(skolemFOFtoCNF_A_6)
| is_reflexive_in(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),skolemFOFtoCNF_C(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6))),skolemFOFtoCNF_A_6) )],[refute_1_9,refute_1_11]) ).
cnf(refute_1_13,plain,
is_reflexive_in(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_6) )],[refute_1_4,refute_1_12]) ).
cnf(refute_1_14,plain,
( ~ relation(skolemFOFtoCNF_A_6)
| reflexive(skolemFOFtoCNF_A_6) ),
inference(resolve,[$cnf( is_reflexive_in(skolemFOFtoCNF_A_6,relation_field(skolemFOFtoCNF_A_6)) )],[refute_1_13,refute_1_1]) ).
cnf(refute_1_15,plain,
reflexive(skolemFOFtoCNF_A_6),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_6) )],[refute_1_4,refute_1_14]) ).
cnf(refute_1_16,plain,
~ reflexive(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_17,plain,
$false,
inference(resolve,[$cnf( reflexive(skolemFOFtoCNF_A_6) )],[refute_1_15,refute_1_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU239+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 00:10:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 40.19/40.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.19/40.35
% 40.19/40.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 40.19/40.35
%------------------------------------------------------------------------------