%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU268+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:39:51 EDT 2022
% Result : Theorem 3.15s 3.35s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 23 unt; 0 def)
% Number of atoms : 208 ( 31 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 254 ( 112 ~; 108 |; 17 &)
% ( 12 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 108 ( 4 sgn 47 !; 7 ?)
% 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(d1_wellord2,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( relation_field(B) = A
& ! [C,D] :
( ( in(C,A)
& in(D,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) ) ) ) ) ).
fof(d9_relat_2,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ) ).
fof(dt_k1_wellord2,axiom,
! [A] : relation(inclusion_relation(A)) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t2_wellord2,conjecture,
! [A] : reflexive(inclusion_relation(A)) ).
fof(subgoal_0,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(strip,[],[t2_wellord2]) ).
fof(negate_0_0,plain,
~ ! [A] : reflexive(inclusion_relation(A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ reflexive(inclusion_relation(A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ reflexive(inclusion_relation(skolemFOFtoCNF_A_9)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(canonicalize,[],[d9_relat_2]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ relation(A)
| ( ~ is_reflexive_in(A,relation_field(A))
<=> ~ reflexive(A) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,plain,
! [A] :
( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ relation(B)
| ( B != inclusion_relation(A)
<=> ( relation_field(B) != A
| ? [C,D] :
( in(C,A)
& in(D,A)
& ( ~ in(ordered_pair(C,D),B)
<=> subset(C,D) ) ) ) ) ),
inference(canonicalize,[],[d1_wellord2]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ relation(B)
| ( B != inclusion_relation(A)
<=> ( relation_field(B) != A
| ? [C,D] :
( in(C,A)
& in(D,A)
& ( ~ in(ordered_pair(C,D),B)
<=> subset(C,D) ) ) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C,D] :
( ( B != inclusion_relation(A)
| ~ relation(B)
| relation_field(B) = A )
& ( relation_field(B) != A
| ~ relation(B)
| B = inclusion_relation(A)
| in(skolemFOFtoCNF_C_1(A,B),A) )
& ( relation_field(B) != A
| ~ relation(B)
| B = inclusion_relation(A)
| in(skolemFOFtoCNF_D(A,B),A) )
& ( relation_field(B) != A
| ~ in(ordered_pair(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D(A,B)),B)
| ~ relation(B)
| ~ subset(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D(A,B))
| B = inclusion_relation(A) )
& ( relation_field(B) != A
| ~ relation(B)
| B = inclusion_relation(A)
| in(ordered_pair(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D(A,B)),B)
| subset(skolemFOFtoCNF_C_1(A,B),skolemFOFtoCNF_D(A,B)) )
& ( B != inclusion_relation(A)
| ~ in(C,A)
| ~ in(D,A)
| ~ in(ordered_pair(C,D),B)
| ~ relation(B)
| subset(C,D) )
& ( B != inclusion_relation(A)
| ~ in(C,A)
| ~ in(D,A)
| ~ relation(B)
| ~ subset(C,D)
| in(ordered_pair(C,D),B) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( B != inclusion_relation(A)
| ~ relation(B)
| relation_field(B) = A ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : relation(inclusion_relation(A)),
inference(canonicalize,[],[dt_k1_wellord2]) ).
fof(normalize_0_11,plain,
! [A] : relation(inclusion_relation(A)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C,D] :
( B != inclusion_relation(A)
| ~ in(C,A)
| ~ in(D,A)
| ~ relation(B)
| ~ subset(C,D)
| in(ordered_pair(C,D),B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_13,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_0_14,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,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_16,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ is_reflexive_in(A,B)
<=> ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) ) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [A,B] :
( ~ relation(A)
| in(skolemFOFtoCNF_C(A,B),B)
| is_reflexive_in(A,B) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,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_0_17]) ).
cnf(refute_0_0,plain,
~ reflexive(inclusion_relation(skolemFOFtoCNF_A_9)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ is_reflexive_in(A,relation_field(A))
| ~ relation(A)
| reflexive(A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ is_reflexive_in(inclusion_relation(A),relation_field(inclusion_relation(A)))
| ~ relation(inclusion_relation(A))
| reflexive(inclusion_relation(A)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(inclusion_relation(A)))]]) ).
cnf(refute_0_3,plain,
( B != inclusion_relation(A)
| ~ relation(B)
| relation_field(B) = A ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( inclusion_relation(A) != inclusion_relation(A)
| ~ relation(inclusion_relation(A))
| relation_field(inclusion_relation(A)) = A ),
inference(subst,[],[refute_0_3:[bind(B,$fot(inclusion_relation(A)))]]) ).
cnf(refute_0_5,plain,
inclusion_relation(A) = inclusion_relation(A),
introduced(tautology,[refl,[$fot(inclusion_relation(A))]]) ).
cnf(refute_0_6,plain,
( ~ relation(inclusion_relation(A))
| relation_field(inclusion_relation(A)) = A ),
inference(resolve,[$cnf( $equal(inclusion_relation(A),inclusion_relation(A)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
relation(inclusion_relation(A)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
relation_field(inclusion_relation(A)) = A,
inference(resolve,[$cnf( relation(inclusion_relation(A)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( relation_field(inclusion_relation(A)) != A
| ~ is_reflexive_in(inclusion_relation(A),A)
| is_reflexive_in(inclusion_relation(A),relation_field(inclusion_relation(A))) ),
introduced(tautology,[equality,[$cnf( ~ is_reflexive_in(inclusion_relation(A),relation_field(inclusion_relation(A))) ),[1],$fot(A)]]) ).
cnf(refute_0_10,plain,
( ~ is_reflexive_in(inclusion_relation(A),A)
| is_reflexive_in(inclusion_relation(A),relation_field(inclusion_relation(A))) ),
inference(resolve,[$cnf( $equal(relation_field(inclusion_relation(A)),A) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ is_reflexive_in(inclusion_relation(A),A)
| ~ relation(inclusion_relation(A))
| reflexive(inclusion_relation(A)) ),
inference(resolve,[$cnf( is_reflexive_in(inclusion_relation(A),relation_field(inclusion_relation(A))) )],[refute_0_10,refute_0_2]) ).
cnf(refute_0_12,plain,
( ~ is_reflexive_in(inclusion_relation(A),A)
| reflexive(inclusion_relation(A)) ),
inference(resolve,[$cnf( relation(inclusion_relation(A)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ is_reflexive_in(inclusion_relation(X_222),X_222)
| reflexive(inclusion_relation(X_222)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_222))]]) ).
cnf(refute_0_14,plain,
( B != inclusion_relation(A)
| ~ in(C,A)
| ~ in(D,A)
| ~ relation(B)
| ~ subset(C,D)
| in(ordered_pair(C,D),B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_15,plain,
( inclusion_relation(A) != inclusion_relation(A)
| ~ in(C,A)
| ~ in(D,A)
| ~ relation(inclusion_relation(A))
| ~ subset(C,D)
| in(ordered_pair(C,D),inclusion_relation(A)) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(inclusion_relation(A)))]]) ).
cnf(refute_0_16,plain,
( ~ in(C,A)
| ~ in(D,A)
| ~ relation(inclusion_relation(A))
| ~ subset(C,D)
| in(ordered_pair(C,D),inclusion_relation(A)) ),
inference(resolve,[$cnf( $equal(inclusion_relation(A),inclusion_relation(A)) )],[refute_0_5,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ in(C,A)
| ~ in(D,A)
| ~ subset(C,D)
| in(ordered_pair(C,D),inclusion_relation(A)) ),
inference(resolve,[$cnf( relation(inclusion_relation(A)) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ in(D,A)
| ~ subset(D,D)
| in(ordered_pair(D,D),inclusion_relation(A)) ),
inference(subst,[],[refute_0_17:[bind(C,$fot(D))]]) ).
cnf(refute_0_19,plain,
subset(A,A),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
subset(D,D),
inference(subst,[],[refute_0_19:[bind(A,$fot(D))]]) ).
cnf(refute_0_21,plain,
( ~ in(D,A)
| in(ordered_pair(D,D),inclusion_relation(A)) ),
inference(resolve,[$cnf( subset(D,D) )],[refute_0_20,refute_0_18]) ).
cnf(refute_0_22,plain,
( ~ in(skolemFOFtoCNF_C(inclusion_relation(X_132),X_133),X_133)
| in(ordered_pair(skolemFOFtoCNF_C(inclusion_relation(X_132),X_133),skolemFOFtoCNF_C(inclusion_relation(X_132),X_133)),inclusion_relation(X_133)) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_133)),bind(D,$fot(skolemFOFtoCNF_C(inclusion_relation(X_132),X_133)))]]) ).
cnf(refute_0_23,plain,
( ~ relation(A)
| in(skolemFOFtoCNF_C(A,B),B)
| is_reflexive_in(A,B) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_24,plain,
( ~ relation(inclusion_relation(A))
| in(skolemFOFtoCNF_C(inclusion_relation(A),X_111),X_111)
| is_reflexive_in(inclusion_relation(A),X_111) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(inclusion_relation(A))),bind(B,$fot(X_111))]]) ).
cnf(refute_0_25,plain,
( in(skolemFOFtoCNF_C(inclusion_relation(A),X_111),X_111)
| is_reflexive_in(inclusion_relation(A),X_111) ),
inference(resolve,[$cnf( relation(inclusion_relation(A)) )],[refute_0_7,refute_0_24]) ).
cnf(refute_0_26,plain,
( in(skolemFOFtoCNF_C(inclusion_relation(X_132),X_133),X_133)
| is_reflexive_in(inclusion_relation(X_132),X_133) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_132)),bind(X_111,$fot(X_133))]]) ).
cnf(refute_0_27,plain,
( in(ordered_pair(skolemFOFtoCNF_C(inclusion_relation(X_132),X_133),skolemFOFtoCNF_C(inclusion_relation(X_132),X_133)),inclusion_relation(X_133))
| is_reflexive_in(inclusion_relation(X_132),X_133) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(inclusion_relation(X_132),X_133),X_133) )],[refute_0_26,refute_0_22]) ).
cnf(refute_0_28,plain,
( in(ordered_pair(skolemFOFtoCNF_C(inclusion_relation(X_132),X_132),skolemFOFtoCNF_C(inclusion_relation(X_132),X_132)),inclusion_relation(X_132))
| is_reflexive_in(inclusion_relation(X_132),X_132) ),
inference(subst,[],[refute_0_27:[bind(X_133,$fot(X_132))]]) ).
cnf(refute_0_29,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_C(A,B)),A)
| ~ relation(A)
| is_reflexive_in(A,B) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_30,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_C(inclusion_relation(X_132),X_132),skolemFOFtoCNF_C(inclusion_relation(X_132),X_132)),inclusion_relation(X_132))
| ~ relation(inclusion_relation(X_132))
| is_reflexive_in(inclusion_relation(X_132),X_132) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(inclusion_relation(X_132))),bind(B,$fot(X_132))]]) ).
cnf(refute_0_31,plain,
( ~ relation(inclusion_relation(X_132))
| is_reflexive_in(inclusion_relation(X_132),X_132) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_C(inclusion_relation(X_132),X_132),skolemFOFtoCNF_C(inclusion_relation(X_132),X_132)),inclusion_relation(X_132)) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
relation(inclusion_relation(X_132)),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_132))]]) ).
cnf(refute_0_33,plain,
is_reflexive_in(inclusion_relation(X_132),X_132),
inference(resolve,[$cnf( relation(inclusion_relation(X_132)) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
is_reflexive_in(inclusion_relation(X_222),X_222),
inference(subst,[],[refute_0_33:[bind(X_132,$fot(X_222))]]) ).
cnf(refute_0_35,plain,
reflexive(inclusion_relation(X_222)),
inference(resolve,[$cnf( is_reflexive_in(inclusion_relation(X_222),X_222) )],[refute_0_34,refute_0_13]) ).
cnf(refute_0_36,plain,
reflexive(inclusion_relation(skolemFOFtoCNF_A_9)),
inference(subst,[],[refute_0_35:[bind(X_222,$fot(skolemFOFtoCNF_A_9))]]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( reflexive(inclusion_relation(skolemFOFtoCNF_A_9)) )],[refute_0_36,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU268+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 : n013.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 04:32:44 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.15/3.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.15/3.35
% 3.15/3.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/3.35
%------------------------------------------------------------------------------