%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU261+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 12:39:47 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 111 ( 26 unt; 0 def)
% Number of atoms : 507 ( 0 equ)
% Maximal formula atoms : 35 ( 4 avg)
% Number of connectives : 718 ( 322 ~; 309 |; 64 &)
% ( 3 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 76 ( 0 sgn 46 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ) ).
fof(t53_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( reflexive(A)
=> reflexive(B) )
& ( transitive(A)
=> transitive(B) )
& ( connected(A)
=> connected(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( well_founded_relation(A)
=> well_founded_relation(B) ) ) ) ) ) ) ).
fof(t54_wellord1,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( ( well_ordering(A)
& relation_isomorphism(A,B,C) )
=> well_ordering(B) ) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( relation(C)
& function(C)
& well_ordering(A)
& relation_isomorphism(A,B,C) )
=> well_ordering(B) ) ) ),
inference(strip,[],[t54_wellord1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( relation(C)
& function(C)
& well_ordering(A)
& relation_isomorphism(A,B,C) )
=> well_ordering(B) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ relation(A)
| ( ~ well_ordering(A)
<=> ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ well_founded_relation(A) ) ) ),
inference(canonicalize,[],[d4_wellord1]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ relation(A)
| ( ~ well_ordering(A)
<=> ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ well_founded_relation(A) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| connected(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) )
& ( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) )
& ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A] :
( relation(A)
& ? [B] :
( relation(B)
& ? [C] :
( ~ well_ordering(B)
& function(C)
& relation(C)
& relation_isomorphism(A,B,C)
& well_ordering(A) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( relation(skolemFOFtoCNF_A_1)
& ? [B] :
( relation(B)
& ? [C] :
( ~ well_ordering(B)
& function(C)
& relation(C)
& relation_isomorphism(skolemFOFtoCNF_A_1,B,C)
& well_ordering(skolemFOFtoCNF_A_1) ) ) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [B] :
( relation(B)
& ? [C] :
( ~ well_ordering(B)
& function(C)
& relation(C)
& relation_isomorphism(skolemFOFtoCNF_A_1,B,C)
& well_ordering(skolemFOFtoCNF_A_1) ) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( relation(skolemFOFtoCNF_B)
& ? [C] :
( ~ well_ordering(skolemFOFtoCNF_B)
& function(C)
& relation(C)
& relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,C)
& well_ordering(skolemFOFtoCNF_A_1) ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [C] :
( ~ well_ordering(skolemFOFtoCNF_B)
& function(C)
& relation(C)
& relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,C)
& well_ordering(skolemFOFtoCNF_A_1) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( ~ well_ordering(skolemFOFtoCNF_B)
& function(skolemFOFtoCNF_C)
& relation(skolemFOFtoCNF_C)
& relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& well_ordering(skolemFOFtoCNF_A_1) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ function(C)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ( ( ~ antisymmetric(A)
| antisymmetric(B) )
& ( ~ connected(A)
| connected(B) )
& ( ~ reflexive(A)
| reflexive(B) )
& ( ~ transitive(A)
| transitive(B) )
& ( ~ well_founded_relation(A)
| well_founded_relation(B) ) ) ) ) ),
inference(canonicalize,[],[t53_wellord1]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ function(C)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ( ( ~ antisymmetric(A)
| antisymmetric(B) )
& ( ~ connected(A)
| connected(B) )
& ( ~ reflexive(A)
| reflexive(B) )
& ( ~ transitive(A)
| transitive(B) )
& ( ~ well_founded_relation(A)
| well_founded_relation(B) ) ) ) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ( ~ antisymmetric(A)
| ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| antisymmetric(B) )
& ( ~ connected(A)
| ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| connected(B) )
& ( ~ function(C)
| ~ reflexive(A)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| reflexive(B) )
& ( ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ~ transitive(A)
| transitive(B) )
& ( ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ~ well_founded_relation(A)
| well_founded_relation(B) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ~ well_founded_relation(A)
| well_founded_relation(B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
function(skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_16,plain,
relation(skolemFOFtoCNF_A_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_17,plain,
relation(skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_18,plain,
relation(skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_19,plain,
well_ordering(skolemFOFtoCNF_A_1),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_20,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_21,plain,
! [A,B,C] :
( ~ antisymmetric(A)
| ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| antisymmetric(B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_22,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_23,plain,
! [A,B,C] :
( ~ connected(A)
| ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| connected(B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_24,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| connected(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_25,plain,
! [A,B,C] :
( ~ function(C)
| ~ reflexive(A)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| reflexive(B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_26,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ~ transitive(A)
| transitive(B) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_28,plain,
! [A] :
( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_29,plain,
~ well_ordering(skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ antisymmetric(skolemFOFtoCNF_B)
| ~ connected(skolemFOFtoCNF_B)
| ~ reflexive(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_B)
| ~ transitive(skolemFOFtoCNF_B)
| ~ well_founded_relation(skolemFOFtoCNF_B)
| well_ordering(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_2,plain,
relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
( ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ~ well_founded_relation(A)
| well_founded_relation(B) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_4,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| ~ well_founded_relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_5,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ well_founded_relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
function(skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_7,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ well_founded_relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_C) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
relation(skolemFOFtoCNF_A_1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ well_founded_relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
relation(skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_11,plain,
( ~ relation(skolemFOFtoCNF_C)
| ~ well_founded_relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
relation(skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_13,plain,
( ~ well_founded_relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
well_ordering(skolemFOFtoCNF_A_1),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_15,plain,
( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_16,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_17,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| well_founded_relation(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
well_founded_relation(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_17]) ).
cnf(refute_0_19,plain,
well_founded_relation(skolemFOFtoCNF_B),
inference(resolve,[$cnf( well_founded_relation(skolemFOFtoCNF_A_1) )],[refute_0_18,refute_0_13]) ).
cnf(refute_0_20,plain,
( ~ antisymmetric(skolemFOFtoCNF_B)
| ~ connected(skolemFOFtoCNF_B)
| ~ reflexive(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_B)
| ~ transitive(skolemFOFtoCNF_B)
| well_ordering(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( well_founded_relation(skolemFOFtoCNF_B) )],[refute_0_19,refute_0_1]) ).
cnf(refute_0_21,plain,
( ~ antisymmetric(A)
| ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| antisymmetric(B) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_22,plain,
( ~ antisymmetric(skolemFOFtoCNF_A_1)
| ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| antisymmetric(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_23,plain,
( ~ antisymmetric(skolemFOFtoCNF_A_1)
| ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| antisymmetric(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_25,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| antisymmetric(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_24:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_26,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| antisymmetric(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_0_14,refute_0_25]) ).
cnf(refute_0_27,plain,
antisymmetric(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| antisymmetric(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( antisymmetric(skolemFOFtoCNF_A_1) )],[refute_0_27,refute_0_23]) ).
cnf(refute_0_29,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| antisymmetric(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_C) )],[refute_0_6,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| antisymmetric(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ relation(skolemFOFtoCNF_C)
| antisymmetric(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_10,refute_0_30]) ).
cnf(refute_0_32,plain,
antisymmetric(skolemFOFtoCNF_B),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_12,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ connected(skolemFOFtoCNF_B)
| ~ reflexive(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_B)
| ~ transitive(skolemFOFtoCNF_B)
| well_ordering(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( antisymmetric(skolemFOFtoCNF_B) )],[refute_0_32,refute_0_20]) ).
cnf(refute_0_34,plain,
( ~ connected(A)
| ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| connected(B) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_35,plain,
( ~ connected(skolemFOFtoCNF_A_1)
| ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| connected(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_34:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_36,plain,
( ~ connected(skolemFOFtoCNF_A_1)
| ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| connected(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ relation(A)
| ~ well_ordering(A)
| connected(A) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_38,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| connected(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_37:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_39,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| connected(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_0_14,refute_0_38]) ).
cnf(refute_0_40,plain,
connected(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| connected(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( connected(skolemFOFtoCNF_A_1) )],[refute_0_40,refute_0_36]) ).
cnf(refute_0_42,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| connected(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_C) )],[refute_0_6,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| connected(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ relation(skolemFOFtoCNF_C)
| connected(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_10,refute_0_43]) ).
cnf(refute_0_45,plain,
connected(skolemFOFtoCNF_B),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_12,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ reflexive(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_B)
| ~ transitive(skolemFOFtoCNF_B)
| well_ordering(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( connected(skolemFOFtoCNF_B) )],[refute_0_45,refute_0_33]) ).
cnf(refute_0_47,plain,
( ~ function(C)
| ~ reflexive(A)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| reflexive(B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_48,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ reflexive(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| reflexive(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_47:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_49,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ reflexive(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| reflexive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_48]) ).
cnf(refute_0_50,plain,
( ~ reflexive(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| reflexive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_C) )],[refute_0_6,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_52,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| reflexive(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_51:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_53,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| reflexive(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_0_14,refute_0_52]) ).
cnf(refute_0_54,plain,
reflexive(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| reflexive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( reflexive(skolemFOFtoCNF_A_1) )],[refute_0_54,refute_0_50]) ).
cnf(refute_0_56,plain,
( ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| reflexive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ relation(skolemFOFtoCNF_C)
| reflexive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_10,refute_0_56]) ).
cnf(refute_0_58,plain,
reflexive(skolemFOFtoCNF_B),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_12,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ relation(skolemFOFtoCNF_B)
| ~ transitive(skolemFOFtoCNF_B)
| well_ordering(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( reflexive(skolemFOFtoCNF_B) )],[refute_0_58,refute_0_46]) ).
cnf(refute_0_60,plain,
( ~ transitive(skolemFOFtoCNF_B)
| well_ordering(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_10,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ function(C)
| ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ relation_isomorphism(A,B,C)
| ~ transitive(A)
| transitive(B) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_62,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| ~ transitive(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_61:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_63,plain,
( ~ function(skolemFOFtoCNF_C)
| ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ transitive(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation_isomorphism(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_2,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ transitive(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_C) )],[refute_0_6,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ relation(skolemFOFtoCNF_B)
| ~ relation(skolemFOFtoCNF_C)
| ~ transitive(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ relation(skolemFOFtoCNF_C)
| ~ transitive(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_10,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ transitive(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C) )],[refute_0_12,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_69,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| ~ well_ordering(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_A_1) ),
inference(subst,[],[refute_0_68:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_70,plain,
( ~ relation(skolemFOFtoCNF_A_1)
| transitive(skolemFOFtoCNF_A_1) ),
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_A_1) )],[refute_0_14,refute_0_69]) ).
cnf(refute_0_71,plain,
transitive(skolemFOFtoCNF_A_1),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_1) )],[refute_0_8,refute_0_70]) ).
cnf(refute_0_72,plain,
transitive(skolemFOFtoCNF_B),
inference(resolve,[$cnf( transitive(skolemFOFtoCNF_A_1) )],[refute_0_71,refute_0_67]) ).
cnf(refute_0_73,plain,
well_ordering(skolemFOFtoCNF_B),
inference(resolve,[$cnf( transitive(skolemFOFtoCNF_B) )],[refute_0_72,refute_0_60]) ).
cnf(refute_0_74,plain,
~ well_ordering(skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( well_ordering(skolemFOFtoCNF_B) )],[refute_0_73,refute_0_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU261+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 16:32:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------