%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% 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 03:36:34 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 14 unt; 0 def)
% Number of atoms : 151 ( 12 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 177 ( 81 ~; 64 |; 13 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 3 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( not_equal(B,C)
<=> B != C ) ) ) ).
fof(p8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ) ).
fof(p22,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_46,conjecture,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ) ).
fof(subgoal_0,plain,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ),
inference(strip,[],[prove_relset_1_46]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> not_equal(identity_relation_of(B),empty_set) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(B)
<=> ? [C] :
( ilf_type(C,set_type)
& member(C,B) ) ) ),
inference(canonicalize,[],[p8]) ).
fof(normalize_0_1,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(B)
<=> ? [C] :
( ilf_type(C,set_type)
& member(C,B) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| empty(B)
| ilf_type(skolemFOFtoCNF_C(B),set_type) )
& ( ~ ilf_type(B,set_type)
| empty(B)
| member(skolemFOFtoCNF_C(B),B) )
& ( ~ empty(B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B] :
( ~ ilf_type(B,set_type)
| empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p22]) ).
fof(normalize_0_5,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,B)
<=> ~ member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_7,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,B)
<=> ~ member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(ordered_pair(C,C),identity_relation_of(B))
| member(C,B) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [B] :
( ~ empty(B)
& ~ not_equal(identity_relation_of(B),empty_set)
& ilf_type(B,set_type) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
? [B] :
( ~ empty(B)
& ~ not_equal(identity_relation_of(B),empty_set) ),
inference(simplify,[],[normalize_0_10,normalize_0_5]) ).
fof(normalize_0_12,plain,
( ~ empty(skolemFOFtoCNF_B_1)
& ~ not_equal(identity_relation_of(skolemFOFtoCNF_B_1),empty_set) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ not_equal(identity_relation_of(skolemFOFtoCNF_B_1),empty_set),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( B != C
<=> not_equal(B,C) ) ) ),
inference(canonicalize,[],[p7]) ).
fof(normalize_0_15,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( B != C
<=> not_equal(B,C) ) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [B,C] :
( ( B != C
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ not_equal(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| B = C
| not_equal(B,C) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| B = C
| not_equal(B,C) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
~ empty(skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_19,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(specialize,[],[normalize_0_19]) ).
cnf(refute_0_0,plain,
( ~ ilf_type(B,set_type)
| empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( empty(B)
| member(skolemFOFtoCNF_C(B),B) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( empty(X_18)
| member(skolemFOFtoCNF_C(X_18),X_18) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(X_18))]]) ).
cnf(refute_0_4,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(C))]]) ).
cnf(refute_0_7,plain,
( ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ member(skolemFOFtoCNF_C(X_18),X_18)
| member(ordered_pair(skolemFOFtoCNF_C(X_18),skolemFOFtoCNF_C(X_18)),identity_relation_of(X_18)) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(X_18)),bind(C,$fot(skolemFOFtoCNF_C(X_18)))]]) ).
cnf(refute_0_9,plain,
( empty(X_18)
| member(ordered_pair(skolemFOFtoCNF_C(X_18),skolemFOFtoCNF_C(X_18)),identity_relation_of(X_18)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C(X_18),X_18) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( empty(skolemFOFtoCNF_B_1)
| member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),identity_relation_of(skolemFOFtoCNF_B_1)) ),
inference(subst,[],[refute_0_9:[bind(X_18,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_11,plain,
~ not_equal(identity_relation_of(skolemFOFtoCNF_B_1),empty_set),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| B = C
| not_equal(B,C) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(C,set_type)
| B = C
| not_equal(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_12]) ).
cnf(refute_0_14,plain,
( B = C
| not_equal(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
( identity_relation_of(skolemFOFtoCNF_B_1) = empty_set
| not_equal(identity_relation_of(skolemFOFtoCNF_B_1),empty_set) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(identity_relation_of(skolemFOFtoCNF_B_1))),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_16,plain,
identity_relation_of(skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( not_equal(identity_relation_of(skolemFOFtoCNF_B_1),empty_set) )],[refute_0_15,refute_0_11]) ).
cnf(refute_0_17,plain,
( identity_relation_of(skolemFOFtoCNF_B_1) != empty_set
| ~ member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),identity_relation_of(skolemFOFtoCNF_B_1))
| member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),empty_set) ),
introduced(tautology,[equality,[$cnf( member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),identity_relation_of(skolemFOFtoCNF_B_1)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_18,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),identity_relation_of(skolemFOFtoCNF_B_1))
| member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),empty_set) ),
inference(resolve,[$cnf( $equal(identity_relation_of(skolemFOFtoCNF_B_1),empty_set) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( empty(skolemFOFtoCNF_B_1)
| member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),empty_set) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),identity_relation_of(skolemFOFtoCNF_B_1)) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
~ empty(skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_21,plain,
member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),empty_set),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_B_1) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_23,plain,
~ member(B,empty_set),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_22]) ).
cnf(refute_0_24,plain,
~ member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),empty_set),
inference(subst,[],[refute_0_23:[bind(B,$fot(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1))))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_C(skolemFOFtoCNF_B_1),skolemFOFtoCNF_C(skolemFOFtoCNF_B_1)),empty_set) )],[refute_0_21,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.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 : Sun Jul 10 16:08:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------