TSTP Solution File: SEU188+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:39:09 EDT 2022
% Result : Theorem 1.17s 1.33s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 100 ( 33 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 41 ~; 44 |; 8 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_rng(A)) ) ).
fof(t64_relat_1,conjecture,
! [A] :
( relation(A)
=> ( ( relation_dom(A) = empty_set
| relation_rng(A) = empty_set )
=> A = empty_set ) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(subgoal_0,plain,
! [A] :
( ( relation(A)
& ( relation_dom(A) = empty_set
| relation_rng(A) = empty_set ) )
=> A = empty_set ),
inference(strip,[],[t64_relat_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( relation(A)
& ( relation_dom(A) = empty_set
| relation_rng(A) = empty_set ) )
=> A = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[fc5_relat_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[fc6_relat_1]) ).
fof(normalize_0_5,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [A] :
( A != empty_set
& relation(A)
& ( relation_dom(A) = empty_set
| relation_rng(A) = empty_set ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( skolemFOFtoCNF_A_4 != empty_set
& relation(skolemFOFtoCNF_A_4)
& ( relation_dom(skolemFOFtoCNF_A_4) = empty_set
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( relation_dom(skolemFOFtoCNF_A_4) = empty_set
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_0_10,plain,
relation(skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_11,plain,
skolemFOFtoCNF_A_4 != empty_set,
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ empty(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_A_4 = empty_set ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_2,plain,
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ empty(relation_dom(skolemFOFtoCNF_A_4))
| ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_4,plain,
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ empty(relation_rng(skolemFOFtoCNF_A_4))
| ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_6,plain,
( relation_dom(skolemFOFtoCNF_A_4) = empty_set
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( relation_rng(skolemFOFtoCNF_A_4) != empty_set
| ~ empty(empty_set)
| empty(relation_rng(skolemFOFtoCNF_A_4)) ),
introduced(tautology,[equality,[$cnf( ~ empty(relation_rng(skolemFOFtoCNF_A_4)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_8,plain,
( ~ empty(empty_set)
| relation_dom(skolemFOFtoCNF_A_4) = empty_set
| empty(relation_rng(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ empty(empty_set)
| ~ relation(skolemFOFtoCNF_A_4)
| relation_dom(skolemFOFtoCNF_A_4) = empty_set
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(relation_rng(skolemFOFtoCNF_A_4)) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( ~ relation(skolemFOFtoCNF_A_4)
| relation_dom(skolemFOFtoCNF_A_4) = empty_set
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
relation(skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_13,plain,
( relation_dom(skolemFOFtoCNF_A_4) = empty_set
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_4) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( relation_dom(skolemFOFtoCNF_A_4) != empty_set
| ~ empty(empty_set)
| empty(relation_dom(skolemFOFtoCNF_A_4)) ),
introduced(tautology,[equality,[$cnf( ~ empty(relation_dom(skolemFOFtoCNF_A_4)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_15,plain,
( ~ empty(empty_set)
| empty(relation_dom(skolemFOFtoCNF_A_4))
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ empty(empty_set)
| ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(relation_dom(skolemFOFtoCNF_A_4)) )],[refute_0_15,refute_0_3]) ).
cnf(refute_0_17,plain,
( ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,plain,
empty(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_4) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
skolemFOFtoCNF_A_4 = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_4) )],[refute_0_18,refute_0_1]) ).
cnf(refute_0_20,plain,
skolemFOFtoCNF_A_4 != empty_set,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_4,empty_set) )],[refute_0_19,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n021.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 02:11:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.17/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.17/1.33
% 1.17/1.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.17/1.33
%------------------------------------------------------------------------------