TSTP Solution File: SEU275+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:39:54 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 28 unt; 0 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 163 ( 76 ~; 67 |; 11 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 4 sgn 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( reflexive(A)
& transitive(A)
& antisymmetric(A)
& connected(A)
& well_founded_relation(A) ) ) ) ).
fof(dt_k1_wellord2,axiom,
! [A] : relation(inclusion_relation(A)) ).
fof(t2_wellord2,axiom,
! [A] : reflexive(inclusion_relation(A)) ).
fof(t3_wellord2,axiom,
! [A] : transitive(inclusion_relation(A)) ).
fof(t4_wellord2,axiom,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ) ).
fof(t5_wellord2,axiom,
! [A] : antisymmetric(inclusion_relation(A)) ).
fof(t6_wellord2,axiom,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ) ).
fof(t7_wellord2,conjecture,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ) ).
fof(subgoal_0,plain,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(strip,[],[t7_wellord2]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( ~ well_ordering(inclusion_relation(A))
& ordinal(A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ well_ordering(inclusion_relation(skolemFOFtoCNF_A_1))
& ordinal(skolemFOFtoCNF_A_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
ordinal(skolemFOFtoCNF_A_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ ordinal(A)
| well_founded_relation(inclusion_relation(A)) ),
inference(canonicalize,[],[t6_wellord2]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ ordinal(A)
| well_founded_relation(inclusion_relation(A)) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_6,plain,
! [A] :
( ~ relation(A)
| ( ~ well_ordering(A)
<=> ( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ well_founded_relation(A) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,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_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(canonicalize,[],[t5_wellord2]) ).
fof(normalize_0_10,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ ordinal(A)
| connected(inclusion_relation(A)) ),
inference(canonicalize,[],[t4_wellord2]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ ordinal(A)
| connected(inclusion_relation(A)) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(canonicalize,[],[t2_wellord2]) ).
fof(normalize_0_14,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A] : relation(inclusion_relation(A)),
inference(canonicalize,[],[dt_k1_wellord2]) ).
fof(normalize_0_16,plain,
! [A] : relation(inclusion_relation(A)),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A] : transitive(inclusion_relation(A)),
inference(canonicalize,[],[t3_wellord2]) ).
fof(normalize_0_18,plain,
! [A] : transitive(inclusion_relation(A)),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
~ well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
ordinal(skolemFOFtoCNF_A_1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ ordinal(A)
| well_founded_relation(inclusion_relation(A)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ ordinal(skolemFOFtoCNF_A_1)
| well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_3,plain,
well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_1) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ antisymmetric(A)
| ~ connected(A)
| ~ reflexive(A)
| ~ relation(A)
| ~ transitive(A)
| ~ well_founded_relation(A)
| well_ordering(A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ connected(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1))
| well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(inclusion_relation(skolemFOFtoCNF_A_1)))]]) ).
cnf(refute_0_6,plain,
( ~ antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ connected(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
| well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( well_founded_relation(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
antisymmetric(inclusion_relation(A)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_9,plain,
( ~ connected(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
| well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( antisymmetric(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
( ~ ordinal(A)
| connected(inclusion_relation(A)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( ~ ordinal(skolemFOFtoCNF_A_1)
| connected(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_12,plain,
connected(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( ordinal(skolemFOFtoCNF_A_1) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ reflexive(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
| well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( connected(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_12,refute_0_9]) ).
cnf(refute_0_14,plain,
reflexive(inclusion_relation(A)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
reflexive(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_16,plain,
( ~ relation(inclusion_relation(skolemFOFtoCNF_A_1))
| ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
| well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( reflexive(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_15,refute_0_13]) ).
cnf(refute_0_17,plain,
relation(inclusion_relation(A)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_18,plain,
relation(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_19,plain,
( ~ transitive(inclusion_relation(skolemFOFtoCNF_A_1))
| well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) ),
inference(resolve,[$cnf( relation(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_18,refute_0_16]) ).
cnf(refute_0_20,plain,
transitive(inclusion_relation(A)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_21,plain,
transitive(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_A_1))]]) ).
cnf(refute_0_22,plain,
well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(resolve,[$cnf( transitive(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_21,refute_0_19]) ).
cnf(refute_0_23,plain,
~ well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( well_ordering(inclusion_relation(skolemFOFtoCNF_A_1)) )],[refute_0_22,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n003.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 Jun 19 03:10:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------