TSTP Solution File: SEU382+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU382+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:40:46 EDT 2022
% Result : Theorem 2.12s 2.27s
% Output : CNFRefutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 32 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 26 ~; 20 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 39 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k1_pcomps_1,axiom,
! [A] : k1_pcomps_1(A) = powerset(A) ).
fof(t1_yellow_1,lemma,
! [A] :
( the_carrier(incl_POSet(A)) = A
& the_InternalRel(incl_POSet(A)) = inclusion_order(A) ) ).
fof(t4_waybel_7,conjecture,
! [A] : the_carrier(boole_POSet(A)) = powerset(A) ).
fof(t4_yellow_1,lemma,
! [A] : boole_POSet(A) = incl_POSet(powerset(A)) ).
fof(subgoal_0,plain,
! [A] : the_carrier(boole_POSet(A)) = powerset(A),
inference(strip,[],[t4_waybel_7]) ).
fof(negate_0_0,plain,
~ ! [A] : the_carrier(boole_POSet(A)) = powerset(A),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : the_carrier(boole_POSet(A)) != powerset(A),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) != powerset(skolemFOFtoCNF_A_49),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] : k1_pcomps_1(A) = powerset(A),
inference(canonicalize,[],[redefinition_k1_pcomps_1]) ).
fof(normalize_0_3,plain,
! [A] : k1_pcomps_1(A) = powerset(A),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( ! [A] : the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& ! [A] : the_carrier(incl_POSet(A)) = A ),
inference(canonicalize,[],[t1_yellow_1]) ).
fof(normalize_0_5,plain,
! [A] : the_carrier(incl_POSet(A)) = A,
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : the_carrier(incl_POSet(A)) = A,
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] : boole_POSet(A) = incl_POSet(powerset(A)),
inference(canonicalize,[],[t4_yellow_1]) ).
fof(normalize_0_8,plain,
! [A] : boole_POSet(A) = incl_POSet(powerset(A)),
inference(specialize,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) != powerset(skolemFOFtoCNF_A_49),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
k1_pcomps_1(A) = powerset(A),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( k1_pcomps_1(A) != powerset(A)
| powerset(A) = k1_pcomps_1(A) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(k1_pcomps_1(A))),bind(Y,$fot(powerset(A)))]]) ).
cnf(refute_0_6,plain,
powerset(A) = k1_pcomps_1(A),
inference(resolve,[$cnf( $equal(k1_pcomps_1(A),powerset(A)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
powerset(skolemFOFtoCNF_A_49) = k1_pcomps_1(skolemFOFtoCNF_A_49),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_A_49))]]) ).
cnf(refute_0_8,plain,
( powerset(skolemFOFtoCNF_A_49) != k1_pcomps_1(skolemFOFtoCNF_A_49)
| the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) != k1_pcomps_1(skolemFOFtoCNF_A_49)
| the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) = powerset(skolemFOFtoCNF_A_49) ),
introduced(tautology,[equality,[$cnf( ~ $equal(the_carrier(boole_POSet(skolemFOFtoCNF_A_49)),powerset(skolemFOFtoCNF_A_49)) ),[1],$fot(k1_pcomps_1(skolemFOFtoCNF_A_49))]]) ).
cnf(refute_0_9,plain,
( the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) != k1_pcomps_1(skolemFOFtoCNF_A_49)
| the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) = powerset(skolemFOFtoCNF_A_49) ),
inference(resolve,[$cnf( $equal(powerset(skolemFOFtoCNF_A_49),k1_pcomps_1(skolemFOFtoCNF_A_49)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) != k1_pcomps_1(skolemFOFtoCNF_A_49),
inference(resolve,[$cnf( $equal(the_carrier(boole_POSet(skolemFOFtoCNF_A_49)),powerset(skolemFOFtoCNF_A_49)) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
the_carrier(incl_POSet(A)) = A,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_12,plain,
the_carrier(incl_POSet(k1_pcomps_1(X_103))) = k1_pcomps_1(X_103),
inference(subst,[],[refute_0_11:[bind(A,$fot(k1_pcomps_1(X_103)))]]) ).
cnf(refute_0_13,plain,
boole_POSet(A) = incl_POSet(powerset(A)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_14,plain,
incl_POSet(powerset(A)) = incl_POSet(powerset(A)),
introduced(tautology,[refl,[$fot(incl_POSet(powerset(A)))]]) ).
cnf(refute_0_15,plain,
( incl_POSet(powerset(A)) != incl_POSet(powerset(A))
| powerset(A) != k1_pcomps_1(A)
| incl_POSet(powerset(A)) = incl_POSet(k1_pcomps_1(A)) ),
introduced(tautology,[equality,[$cnf( $equal(incl_POSet(powerset(A)),incl_POSet(powerset(A))) ),[1,0],$fot(k1_pcomps_1(A))]]) ).
cnf(refute_0_16,plain,
( powerset(A) != k1_pcomps_1(A)
| incl_POSet(powerset(A)) = incl_POSet(k1_pcomps_1(A)) ),
inference(resolve,[$cnf( $equal(incl_POSet(powerset(A)),incl_POSet(powerset(A))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
incl_POSet(powerset(A)) = incl_POSet(k1_pcomps_1(A)),
inference(resolve,[$cnf( $equal(powerset(A),k1_pcomps_1(A)) )],[refute_0_6,refute_0_16]) ).
cnf(refute_0_18,plain,
( boole_POSet(A) != incl_POSet(powerset(A))
| incl_POSet(powerset(A)) != incl_POSet(k1_pcomps_1(A))
| boole_POSet(A) = incl_POSet(k1_pcomps_1(A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(boole_POSet(A),incl_POSet(k1_pcomps_1(A))) ),[0],$fot(incl_POSet(powerset(A)))]]) ).
cnf(refute_0_19,plain,
( boole_POSet(A) != incl_POSet(powerset(A))
| boole_POSet(A) = incl_POSet(k1_pcomps_1(A)) ),
inference(resolve,[$cnf( $equal(incl_POSet(powerset(A)),incl_POSet(k1_pcomps_1(A))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
boole_POSet(A) = incl_POSet(k1_pcomps_1(A)),
inference(resolve,[$cnf( $equal(boole_POSet(A),incl_POSet(powerset(A))) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
boole_POSet(X_103) = incl_POSet(k1_pcomps_1(X_103)),
inference(subst,[],[refute_0_20:[bind(A,$fot(X_103))]]) ).
cnf(refute_0_22,plain,
( boole_POSet(X_103) != incl_POSet(k1_pcomps_1(X_103))
| incl_POSet(k1_pcomps_1(X_103)) = boole_POSet(X_103) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(boole_POSet(X_103))),bind(Y,$fot(incl_POSet(k1_pcomps_1(X_103))))]]) ).
cnf(refute_0_23,plain,
incl_POSet(k1_pcomps_1(X_103)) = boole_POSet(X_103),
inference(resolve,[$cnf( $equal(boole_POSet(X_103),incl_POSet(k1_pcomps_1(X_103))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( incl_POSet(k1_pcomps_1(X_103)) != boole_POSet(X_103)
| the_carrier(incl_POSet(k1_pcomps_1(X_103))) != k1_pcomps_1(X_103)
| the_carrier(boole_POSet(X_103)) = k1_pcomps_1(X_103) ),
introduced(tautology,[equality,[$cnf( $equal(the_carrier(incl_POSet(k1_pcomps_1(X_103))),k1_pcomps_1(X_103)) ),[0,0],$fot(boole_POSet(X_103))]]) ).
cnf(refute_0_25,plain,
( the_carrier(incl_POSet(k1_pcomps_1(X_103))) != k1_pcomps_1(X_103)
| the_carrier(boole_POSet(X_103)) = k1_pcomps_1(X_103) ),
inference(resolve,[$cnf( $equal(incl_POSet(k1_pcomps_1(X_103)),boole_POSet(X_103)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
the_carrier(boole_POSet(X_103)) = k1_pcomps_1(X_103),
inference(resolve,[$cnf( $equal(the_carrier(incl_POSet(k1_pcomps_1(X_103))),k1_pcomps_1(X_103)) )],[refute_0_12,refute_0_25]) ).
cnf(refute_0_27,plain,
the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) = k1_pcomps_1(skolemFOFtoCNF_A_49),
inference(subst,[],[refute_0_26:[bind(X_103,$fot(skolemFOFtoCNF_A_49))]]) ).
cnf(refute_0_28,plain,
( k1_pcomps_1(skolemFOFtoCNF_A_49) != k1_pcomps_1(skolemFOFtoCNF_A_49)
| the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) != k1_pcomps_1(skolemFOFtoCNF_A_49)
| the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) = k1_pcomps_1(skolemFOFtoCNF_A_49) ),
introduced(tautology,[equality,[$cnf( $equal(the_carrier(boole_POSet(skolemFOFtoCNF_A_49)),k1_pcomps_1(skolemFOFtoCNF_A_49)) ),[1],$fot(k1_pcomps_1(skolemFOFtoCNF_A_49))]]) ).
cnf(refute_0_29,plain,
( k1_pcomps_1(skolemFOFtoCNF_A_49) != k1_pcomps_1(skolemFOFtoCNF_A_49)
| the_carrier(boole_POSet(skolemFOFtoCNF_A_49)) = k1_pcomps_1(skolemFOFtoCNF_A_49) ),
inference(resolve,[$cnf( $equal(the_carrier(boole_POSet(skolemFOFtoCNF_A_49)),k1_pcomps_1(skolemFOFtoCNF_A_49)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
k1_pcomps_1(skolemFOFtoCNF_A_49) != k1_pcomps_1(skolemFOFtoCNF_A_49),
inference(resolve,[$cnf( $equal(the_carrier(boole_POSet(skolemFOFtoCNF_A_49)),k1_pcomps_1(skolemFOFtoCNF_A_49)) )],[refute_0_29,refute_0_10]) ).
cnf(refute_0_31,plain,
k1_pcomps_1(skolemFOFtoCNF_A_49) = k1_pcomps_1(skolemFOFtoCNF_A_49),
introduced(tautology,[refl,[$fot(k1_pcomps_1(skolemFOFtoCNF_A_49))]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( $equal(k1_pcomps_1(skolemFOFtoCNF_A_49),k1_pcomps_1(skolemFOFtoCNF_A_49)) )],[refute_0_31,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU382+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 20 08:18:53 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.12/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.12/2.27
% 2.12/2.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.12/2.28
%------------------------------------------------------------------------------