TSTP Solution File: SET931+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 03:38:27 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 118 ( 86 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 156 ( 83 ~; 17 |; 41 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 48 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l46_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t75_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( set_difference(A,unordered_pair(B,C)) = empty_set
& A != empty_set
& A != singleton(B)
& A != singleton(C) )
=> A = unordered_pair(B,C) ),
inference(strip,[],[t75_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) )
=> set_difference(A,unordered_pair(B,C)) = empty_set ),
inference(strip,[],[t75_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( set_difference(A,unordered_pair(B,C)) = empty_set
& A != empty_set
& A != singleton(B)
& A != singleton(C) )
=> A = unordered_pair(B,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( ~ subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_difference(A,B) != empty_set
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C] :
( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C)
& set_difference(A,unordered_pair(B,C)) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
<=> ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(canonicalize,[],[l46_zfmisc_1]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
<=> ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
& set_difference(A,unordered_pair(B,C)) = empty_set ),
inference(simplify,[],[normalize_0_4,normalize_0_6]) ).
fof(normalize_0_8,plain,
( ~ subset(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
& set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = empty_set ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = empty_set,
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
~ subset(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(conjunct,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
( set_difference(A,B) != empty_set
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != empty_set
| subset(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_2,plain,
set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = empty_set,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( empty_set != empty_set
| set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) != empty_set
| set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_4,plain,
( empty_set != empty_set
| set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),empty_set) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( empty_set != empty_set
| subset(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),empty_set) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_7,plain,
subset(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
~ subset(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,unordered_pair(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_7,refute_0_8]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) )
=> set_difference(A,unordered_pair(B,C)) = empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C] :
( set_difference(A,unordered_pair(B,C)) != empty_set
& ( A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
<=> ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(canonicalize,[],[l46_zfmisc_1]) ).
fof(normalize_1_2,plain,
! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
<=> ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [A,B,C] :
( set_difference(A,unordered_pair(B,C)) != empty_set
& subset(A,unordered_pair(B,C)) ),
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
fof(normalize_1_4,plain,
( set_difference(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) != empty_set
& subset(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
subset(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_1_7,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( ~ subset(A,B)
| set_difference(A,B) = empty_set ) ),
inference(clausify,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
set_difference(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) != empty_set,
inference(conjunct,[],[normalize_1_4]) ).
cnf(refute_1_0,plain,
subset(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_1,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
( ~ subset(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1))
| set_difference(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) = empty_set ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_3,plain,
set_difference(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
set_difference(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) != empty_set,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_5,plain,
$false,
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_3,unordered_pair(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)),empty_set) )],[refute_1_3,refute_1_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 21:57:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------