TSTP Solution File: SET927+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:38:26 EDT 2022
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 18 unt; 0 def)
% Number of atoms : 140 ( 77 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 160 ( 72 ~; 44 |; 30 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 69 ( 1 sgn 54 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t70_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) ) ).
fof(l39_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
=> ~ in(A,C) ),
inference(strip,[],[t70_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A)
& ~ in(A,C)
& ~ in(B,C) )
=> A = B ),
inference(strip,[],[t70_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C] :
( ( ~ in(A,C)
& ( in(B,C)
| A = B ) )
=> set_difference(unordered_pair(A,B),C) = singleton(A) ),
inference(strip,[],[t70_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
=> ~ in(A,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(canonicalize,[],[l39_zfmisc_1]) ).
fof(normalize_0_1,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != singleton(A)
| ~ in(A,C) )
& ( A != B
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) )
& ( set_difference(unordered_pair(A,B),C) != singleton(A)
| A = B
| in(B,C) )
& ( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
| ~ in(A,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
& in(A,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2)
& in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( set_difference(unordered_pair(A,B),C) != singleton(A)
| ~ in(A,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) ),[0],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_4,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( singleton(skolemFOFtoCNF_A_2) != singleton(skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
singleton(skolemFOFtoCNF_A_2) = singleton(skolemFOFtoCNF_A_2),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_7,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_8,refute_0_7]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = singleton(A)
& ~ in(A,C)
& ~ in(B,C) )
=> A = B ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(canonicalize,[],[l39_zfmisc_1]) ).
fof(normalize_1_1,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) != singleton(A)
| ~ in(A,C) )
& ( A != B
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) )
& ( set_difference(unordered_pair(A,B),C) != singleton(A)
| A = B
| in(B,C) )
& ( ~ in(B,C)
| set_difference(unordered_pair(A,B),C) = singleton(A)
| in(A,C) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
| A = B
| in(B,C) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B,C] :
( A != B
& ~ in(A,C)
& ~ in(B,C)
& set_difference(unordered_pair(A,B),C) = singleton(A) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1
& ~ in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1)
& ~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = singleton(skolemFOFtoCNF_A_3) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = singleton(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1,
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_8,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( set_difference(unordered_pair(A,B),C) != singleton(A)
| A = B
| in(B,C) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) != singleton(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_A_3 = skolemFOFtoCNF_B_1
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = singleton(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) != singleton(skolemFOFtoCNF_A_3)
| singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
| set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = singleton(skolemFOFtoCNF_A_3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),singleton(skolemFOFtoCNF_A_3)) ),[0],$fot(singleton(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_4,plain,
( singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
| set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = singleton(skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( singleton(skolemFOFtoCNF_A_3) != singleton(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_A_3 = skolemFOFtoCNF_B_1
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_4,refute_1_1]) ).
cnf(refute_1_6,plain,
singleton(skolemFOFtoCNF_A_3) = singleton(skolemFOFtoCNF_A_3),
introduced(tautology,[refl,[$fot(singleton(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_7,plain,
( skolemFOFtoCNF_A_3 = skolemFOFtoCNF_B_1
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),singleton(skolemFOFtoCNF_A_3)) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
skolemFOFtoCNF_A_3 != skolemFOFtoCNF_B_1,
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_9,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_11,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_1_9,refute_1_10]) ).
fof(negate_2_0,plain,
~ ! [A,B,C] :
( ( ~ in(A,C)
& ( in(B,C)
| A = B ) )
=> set_difference(unordered_pair(A,B),C) = singleton(A) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
& ~ in(A,C)
& ( A = B
| in(B,C) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(canonicalize,[],[l39_zfmisc_1]) ).
fof(normalize_2_2,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) != singleton(A)
<=> ( in(A,C)
| ( A != B
& ~ in(B,C) ) ) ),
inference(specialize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
$false,
inference(simplify,[],[normalize_2_0,normalize_2_2]) ).
cnf(refute_2_0,plain,
$false,
inference(canonicalize,[],[normalize_2_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET927+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 04:58:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------