TSTP Solution File: SET929+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 76 ( 22 unt; 0 def)
% Number of atoms : 163 ( 57 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 170 ( 83 ~; 43 |; 23 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 104 ( 2 sgn 80 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(A,C)
& in(B,C) ) ) ).
fof(t73_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(A,C)
& in(B,C) ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
=> in(A,C) ),
inference(strip,[],[t73_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = empty_set
& in(A,C) )
=> in(B,C) ),
inference(strip,[],[t73_zfmisc_1]) ).
fof(subgoal_2,plain,
! [A,B,C] :
( ( in(A,C)
& in(B,C) )
=> set_difference(unordered_pair(A,B),C) = empty_set ),
inference(strip,[],[t73_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
=> in(A,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] :
( ~ in(A,C)
& set_difference(unordered_pair(A,B),C) = empty_set ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
& set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set,
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(canonicalize,[],[t38_zfmisc_1]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ( ~ subset(unordered_pair(A,B),C)
| in(A,C) )
& ( ~ subset(unordered_pair(A,B),C)
| in(B,C) )
& ( ~ in(A,C)
| ~ in(B,C)
| subset(unordered_pair(A,B),C) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
| in(A,C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_5]) ).
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(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != empty_set
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B))),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( empty_set != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_4,plain,
( empty_set != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),empty_set) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( empty_set != empty_set
| subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),empty_set) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_7,plain,
subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ subset(unordered_pair(A,B),C)
| in(A,C) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_10,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),skolemFOFtoCNF_C) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_10,refute_0_11]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = empty_set
& in(A,C) )
=> in(B,C) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_1_1,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_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_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( set_difference(A,B) != empty_set
| subset(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B,C] :
( ~ in(B,C)
& set_difference(unordered_pair(A,B),C) = empty_set
& in(A,C) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = empty_set
& in(skolemFOFtoCNF_A_3,skolemFOFtoCNF_C_1) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = empty_set,
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(canonicalize,[],[t38_zfmisc_1]) ).
fof(normalize_1_8,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B,C] :
( ( ~ subset(unordered_pair(A,B),C)
| in(A,C) )
& ( ~ subset(unordered_pair(A,B),C)
| in(B,C) )
& ( ~ in(A,C)
| ~ in(B,C)
| subset(unordered_pair(A,B),C) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
| in(B,C) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( set_difference(A,B) != empty_set
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) != empty_set
| subset(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1))),bind(B,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_2,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = empty_set,
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( empty_set != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_1_4,plain,
( empty_set != empty_set
| set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) = empty_set ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),empty_set) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( empty_set != empty_set
| subset(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),empty_set) )],[refute_1_4,refute_1_1]) ).
cnf(refute_1_6,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_1_7,plain,
subset(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
( ~ subset(unordered_pair(A,B),C)
| in(B,C) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_9,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1)
| in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(subst,[],[refute_1_8:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_10,plain,
in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_1) )],[refute_1_7,refute_1_9]) ).
cnf(refute_1_11,plain,
~ in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_12,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) )],[refute_1_10,refute_1_11]) ).
fof(negate_2_0,plain,
~ ! [A,B,C] :
( ( in(A,C)
& in(B,C) )
=> set_difference(unordered_pair(A,B),C) = empty_set ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != empty_set
& in(A,C)
& in(B,C) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(canonicalize,[],[t38_zfmisc_1]) ).
fof(normalize_2_2,plain,
! [A,B,C] :
( ~ subset(unordered_pair(A,B),C)
<=> ( ~ in(A,C)
| ~ in(B,C) ) ),
inference(specialize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != empty_set
& subset(unordered_pair(A,B),C) ),
inference(simplify,[],[normalize_2_0,normalize_2_2]) ).
fof(normalize_2_4,plain,
( set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) != empty_set
& subset(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) ),
inference(skolemize,[],[normalize_2_3]) ).
fof(normalize_2_5,plain,
subset(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_2_7,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_2_6]) ).
fof(normalize_2_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_2_7]) ).
fof(normalize_2_9,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) != empty_set,
inference(conjunct,[],[normalize_2_4]) ).
cnf(refute_2_0,plain,
subset(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_1,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_2,plain,
( ~ subset(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2)
| set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) = empty_set ),
inference(subst,[],[refute_2_1:[bind(A,$fot(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2))),bind(B,$fot(skolemFOFtoCNF_C_2))]]) ).
cnf(refute_2_3,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) = empty_set,
inference(resolve,[$cnf( subset(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) )],[refute_2_0,refute_2_2]) ).
cnf(refute_2_4,plain,
set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2) != empty_set,
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_5,plain,
$false,
inference(resolve,[$cnf( $equal(set_difference(unordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_2),empty_set) )],[refute_2_3,refute_2_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n017.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 : Sat Jul 9 21:10:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38
%------------------------------------------------------------------------------