%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU146+1 : 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 12:38:44 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 89 ( 31 unt; 0 def)
% Number of atoms : 181 ( 68 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 166 ( 74 ~; 63 |; 13 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 2 sgn 61 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(l3_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) ) ).
fof(l4_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ) ).
fof(subgoal_0,plain,
! [A,B] :
( ( subset(A,singleton(B))
& A != empty_set )
=> A = singleton(B) ),
inference(strip,[],[l4_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( ( A = empty_set
| A = singleton(B) )
=> subset(A,singleton(B)) ),
inference(strip,[],[l4_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ( subset(A,singleton(B))
& A != empty_set )
=> A = singleton(B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[d10_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( A != B
| subset(A,B) )
& ( A != B
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| A = B ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(canonicalize,[],[l2_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ in(A,B)
<=> ~ subset(singleton(A),B) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( ~ subset(singleton(A),B)
| in(A,B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[t3_xboole_1]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_0_11,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ subset(A,B)
| in(C,A)
| subset(A,set_difference(B,singleton(C))) ),
inference(canonicalize,[],[l3_zfmisc_1]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ subset(A,B)
| in(C,A)
| subset(A,set_difference(B,singleton(C))) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [A,B] :
( A != empty_set
& A != singleton(B)
& subset(A,singleton(B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_15,plain,
( skolemFOFtoCNF_A_2 != empty_set
& skolemFOFtoCNF_A_2 != singleton(skolemFOFtoCNF_B)
& subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t37_xboole_1]) ).
fof(normalize_0_18,plain,
! [A,B] :
( set_difference(A,B) != empty_set
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,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_18]) ).
fof(normalize_0_20,plain,
! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_22,plain,
skolemFOFtoCNF_A_2 != singleton(skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ subset(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
| skolemFOFtoCNF_A_2 = singleton(skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_2,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)
| subset(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_4,plain,
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ subset(skolemFOFtoCNF_A_2,empty_set)
| skolemFOFtoCNF_A_2 = empty_set ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_6,plain,
subset(A,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_7,plain,
subset(X_20,X_20),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_8,plain,
( ~ subset(A,B)
| in(C,A)
| subset(A,set_difference(B,singleton(C))) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ subset(X_20,X_20)
| in(X_21,X_20)
| subset(X_20,set_difference(X_20,singleton(X_21))) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_20)),bind(B,$fot(X_20)),bind(C,$fot(X_21))]]) ).
cnf(refute_0_10,plain,
( in(X_21,X_20)
| subset(X_20,set_difference(X_20,singleton(X_21))) ),
inference(resolve,[$cnf( subset(X_20,X_20) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)
| subset(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))) ),
inference(subst,[],[refute_0_10:[bind(X_20,$fot(skolemFOFtoCNF_A_2)),bind(X_21,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_12,plain,
subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_14,plain,
( ~ subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
| set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = empty_set ),
inference(subst,[],[refute_0_13:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(singleton(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_15,plain,
set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) != empty_set
| ~ subset(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)))
| subset(skolemFOFtoCNF_A_2,empty_set) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_17,plain,
( ~ subset(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)))
| subset(skolemFOFtoCNF_A_2,empty_set) ),
inference(resolve,[$cnf( $equal(set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)),empty_set) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2)
| subset(skolemFOFtoCNF_A_2,empty_set) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,set_difference(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))) )],[refute_0_11,refute_0_17]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_A_2 = empty_set
| in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_18,refute_0_5]) ).
cnf(refute_0_20,plain,
skolemFOFtoCNF_A_2 != empty_set,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_21,plain,
in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,empty_set) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
subset(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B,skolemFOFtoCNF_A_2) )],[refute_0_21,refute_0_3]) ).
cnf(refute_0_23,plain,
( ~ subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B))
| skolemFOFtoCNF_A_2 = singleton(skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_B),skolemFOFtoCNF_A_2) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
skolemFOFtoCNF_A_2 = singleton(skolemFOFtoCNF_B),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_A_2 != singleton(skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_2,singleton(skolemFOFtoCNF_B)) )],[refute_0_24,refute_0_25]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ( A = empty_set
| A = singleton(B) )
=> subset(A,singleton(B)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B] :
( ~ subset(A,singleton(B))
& ( A = empty_set
| A = singleton(B) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1))
& ( skolemFOFtoCNF_A_3 = empty_set
| skolemFOFtoCNF_A_3 = singleton(skolemFOFtoCNF_B_1) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( skolemFOFtoCNF_A_3 = empty_set
| skolemFOFtoCNF_A_3 = singleton(skolemFOFtoCNF_B_1) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_4,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_1_5,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A] : subset(empty_set,A),
inference(canonicalize,[],[t2_xboole_1]) ).
fof(normalize_1_7,plain,
! [A] : subset(empty_set,A),
inference(specialize,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( skolemFOFtoCNF_A_3 = empty_set
| skolemFOFtoCNF_A_3 = singleton(skolemFOFtoCNF_B_1) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( skolemFOFtoCNF_A_3 != singleton(skolemFOFtoCNF_B_1)
| singleton(skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_3 ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_A_3)),bind(Y,$fot(singleton(skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_1_6,plain,
( singleton(skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_3
| skolemFOFtoCNF_A_3 = empty_set ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
( singleton(skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_3
| ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3)
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),[1],$fot(skolemFOFtoCNF_A_3)]]) ).
cnf(refute_1_8,plain,
( ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_A_3 = empty_set
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_3) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
( ~ subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_A_3 = empty_set ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) )],[refute_1_8,refute_1_0]) ).
cnf(refute_1_10,plain,
subset(A,A),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_11,plain,
subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_A_3 = empty_set,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,skolemFOFtoCNF_A_3) )],[refute_1_11,refute_1_9]) ).
cnf(refute_1_13,plain,
( skolemFOFtoCNF_A_3 != empty_set
| ~ subset(empty_set,singleton(skolemFOFtoCNF_B_1))
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_14,plain,
( ~ subset(empty_set,singleton(skolemFOFtoCNF_B_1))
| subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_3,empty_set) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
~ subset(empty_set,singleton(skolemFOFtoCNF_B_1)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_3,singleton(skolemFOFtoCNF_B_1)) )],[refute_1_14,refute_1_0]) ).
cnf(refute_1_16,plain,
subset(empty_set,A),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_17,plain,
subset(empty_set,singleton(skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_1_16:[bind(A,$fot(singleton(skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_1_18,plain,
$false,
inference(resolve,[$cnf( subset(empty_set,singleton(skolemFOFtoCNF_B_1)) )],[refute_1_17,refute_1_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU146+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n004.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 : Sat Jun 18 22:43:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------