TSTP Solution File: SEU144+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 12:38:43 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 18 unt; 0 def)
% Number of atoms : 164 ( 48 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 172 ( 74 ~; 59 |; 18 &)
% ( 16 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 57 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(l2_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(singleton(A),B)
=> in(A,B) ),
inference(strip,[],[l2_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B] :
( in(A,B)
=> subset(singleton(A),B) ),
inference(strip,[],[l2_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(singleton(A),B)
=> in(A,B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B] :
( ~ in(A,B)
& subset(singleton(A),B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
& subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_0_0:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_0_2,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_3,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_5,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
in(skolemFOFtoCNF_A,singleton(skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_7,plain,
subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ in(X_19,singleton(skolemFOFtoCNF_A))
| ~ subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B)
| in(X_19,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(singleton(skolemFOFtoCNF_A))),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_19))]]) ).
cnf(refute_0_10,plain,
( ~ in(X_19,singleton(skolemFOFtoCNF_A))
| in(X_19,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A),skolemFOFtoCNF_B) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_A,singleton(skolemFOFtoCNF_A))
| in(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_10:[bind(X_19,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_12,plain,
in(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,singleton(skolemFOFtoCNF_A)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
~ in(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_12,refute_0_13]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( in(A,B)
=> subset(singleton(A),B) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_1_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B] :
( ~ subset(singleton(A),B)
& in(A,B) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( ~ subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1)
& in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
~ subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_1_8,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_12,plain,
in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_1_5]) ).
cnf(refute_1_0,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1)
| subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(singleton(skolemFOFtoCNF_A_1))),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_2,plain,
~ subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_3,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_4,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_1_3:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_1_5,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_1_6,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
( ~ in(skolemFOFtoCNF_C_1(singleton(A),X_31),singleton(A))
| skolemFOFtoCNF_C_1(singleton(A),X_31) = A ),
inference(subst,[],[refute_1_6:[bind(C,$fot(skolemFOFtoCNF_C_1(singleton(A),X_31)))]]) ).
cnf(refute_1_8,plain,
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_9,plain,
( in(skolemFOFtoCNF_C_1(singleton(A),X_31),singleton(A))
| subset(singleton(A),X_31) ),
inference(subst,[],[refute_1_8:[bind(A,$fot(singleton(A))),bind(B,$fot(X_31))]]) ).
cnf(refute_1_10,plain,
( skolemFOFtoCNF_C_1(singleton(A),X_31) = A
| subset(singleton(A),X_31) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(singleton(A),X_31),singleton(A)) )],[refute_1_9,refute_1_7]) ).
cnf(refute_1_11,plain,
( skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_1
| subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_1_10:[bind(A,$fot(skolemFOFtoCNF_A_1)),bind(X_31,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_12,plain,
skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_1,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) )],[refute_1_11,refute_1_2]) ).
cnf(refute_1_13,plain,
( skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_1
| ~ in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) ),[0],$fot(skolemFOFtoCNF_A_1)]]) ).
cnf(refute_1_14,plain,
( ~ in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)
| in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_1) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( ~ in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1)
| subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),skolemFOFtoCNF_B_1) )],[refute_1_14,refute_1_1]) ).
cnf(refute_1_16,plain,
in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_17,plain,
subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_1,skolemFOFtoCNF_B_1) )],[refute_1_16,refute_1_15]) ).
cnf(refute_1_18,plain,
$false,
inference(resolve,[$cnf( subset(singleton(skolemFOFtoCNF_A_1),skolemFOFtoCNF_B_1) )],[refute_1_17,refute_1_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU144+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 06:06:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------