%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 03:34:18 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 100 ( 47 ~; 33 |; 10 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 6 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set) ).
fof(sum,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ) ).
fof(thI38,conjecture,
equal_set(sum(empty_set),empty_set) ).
fof(subgoal_0,plain,
equal_set(sum(empty_set),empty_set),
inference(strip,[],[thI38]) ).
fof(negate_0_0,plain,
~ equal_set(sum(empty_set),empty_set),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : ~ member(X,empty_set),
inference(canonicalize,[],[empty_set]) ).
fof(normalize_0_1,plain,
! [X] : ~ member(X,empty_set),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(canonicalize,[],[subset]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [X] :
( ~ member(X,B)
& member(X,A) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,X] :
( ( ~ member(skolemFOFtoCNF_X(A,B),B)
| subset(A,B) )
& ( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) )
& ( ~ member(X,A)
| ~ subset(A,B)
| member(X,B) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,X] :
( ~ member(X,sum(A))
<=> ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) ) ),
inference(canonicalize,[],[sum]) ).
fof(normalize_0_7,plain,
! [A,X] :
( ~ member(X,sum(A))
<=> ! [Y] :
( ~ member(X,Y)
| ~ member(Y,A) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,X,Y] :
( ( ~ member(X,sum(A))
| member(X,skolemFOFtoCNF_Y(A,X)) )
& ( ~ member(X,sum(A))
| member(skolemFOFtoCNF_Y(A,X),A) )
& ( ~ member(X,Y)
| ~ member(Y,A)
| member(X,sum(A)) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,X] :
( ~ member(X,sum(A))
| member(skolemFOFtoCNF_Y(A,X),A) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[equal_set]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ equal_set(A,B)
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ( ~ equal_set(A,B)
| subset(A,B) )
& ( ~ equal_set(A,B)
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
~ equal_set(sum(empty_set),empty_set),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
~ member(X,empty_set),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ member(skolemFOFtoCNF_Y(empty_set,skolemFOFtoCNF_X(sum(empty_set),X_88)),empty_set),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y(empty_set,skolemFOFtoCNF_X(sum(empty_set),X_88))))]]) ).
cnf(refute_0_2,plain,
( member(skolemFOFtoCNF_X(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( member(skolemFOFtoCNF_X(sum(X_42),B),sum(X_42))
| subset(sum(X_42),B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(sum(X_42)))]]) ).
cnf(refute_0_4,plain,
( ~ member(X,sum(A))
| member(skolemFOFtoCNF_Y(A,X),A) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_X(sum(X_42),B),sum(X_42))
| member(skolemFOFtoCNF_Y(X_42,skolemFOFtoCNF_X(sum(X_42),B)),X_42) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_42)),bind(X,$fot(skolemFOFtoCNF_X(sum(X_42),B)))]]) ).
cnf(refute_0_6,plain,
( member(skolemFOFtoCNF_Y(X_42,skolemFOFtoCNF_X(sum(X_42),B)),X_42)
| subset(sum(X_42),B) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(sum(X_42),B),sum(X_42)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( member(skolemFOFtoCNF_Y(empty_set,skolemFOFtoCNF_X(sum(empty_set),X_88)),empty_set)
| subset(sum(empty_set),X_88) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(X_88)),bind(X_42,$fot(empty_set))]]) ).
cnf(refute_0_8,plain,
subset(sum(empty_set),X_88),
inference(resolve,[$cnf( member(skolemFOFtoCNF_Y(empty_set,skolemFOFtoCNF_X(sum(empty_set),X_88)),empty_set) )],[refute_0_7,refute_0_1]) ).
cnf(refute_0_9,plain,
subset(sum(empty_set),empty_set),
inference(subst,[],[refute_0_8:[bind(X_88,$fot(empty_set))]]) ).
cnf(refute_0_10,plain,
~ member(skolemFOFtoCNF_X(empty_set,X_21),empty_set),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X(empty_set,X_21)))]]) ).
cnf(refute_0_11,plain,
( member(skolemFOFtoCNF_X(empty_set,X_21),empty_set)
| subset(empty_set,X_21) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(empty_set)),bind(B,$fot(X_21))]]) ).
cnf(refute_0_12,plain,
subset(empty_set,X_21),
inference(resolve,[$cnf( member(skolemFOFtoCNF_X(empty_set,X_21),empty_set) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
subset(empty_set,X_558),
inference(subst,[],[refute_0_12:[bind(X_21,$fot(X_558))]]) ).
cnf(refute_0_14,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| equal_set(A,B) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ subset(X_558,empty_set)
| ~ subset(empty_set,X_558)
| equal_set(X_558,empty_set) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_558)),bind(B,$fot(empty_set))]]) ).
cnf(refute_0_16,plain,
( ~ subset(X_558,empty_set)
| equal_set(X_558,empty_set) ),
inference(resolve,[$cnf( subset(empty_set,X_558) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ subset(sum(empty_set),empty_set)
| equal_set(sum(empty_set),empty_set) ),
inference(subst,[],[refute_0_16:[bind(X_558,$fot(sum(empty_set)))]]) ).
cnf(refute_0_18,plain,
equal_set(sum(empty_set),empty_set),
inference(resolve,[$cnf( subset(sum(empty_set),empty_set) )],[refute_0_9,refute_0_17]) ).
cnf(refute_0_19,plain,
~ equal_set(sum(empty_set),empty_set),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( equal_set(sum(empty_set),empty_set) )],[refute_0_18,refute_0_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET347+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.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 : Mon Jul 11 03:15:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.56
% 0.19/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.57
%------------------------------------------------------------------------------