TSTP Solution File: SEU062+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:38:17 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 106 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 112 ( 47 ~; 39 |; 14 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(t142_funct_1,axiom,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ) ).
fof(t143_funct_1,conjecture,
! [A,B] :
( relation(B)
=> ( ! [C] :
~ ( in(C,A)
& relation_inverse_image(B,singleton(C)) = empty_set )
=> subset(A,relation_rng(B)) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ( relation(B)
& ! [C] :
~ ( in(C,A)
& relation_inverse_image(B,singleton(C)) = empty_set ) )
=> subset(A,relation_rng(B)) ),
inference(strip,[],[t143_funct_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ( relation(B)
& ! [C] :
~ ( in(C,A)
& relation_inverse_image(B,singleton(C)) = empty_set ) )
=> subset(A,relation_rng(B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
? [A,B] :
( ~ subset(A,relation_rng(B))
& relation(B)
& ! [C] :
( relation_inverse_image(B,singleton(C)) != empty_set
| ~ in(C,A) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
( ~ subset(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3))
& relation(skolemFOFtoCNF_B_3)
& ! [C] :
( relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) != empty_set
| ~ in(C,skolemFOFtoCNF_A_8) ) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [C] :
( relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) != empty_set
| ~ in(C,skolemFOFtoCNF_A_8) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [C] :
( relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) != empty_set
| ~ in(C,skolemFOFtoCNF_A_8) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
relation(skolemFOFtoCNF_B_3),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ relation(B)
| ( relation_inverse_image(B,singleton(A)) != empty_set
<=> in(A,relation_rng(B)) ) ),
inference(canonicalize,[],[t142_funct_1]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ relation(B)
| ( relation_inverse_image(B,singleton(A)) != empty_set
<=> in(A,relation_rng(B)) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ( relation_inverse_image(B,singleton(A)) != empty_set
| ~ in(A,relation_rng(B))
| ~ relation(B) )
& ( ~ relation(B)
| relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ relation(B)
| relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
~ subset(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)),relation_rng(skolemFOFtoCNF_B_3))
| subset(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_8)),bind(B,$fot(relation_rng(skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_2,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,B),skolemFOFtoCNF_A_8)
| subset(skolemFOFtoCNF_A_8,B) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_8))]]) ).
cnf(refute_0_4,plain,
( relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) != empty_set
| ~ in(C,skolemFOFtoCNF_A_8) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
relation(skolemFOFtoCNF_B_3),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ relation(B)
| relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_7,plain,
( ~ relation(skolemFOFtoCNF_B_3)
| relation_inverse_image(skolemFOFtoCNF_B_3,singleton(X_83)) = empty_set
| in(X_83,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_83)),bind(B,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_8,plain,
( relation_inverse_image(skolemFOFtoCNF_B_3,singleton(X_83)) = empty_set
| in(X_83,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B_3) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) = empty_set
| in(C,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_8:[bind(X_83,$fot(C))]]) ).
cnf(refute_0_10,plain,
( empty_set != empty_set
| relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) != empty_set
| relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_11,plain,
( empty_set != empty_set
| relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)) = empty_set
| in(C,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)),empty_set) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( empty_set != empty_set
| ~ in(C,skolemFOFtoCNF_A_8)
| in(C,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(relation_inverse_image(skolemFOFtoCNF_B_3,singleton(C)),empty_set) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_14,plain,
( ~ in(C,skolemFOFtoCNF_A_8)
| in(C,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
( ~ in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,B),skolemFOFtoCNF_A_8)
| in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,B),relation_rng(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_14:[bind(C,$fot(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,B)))]]) ).
cnf(refute_0_16,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,B),relation_rng(skolemFOFtoCNF_B_3))
| subset(skolemFOFtoCNF_A_8,B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,B),skolemFOFtoCNF_A_8) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)),relation_rng(skolemFOFtoCNF_B_3))
| subset(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(relation_rng(skolemFOFtoCNF_B_3)))]]) ).
cnf(refute_0_18,plain,
subset(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)),relation_rng(skolemFOFtoCNF_B_3)) )],[refute_0_17,refute_0_1]) ).
cnf(refute_0_19,plain,
~ subset(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_8,relation_rng(skolemFOFtoCNF_B_3)) )],[refute_0_18,refute_0_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 01:28:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.39
% 0.19/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.39
%------------------------------------------------------------------------------