TSTP Solution File: SEU355+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:40:33 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 21 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 221 ( 89 ~; 74 |; 34 &)
% ( 6 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 88 ( 2 sgn 54 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ) ).
fof(d9_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,D,C) ) ) ) ) ) ).
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(t6_yellow_0,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_set_smaller(A,empty_set,B)
& relstr_element_smaller(A,empty_set,B) ) ) ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ) ).
fof(subgoal_0,plain,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> relstr_set_smaller(A,empty_set,B) ) ),
inference(strip,[],[t6_yellow_0]) ).
fof(subgoal_1,plain,
! [A] :
( rel_str(A)
=> ! [B] :
( ( element(B,the_carrier(A))
& relstr_set_smaller(A,empty_set,B) )
=> relstr_element_smaller(A,empty_set,B) ) ),
inference(strip,[],[t6_yellow_0]) ).
fof(negate_0_0,plain,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> relstr_set_smaller(A,empty_set,B) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[t7_boole]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [A] :
( rel_str(A)
& ? [B] :
( ~ relstr_set_smaller(A,empty_set,B)
& element(B,the_carrier(A)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( rel_str(skolemFOFtoCNF_A_5)
& ? [B] :
( ~ relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,B)
& element(B,the_carrier(skolemFOFtoCNF_A_5)) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [B] :
( ~ relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,B)
& element(B,the_carrier(skolemFOFtoCNF_A_5)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( ~ relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,skolemFOFtoCNF_B_1)
& element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_5)) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_5)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_set_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,D,C)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(canonicalize,[],[d9_lattice3]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_set_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,D,C)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,skolemFOFtoCNF_D_1(A,B,C),C)
| relstr_set_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| element(skolemFOFtoCNF_D_1(A,B,C),the_carrier(A))
| relstr_set_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D_1(A,B,C),B)
| relstr_set_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_set_smaller(A,B,C)
| related(A,D,C) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D_1(A,B,C),B)
| relstr_set_smaller(A,B,C) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
rel_str(skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_13,plain,
~ relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ empty(X_37)
| ~ in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,X_37,skolemFOFtoCNF_B_1),X_37) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,X_37,skolemFOFtoCNF_B_1))),bind(B,$fot(X_37))]]) ).
cnf(refute_0_3,plain,
element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_5)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D_1(A,B,C),B)
| relstr_set_smaller(A,B,C) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_5))
| ~ rel_str(skolemFOFtoCNF_A_5)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,X_35,skolemFOFtoCNF_B_1),X_35)
| relstr_set_smaller(skolemFOFtoCNF_A_5,X_35,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A_5)),bind(B,$fot(X_35)),bind(C,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_6,plain,
( ~ rel_str(skolemFOFtoCNF_A_5)
| in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,X_35,skolemFOFtoCNF_B_1),X_35)
| relstr_set_smaller(skolemFOFtoCNF_A_5,X_35,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_1,the_carrier(skolemFOFtoCNF_A_5)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
rel_str(skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,X_35,skolemFOFtoCNF_B_1),X_35)
| relstr_set_smaller(skolemFOFtoCNF_A_5,X_35,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_5) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,X_37,skolemFOFtoCNF_B_1),X_37)
| relstr_set_smaller(skolemFOFtoCNF_A_5,X_37,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_8:[bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_10,plain,
( ~ empty(X_37)
| relstr_set_smaller(skolemFOFtoCNF_A_5,X_37,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D_1(skolemFOFtoCNF_A_5,X_37,skolemFOFtoCNF_B_1),X_37) )],[refute_0_9,refute_0_2]) ).
cnf(refute_0_11,plain,
( ~ empty(empty_set)
| relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_10:[bind(X_37,$fot(empty_set))]]) ).
cnf(refute_0_12,plain,
relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
~ relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( relstr_set_smaller(skolemFOFtoCNF_A_5,empty_set,skolemFOFtoCNF_B_1) )],[refute_0_12,refute_0_13]) ).
fof(negate_1_0,plain,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( ( element(B,the_carrier(A))
& relstr_set_smaller(A,empty_set,B) )
=> relstr_element_smaller(A,empty_set,B) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_1_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[t7_boole]) ).
fof(normalize_1_2,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [A] :
( rel_str(A)
& ? [B] :
( ~ relstr_element_smaller(A,empty_set,B)
& element(B,the_carrier(A))
& relstr_set_smaller(A,empty_set,B) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_4,plain,
( rel_str(skolemFOFtoCNF_A_6)
& ? [B] :
( ~ relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,B)
& element(B,the_carrier(skolemFOFtoCNF_A_6))
& relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,B) ) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [B] :
( ~ relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,B)
& element(B,the_carrier(skolemFOFtoCNF_A_6))
& relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,B) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( ~ relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_2)
& element(skolemFOFtoCNF_B_2,the_carrier(skolemFOFtoCNF_A_6))
& relstr_set_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_2) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
element(skolemFOFtoCNF_B_2,the_carrier(skolemFOFtoCNF_A_6)),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_element_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(canonicalize,[],[d8_lattice3]) ).
fof(normalize_1_9,plain,
! [A] :
( ~ rel_str(A)
| ! [B,C] :
( ~ element(C,the_carrier(A))
| ( ~ relstr_element_smaller(A,B,C)
<=> ? [D] :
( ~ related(A,C,D)
& element(D,the_carrier(A))
& in(D,B) ) ) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B,C,D] :
( ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ related(A,C,skolemFOFtoCNF_D(A,B,C))
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| element(skolemFOFtoCNF_D(A,B,C),the_carrier(A))
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| relstr_element_smaller(A,B,C) )
& ( ~ element(C,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ in(D,B)
| ~ rel_str(A)
| ~ relstr_element_smaller(A,B,C)
| related(A,C,D) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B,C] :
( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| relstr_element_smaller(A,B,C) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
rel_str(skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_13,plain,
~ relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_1_0]) ).
cnf(refute_1_1,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_2,plain,
( ~ empty(X_59)
| ~ in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6,X_59,skolemFOFtoCNF_B_2),X_59) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6,X_59,skolemFOFtoCNF_B_2))),bind(B,$fot(X_59))]]) ).
cnf(refute_1_3,plain,
element(skolemFOFtoCNF_B_2,the_carrier(skolemFOFtoCNF_A_6)),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_4,plain,
( ~ element(C,the_carrier(A))
| ~ rel_str(A)
| in(skolemFOFtoCNF_D(A,B,C),B)
| relstr_element_smaller(A,B,C) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_5,plain,
( ~ element(skolemFOFtoCNF_B_2,the_carrier(skolemFOFtoCNF_A_6))
| ~ rel_str(skolemFOFtoCNF_A_6)
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6,X_57,skolemFOFtoCNF_B_2),X_57)
| relstr_element_smaller(skolemFOFtoCNF_A_6,X_57,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(B,$fot(X_57)),bind(C,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_6,plain,
( ~ rel_str(skolemFOFtoCNF_A_6)
| in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6,X_57,skolemFOFtoCNF_B_2),X_57)
| relstr_element_smaller(skolemFOFtoCNF_A_6,X_57,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_B_2,the_carrier(skolemFOFtoCNF_A_6)) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
rel_str(skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_8,plain,
( in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6,X_57,skolemFOFtoCNF_B_2),X_57)
| relstr_element_smaller(skolemFOFtoCNF_A_6,X_57,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( rel_str(skolemFOFtoCNF_A_6) )],[refute_1_7,refute_1_6]) ).
cnf(refute_1_9,plain,
( in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6,X_59,skolemFOFtoCNF_B_2),X_59)
| relstr_element_smaller(skolemFOFtoCNF_A_6,X_59,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_1_8:[bind(X_57,$fot(X_59))]]) ).
cnf(refute_1_10,plain,
( ~ empty(X_59)
| relstr_element_smaller(skolemFOFtoCNF_A_6,X_59,skolemFOFtoCNF_B_2) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(skolemFOFtoCNF_A_6,X_59,skolemFOFtoCNF_B_2),X_59) )],[refute_1_9,refute_1_2]) ).
cnf(refute_1_11,plain,
( ~ empty(empty_set)
| relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_2) ),
inference(subst,[],[refute_1_10:[bind(X_59,$fot(empty_set))]]) ).
cnf(refute_1_12,plain,
relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_2),
inference(resolve,[$cnf( empty(empty_set) )],[refute_1_0,refute_1_11]) ).
cnf(refute_1_13,plain,
~ relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_14,plain,
$false,
inference(resolve,[$cnf( relstr_element_smaller(skolemFOFtoCNF_A_6,empty_set,skolemFOFtoCNF_B_2) )],[refute_1_12,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 10:34:25 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.40
%------------------------------------------------------------------------------