TSTP Solution File: SEU177+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 12:39:04 EDT 2022
% Result : Theorem 3.73s 3.91s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 146 ( 22 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 169 ( 70 ~; 56 |; 23 &)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 83 ( 6 sgn 45 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t20_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(A,relation_dom(C))
& in(B,relation_rng(C)) ) ) ) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C) )
=> in(A,relation_dom(C)) ),
inference(strip,[],[t20_relat_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C)
& in(A,relation_dom(C)) )
=> in(B,relation_rng(C)) ),
inference(strip,[],[t20_relat_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C) )
=> in(A,relation_dom(C)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( ~ in(A,relation_dom(C))
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2))
& in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2)
& relation(skolemFOFtoCNF_C_2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_dom(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(canonicalize,[],[d4_relat_1]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_dom(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C,D] :
( ( B != relation_dom(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) )
& ( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) )
& ( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),D),A)
| ~ in(skolemFOFtoCNF_C(A,B),B)
| ~ relation(A)
| B = relation_dom(A) )
& ( ~ relation(A)
| B = relation_dom(A)
| in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_D(A,B)),A)
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C,D] :
( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
relation(skolemFOFtoCNF_C_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
~ in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( B != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( relation_dom(A) != relation_dom(A)
| ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,relation_dom(A)) ),
inference(subst,[],[refute_0_1:[bind(B,$fot(relation_dom(A)))]]) ).
cnf(refute_0_3,plain,
relation_dom(A) = relation_dom(A),
introduced(tautology,[refl,[$fot(relation_dom(A))]]) ).
cnf(refute_0_4,plain,
( ~ in(ordered_pair(C,D),A)
| ~ relation(A)
| in(C,relation_dom(A)) ),
inference(resolve,[$cnf( $equal(relation_dom(A),relation_dom(A)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2)
| ~ relation(skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_C_2)),bind(C,$fot(skolemFOFtoCNF_A_3)),bind(D,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_6,plain,
( ~ relation(skolemFOFtoCNF_C_2)
| in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_1),skolemFOFtoCNF_C_2) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
relation(skolemFOFtoCNF_C_2),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_2) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
~ in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_3,relation_dom(skolemFOFtoCNF_C_2)) )],[refute_0_8,refute_0_9]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( relation(C)
& in(ordered_pair(A,B),C)
& in(A,relation_dom(C)) )
=> in(B,relation_rng(C)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B,C] :
( ~ in(B,relation_rng(C))
& in(A,relation_dom(C))
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3))
& in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)
& in(skolemFOFtoCNF_A_4,relation_dom(skolemFOFtoCNF_C_3))
& relation(skolemFOFtoCNF_C_3) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_rng(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(canonicalize,[],[d5_relat_1]) ).
fof(normalize_1_4,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B != relation_rng(A)
<=> ? [C] :
( ~ in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C,D] :
( ( B != relation_rng(A)
| ~ in(C,B)
| ~ relation(A)
| in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) )
& ( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) )
& ( ~ in(ordered_pair(D,skolemFOFtoCNF_C_1(A,B)),A)
| ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ relation(A)
| B = relation_rng(A) )
& ( ~ relation(A)
| B = relation_rng(A)
| in(ordered_pair(skolemFOFtoCNF_D_2(A,B),skolemFOFtoCNF_C_1(A,B)),A)
| in(skolemFOFtoCNF_C_1(A,B),B) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C,D] :
( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
relation(skolemFOFtoCNF_C_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_8,plain,
~ in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( B != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,B) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( relation_rng(A) != relation_rng(A)
| ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,relation_rng(A)) ),
inference(subst,[],[refute_1_1:[bind(B,$fot(relation_rng(A)))]]) ).
cnf(refute_1_3,plain,
relation_rng(A) = relation_rng(A),
introduced(tautology,[refl,[$fot(relation_rng(A))]]) ).
cnf(refute_1_4,plain,
( ~ in(ordered_pair(D,C),A)
| ~ relation(A)
| in(C,relation_rng(A)) ),
inference(resolve,[$cnf( $equal(relation_rng(A),relation_rng(A)) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
( ~ in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3)
| ~ relation(skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_C_3)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_1_6,plain,
( ~ relation(skolemFOFtoCNF_C_3)
| in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)) ),
inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_A_4,skolemFOFtoCNF_B_2),skolemFOFtoCNF_C_3) )],[refute_1_0,refute_1_5]) ).
cnf(refute_1_7,plain,
relation(skolemFOFtoCNF_C_3),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_8,plain,
in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_C_3) )],[refute_1_7,refute_1_6]) ).
cnf(refute_1_9,plain,
~ in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_10,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_2,relation_rng(skolemFOFtoCNF_C_3)) )],[refute_1_8,refute_1_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 07:10:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.73/3.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.73/3.91
% 3.73/3.91 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.73/3.92
%------------------------------------------------------------------------------