TSTP Solution File: SEU247+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU247+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:39:41 EDT 2022
% Result : Theorem 0.41s 0.58s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 70 ( 52 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 29 ~; 23 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t140_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ) ).
fof(t17_wellord1,axiom,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ) ).
fof(t18_wellord1,conjecture,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ) ).
fof(subgoal_0,plain,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ),
inference(strip,[],[t18_wellord1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( relation_restriction(B,A) != relation_rng_restriction(A,relation_dom_restriction(B,A))
& relation(B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) != relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
& relation(skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) != relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
relation(skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ relation(B)
| relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
inference(canonicalize,[],[t17_wellord1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ relation(B)
| relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ~ relation(C)
| relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
inference(canonicalize,[],[t140_relat_1]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( ~ relation(C)
| relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) != relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
relation(skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ relation(B)
| relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ relation(skolemFOFtoCNF_B)
| relation_restriction(skolemFOFtoCNF_B,X_206) = relation_dom_restriction(relation_rng_restriction(X_206,skolemFOFtoCNF_B),X_206) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_206)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_4,plain,
relation_restriction(skolemFOFtoCNF_B,X_206) = relation_dom_restriction(relation_rng_restriction(X_206,skolemFOFtoCNF_B),X_206),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( relation_restriction(skolemFOFtoCNF_B,X_206) != relation_dom_restriction(relation_rng_restriction(X_206,skolemFOFtoCNF_B),X_206)
| relation_dom_restriction(relation_rng_restriction(X_206,skolemFOFtoCNF_B),X_206) = relation_restriction(skolemFOFtoCNF_B,X_206) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(relation_restriction(skolemFOFtoCNF_B,X_206))),bind(Y,$fot(relation_dom_restriction(relation_rng_restriction(X_206,skolemFOFtoCNF_B),X_206)))]]) ).
cnf(refute_0_9,plain,
relation_dom_restriction(relation_rng_restriction(X_206,skolemFOFtoCNF_B),X_206) = relation_restriction(skolemFOFtoCNF_B,X_206),
inference(resolve,[$cnf( $equal(relation_restriction(skolemFOFtoCNF_B,X_206),relation_dom_restriction(relation_rng_restriction(X_206,skolemFOFtoCNF_B),X_206)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A) = relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(subst,[],[refute_0_9:[bind(X_206,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_11,plain,
( ~ relation(C)
| relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_12,plain,
( ~ relation(skolemFOFtoCNF_B)
| relation_dom_restriction(relation_rng_restriction(X_484,skolemFOFtoCNF_B),X_485) = relation_rng_restriction(X_484,relation_dom_restriction(skolemFOFtoCNF_B,X_485)) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_484)),bind(B,$fot(X_485)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_13,plain,
relation_dom_restriction(relation_rng_restriction(X_484,skolemFOFtoCNF_B),X_485) = relation_rng_restriction(X_484,relation_dom_restriction(skolemFOFtoCNF_B,X_485)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_B) )],[refute_0_1,refute_0_12]) ).
cnf(refute_0_14,plain,
( relation_dom_restriction(relation_rng_restriction(X_484,skolemFOFtoCNF_B),X_485) != relation_rng_restriction(X_484,relation_dom_restriction(skolemFOFtoCNF_B,X_485))
| relation_rng_restriction(X_484,relation_dom_restriction(skolemFOFtoCNF_B,X_485)) = relation_dom_restriction(relation_rng_restriction(X_484,skolemFOFtoCNF_B),X_485) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(relation_dom_restriction(relation_rng_restriction(X_484,skolemFOFtoCNF_B),X_485))),bind(Y,$fot(relation_rng_restriction(X_484,relation_dom_restriction(skolemFOFtoCNF_B,X_485))))]]) ).
cnf(refute_0_15,plain,
relation_rng_restriction(X_484,relation_dom_restriction(skolemFOFtoCNF_B,X_485)) = relation_dom_restriction(relation_rng_restriction(X_484,skolemFOFtoCNF_B),X_485),
inference(resolve,[$cnf( $equal(relation_dom_restriction(relation_rng_restriction(X_484,skolemFOFtoCNF_B),X_485),relation_rng_restriction(X_484,relation_dom_restriction(skolemFOFtoCNF_B,X_485))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) = relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A),
inference(subst,[],[refute_0_15:[bind(X_484,$fot(skolemFOFtoCNF_A)),bind(X_485,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_17,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_17]) ).
cnf(refute_0_19,plain,
( relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A) != relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) != relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A)
| relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) = relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)))),bind(Y,$fot(relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A))),bind(Z,$fot(relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_20,plain,
( relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A) != relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) = relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( $equal(relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) = relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( $equal(relation_dom_restriction(relation_rng_restriction(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_A),relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) )],[refute_0_10,refute_0_20]) ).
cnf(refute_0_22,plain,
( relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) != relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) != relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) = relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A),relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A))) ),[1],$fot(relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A))]]) ).
cnf(refute_0_23,plain,
( relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) != relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) = relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( $equal(relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) != relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( $equal(relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A),relation_rng_restriction(skolemFOFtoCNF_A,relation_dom_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A))) )],[refute_0_23,refute_0_0]) ).
cnf(refute_0_25,plain,
relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A) = relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A),
introduced(tautology,[refl,[$fot(relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A),relation_restriction(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) )],[refute_0_25,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU247+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.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 : Sun Jun 19 18:26:59 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.58
% 0.41/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.41/0.58
%------------------------------------------------------------------------------