%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU219+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:39:25 EDT 2022
% Result : Theorem 0.48s 0.66s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 102 ( 38 unt; 0 def)
% Number of atoms : 226 ( 121 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 214 ( 90 ~; 79 |; 34 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 43 ( 0 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d9_funct_1,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ) ).
fof(t37_relat_1,axiom,
! [A] :
( relation(A)
=> ( relation_rng(A) = relation_dom(relation_inverse(A))
& relation_dom(A) = relation_rng(relation_inverse(A)) ) ) ).
fof(t55_funct_1,conjecture,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( relation_rng(A) = relation_dom(function_inverse(A))
& relation_dom(A) = relation_rng(function_inverse(A)) ) ) ) ).
fof(subgoal_0,plain,
! [A] :
( ( relation(A)
& function(A)
& one_to_one(A) )
=> relation_rng(A) = relation_dom(function_inverse(A)) ),
inference(strip,[],[t55_funct_1]) ).
fof(subgoal_1,plain,
! [A] :
( ( relation(A)
& function(A)
& one_to_one(A)
& relation_rng(A) = relation_dom(function_inverse(A)) )
=> relation_dom(A) = relation_rng(function_inverse(A)) ),
inference(strip,[],[t55_funct_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( relation(A)
& function(A)
& one_to_one(A) )
=> relation_rng(A) = relation_dom(function_inverse(A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( relation_rng(A) != relation_dom(function_inverse(A))
& function(A)
& one_to_one(A)
& relation(A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( relation_rng(skolemFOFtoCNF_A_2) != relation_dom(function_inverse(skolemFOFtoCNF_A_2))
& function(skolemFOFtoCNF_A_2)
& one_to_one(skolemFOFtoCNF_A_2)
& relation(skolemFOFtoCNF_A_2) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
relation(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ relation(A)
| relation(relation_inverse(A)) ),
inference(canonicalize,[],[dt_k4_relat_1]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ relation(A)
| relation(relation_inverse(A)) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] :
( ~ relation(A)
| ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(canonicalize,[],[t37_relat_1]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ relation(A)
| ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] :
( ( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) )
& ( ~ relation(A)
| relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ relation(A)
| relation_inverse(relation_inverse(A)) = A ),
inference(canonicalize,[],[involutiveness_k4_relat_1]) ).
fof(normalize_0_10,plain,
! [A] :
( ~ relation(A)
| relation_inverse(relation_inverse(A)) = A ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] :
( ~ function(A)
| ~ one_to_one(A)
| ~ relation(A)
| function_inverse(A) = relation_inverse(A) ),
inference(canonicalize,[],[d9_funct_1]) ).
fof(normalize_0_12,plain,
! [A] :
( ~ function(A)
| ~ one_to_one(A)
| ~ relation(A)
| function_inverse(A) = relation_inverse(A) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
function(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,plain,
one_to_one(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_15,plain,
relation_rng(skolemFOFtoCNF_A_2) != relation_dom(function_inverse(skolemFOFtoCNF_A_2)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
relation(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ relation(A)
| relation(relation_inverse(A)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ relation(skolemFOFtoCNF_A_2)
| relation(relation_inverse(skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_3,plain,
relation(relation_inverse(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_2) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ relation(relation_inverse(skolemFOFtoCNF_A_2))
| relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(relation_inverse(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_6,plain,
relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))),
inference(resolve,[$cnf( relation(relation_inverse(skolemFOFtoCNF_A_2)) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ relation(A)
| relation_inverse(relation_inverse(A)) = A ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ relation(skolemFOFtoCNF_A_2)
| relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2 ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_9,plain,
relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)) = skolemFOFtoCNF_A_2,
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_2) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))) = relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))),
introduced(tautology,[refl,[$fot(relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_11,plain,
( relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))) != relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)))
| relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))) = relation_rng(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))),relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)))) ),[1,0],$fot(skolemFOFtoCNF_A_2)]]) ).
cnf(refute_0_12,plain,
( relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)) != skolemFOFtoCNF_A_2
| relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))) = relation_rng(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))),relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))) = relation_rng(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)),skolemFOFtoCNF_A_2) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) != relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)))
| relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))) != relation_rng(skolemFOFtoCNF_A_2)
| relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_rng(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),relation_rng(skolemFOFtoCNF_A_2)) ),[0],$fot(relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))))]]) ).
cnf(refute_0_15,plain,
( relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) != relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)))
| relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_rng(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2))),relation_rng(skolemFOFtoCNF_A_2)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_rng(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),relation_rng(relation_inverse(relation_inverse(skolemFOFtoCNF_A_2)))) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ function(A)
| ~ one_to_one(A)
| ~ relation(A)
| function_inverse(A) = relation_inverse(A) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_18,plain,
( ~ function(skolemFOFtoCNF_A_2)
| ~ one_to_one(skolemFOFtoCNF_A_2)
| ~ relation(skolemFOFtoCNF_A_2)
| function_inverse(skolemFOFtoCNF_A_2) = relation_inverse(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_17:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_19,plain,
( ~ function(skolemFOFtoCNF_A_2)
| ~ one_to_one(skolemFOFtoCNF_A_2)
| function_inverse(skolemFOFtoCNF_A_2) = relation_inverse(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_2) )],[refute_0_0,refute_0_18]) ).
cnf(refute_0_20,plain,
function(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
( ~ one_to_one(skolemFOFtoCNF_A_2)
| function_inverse(skolemFOFtoCNF_A_2) = relation_inverse(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_A_2) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
one_to_one(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_23,plain,
function_inverse(skolemFOFtoCNF_A_2) = relation_inverse(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( one_to_one(skolemFOFtoCNF_A_2) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_26,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( function_inverse(skolemFOFtoCNF_A_2) != relation_inverse(skolemFOFtoCNF_A_2)
| relation_inverse(skolemFOFtoCNF_A_2) = function_inverse(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(function_inverse(skolemFOFtoCNF_A_2))),bind(Y,$fot(relation_inverse(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_28,plain,
relation_inverse(skolemFOFtoCNF_A_2) = function_inverse(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(function_inverse(skolemFOFtoCNF_A_2),relation_inverse(skolemFOFtoCNF_A_2)) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),
introduced(tautology,[refl,[$fot(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_30,plain,
( relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) != relation_dom(relation_inverse(skolemFOFtoCNF_A_2))
| relation_inverse(skolemFOFtoCNF_A_2) != function_inverse(skolemFOFtoCNF_A_2)
| relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_dom(function_inverse(skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),relation_dom(relation_inverse(skolemFOFtoCNF_A_2))) ),[1,0],$fot(function_inverse(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_31,plain,
( relation_inverse(skolemFOFtoCNF_A_2) != function_inverse(skolemFOFtoCNF_A_2)
| relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_dom(function_inverse(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),relation_dom(relation_inverse(skolemFOFtoCNF_A_2))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) = relation_dom(function_inverse(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( $equal(relation_inverse(skolemFOFtoCNF_A_2),function_inverse(skolemFOFtoCNF_A_2)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) != relation_dom(function_inverse(skolemFOFtoCNF_A_2))
| relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) != relation_rng(skolemFOFtoCNF_A_2)
| relation_dom(function_inverse(skolemFOFtoCNF_A_2)) = relation_rng(skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),relation_rng(skolemFOFtoCNF_A_2)) ),[0],$fot(relation_dom(function_inverse(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_34,plain,
( relation_dom(relation_inverse(skolemFOFtoCNF_A_2)) != relation_rng(skolemFOFtoCNF_A_2)
| relation_dom(function_inverse(skolemFOFtoCNF_A_2)) = relation_rng(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),relation_dom(function_inverse(skolemFOFtoCNF_A_2))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
relation_dom(function_inverse(skolemFOFtoCNF_A_2)) = relation_rng(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_2)),relation_rng(skolemFOFtoCNF_A_2)) )],[refute_0_16,refute_0_34]) ).
cnf(refute_0_36,plain,
relation_rng(skolemFOFtoCNF_A_2) != relation_dom(function_inverse(skolemFOFtoCNF_A_2)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_37,plain,
( relation_dom(function_inverse(skolemFOFtoCNF_A_2)) != relation_rng(skolemFOFtoCNF_A_2)
| relation_rng(skolemFOFtoCNF_A_2) = relation_dom(function_inverse(skolemFOFtoCNF_A_2)) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(relation_dom(function_inverse(skolemFOFtoCNF_A_2)))),bind(Y,$fot(relation_rng(skolemFOFtoCNF_A_2)))]]) ).
cnf(refute_0_38,plain,
relation_dom(function_inverse(skolemFOFtoCNF_A_2)) != relation_rng(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_2),relation_dom(function_inverse(skolemFOFtoCNF_A_2))) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
$false,
inference(resolve,[$cnf( $equal(relation_dom(function_inverse(skolemFOFtoCNF_A_2)),relation_rng(skolemFOFtoCNF_A_2)) )],[refute_0_35,refute_0_38]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( relation(A)
& function(A)
& one_to_one(A)
& relation_rng(A) = relation_dom(function_inverse(A)) )
=> relation_dom(A) = relation_rng(function_inverse(A)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A] :
( relation_dom(A) != relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A))
& function(A)
& one_to_one(A)
& relation(A) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( relation_dom(skolemFOFtoCNF_A_3) != relation_rng(function_inverse(skolemFOFtoCNF_A_3))
& relation_rng(skolemFOFtoCNF_A_3) = relation_dom(function_inverse(skolemFOFtoCNF_A_3))
& function(skolemFOFtoCNF_A_3)
& one_to_one(skolemFOFtoCNF_A_3)
& relation(skolemFOFtoCNF_A_3) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
relation(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( ~ relation(A)
| ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(canonicalize,[],[t37_relat_1]) ).
fof(normalize_1_4,plain,
! [A] :
( ~ relation(A)
| ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] :
( ( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) )
& ( ~ relation(A)
| relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A] :
( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A] :
( ~ function(A)
| ~ one_to_one(A)
| ~ relation(A)
| function_inverse(A) = relation_inverse(A) ),
inference(canonicalize,[],[d9_funct_1]) ).
fof(normalize_1_8,plain,
! [A] :
( ~ function(A)
| ~ one_to_one(A)
| ~ relation(A)
| function_inverse(A) = relation_inverse(A) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
function(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_10,plain,
one_to_one(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_11,plain,
relation_dom(skolemFOFtoCNF_A_3) != relation_rng(function_inverse(skolemFOFtoCNF_A_3)),
inference(conjunct,[],[normalize_1_1]) ).
cnf(refute_1_0,plain,
relation(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ relation(skolemFOFtoCNF_A_3)
| relation_dom(skolemFOFtoCNF_A_3) = relation_rng(relation_inverse(skolemFOFtoCNF_A_3)) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_3,plain,
relation_dom(skolemFOFtoCNF_A_3) = relation_rng(relation_inverse(skolemFOFtoCNF_A_3)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_3) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
( ~ function(A)
| ~ one_to_one(A)
| ~ relation(A)
| function_inverse(A) = relation_inverse(A) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
( ~ function(skolemFOFtoCNF_A_3)
| ~ one_to_one(skolemFOFtoCNF_A_3)
| ~ relation(skolemFOFtoCNF_A_3)
| function_inverse(skolemFOFtoCNF_A_3) = relation_inverse(skolemFOFtoCNF_A_3) ),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_6,plain,
( ~ function(skolemFOFtoCNF_A_3)
| ~ one_to_one(skolemFOFtoCNF_A_3)
| function_inverse(skolemFOFtoCNF_A_3) = relation_inverse(skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_3) )],[refute_1_0,refute_1_5]) ).
cnf(refute_1_7,plain,
function(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_8,plain,
( ~ one_to_one(skolemFOFtoCNF_A_3)
| function_inverse(skolemFOFtoCNF_A_3) = relation_inverse(skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( function(skolemFOFtoCNF_A_3) )],[refute_1_7,refute_1_6]) ).
cnf(refute_1_9,plain,
one_to_one(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_10,plain,
function_inverse(skolemFOFtoCNF_A_3) = relation_inverse(skolemFOFtoCNF_A_3),
inference(resolve,[$cnf( one_to_one(skolemFOFtoCNF_A_3) )],[refute_1_9,refute_1_8]) ).
cnf(refute_1_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_11,refute_1_12]) ).
cnf(refute_1_14,plain,
( function_inverse(skolemFOFtoCNF_A_3) != relation_inverse(skolemFOFtoCNF_A_3)
| relation_inverse(skolemFOFtoCNF_A_3) = function_inverse(skolemFOFtoCNF_A_3) ),
inference(subst,[],[refute_1_13:[bind(X,$fot(function_inverse(skolemFOFtoCNF_A_3))),bind(Y,$fot(relation_inverse(skolemFOFtoCNF_A_3)))]]) ).
cnf(refute_1_15,plain,
relation_inverse(skolemFOFtoCNF_A_3) = function_inverse(skolemFOFtoCNF_A_3),
inference(resolve,[$cnf( $equal(function_inverse(skolemFOFtoCNF_A_3),relation_inverse(skolemFOFtoCNF_A_3)) )],[refute_1_10,refute_1_14]) ).
cnf(refute_1_16,plain,
relation_rng(relation_inverse(skolemFOFtoCNF_A_3)) = relation_rng(relation_inverse(skolemFOFtoCNF_A_3)),
introduced(tautology,[refl,[$fot(relation_rng(relation_inverse(skolemFOFtoCNF_A_3)))]]) ).
cnf(refute_1_17,plain,
( relation_inverse(skolemFOFtoCNF_A_3) != function_inverse(skolemFOFtoCNF_A_3)
| relation_rng(relation_inverse(skolemFOFtoCNF_A_3)) != relation_rng(relation_inverse(skolemFOFtoCNF_A_3))
| relation_rng(relation_inverse(skolemFOFtoCNF_A_3)) = relation_rng(function_inverse(skolemFOFtoCNF_A_3)) ),
introduced(tautology,[equality,[$cnf( $equal(relation_rng(relation_inverse(skolemFOFtoCNF_A_3)),relation_rng(relation_inverse(skolemFOFtoCNF_A_3))) ),[1,0],$fot(function_inverse(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_18,plain,
( relation_inverse(skolemFOFtoCNF_A_3) != function_inverse(skolemFOFtoCNF_A_3)
| relation_rng(relation_inverse(skolemFOFtoCNF_A_3)) = relation_rng(function_inverse(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( $equal(relation_rng(relation_inverse(skolemFOFtoCNF_A_3)),relation_rng(relation_inverse(skolemFOFtoCNF_A_3))) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
relation_rng(relation_inverse(skolemFOFtoCNF_A_3)) = relation_rng(function_inverse(skolemFOFtoCNF_A_3)),
inference(resolve,[$cnf( $equal(relation_inverse(skolemFOFtoCNF_A_3),function_inverse(skolemFOFtoCNF_A_3)) )],[refute_1_15,refute_1_18]) ).
cnf(refute_1_20,plain,
( relation_dom(skolemFOFtoCNF_A_3) != relation_rng(relation_inverse(skolemFOFtoCNF_A_3))
| relation_rng(relation_inverse(skolemFOFtoCNF_A_3)) != relation_rng(function_inverse(skolemFOFtoCNF_A_3))
| relation_dom(skolemFOFtoCNF_A_3) = relation_rng(function_inverse(skolemFOFtoCNF_A_3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(relation_dom(skolemFOFtoCNF_A_3),relation_rng(function_inverse(skolemFOFtoCNF_A_3))) ),[0],$fot(relation_rng(relation_inverse(skolemFOFtoCNF_A_3)))]]) ).
cnf(refute_1_21,plain,
( relation_dom(skolemFOFtoCNF_A_3) != relation_rng(relation_inverse(skolemFOFtoCNF_A_3))
| relation_dom(skolemFOFtoCNF_A_3) = relation_rng(function_inverse(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( $equal(relation_rng(relation_inverse(skolemFOFtoCNF_A_3)),relation_rng(function_inverse(skolemFOFtoCNF_A_3))) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
relation_dom(skolemFOFtoCNF_A_3) = relation_rng(function_inverse(skolemFOFtoCNF_A_3)),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_3),relation_rng(relation_inverse(skolemFOFtoCNF_A_3))) )],[refute_1_3,refute_1_21]) ).
cnf(refute_1_23,plain,
relation_dom(skolemFOFtoCNF_A_3) != relation_rng(function_inverse(skolemFOFtoCNF_A_3)),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_24,plain,
$false,
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_3),relation_rng(function_inverse(skolemFOFtoCNF_A_3))) )],[refute_1_22,refute_1_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU219+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n029.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 17:17:30 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.66
% 0.48/0.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.66
%------------------------------------------------------------------------------