TSTP Solution File: SWW288+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWW288+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Thu Jul 21 00:59:28 EDT 2022
% Result : Theorem 6.51s 6.75s
% Output : CNFRefutation 6.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 23 unt; 0 def)
% Number of atoms : 87 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 34 ~; 31 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 36 ( 13 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096_B_Bx_O_Apoly_Ap_Ax_A_061_Apoly_Ap_A_I0_058_058_Ha_J_096,axiom,
! [V_x] :
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> hAPP(c_Polynomial_Opoly(t_a,v_p),V_x) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) ) ).
fof(fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096,axiom,
( ( class_Int_Oring__char__0(t_a)
& class_Rings_Oidom(t_a) )
=> v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ) ).
fof(fact_degree__pCons__0,axiom,
! [V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
fof(clrel_Int_Oring__char__0__Groups_Ozero,axiom,
! [T] :
( class_Int_Oring__char__0(T)
=> class_Groups_Ozero(T) ) ).
fof(conj_0,conjecture,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
fof(tfree_0,hypothesis,
class_Int_Oring__char__0(t_a) ).
fof(tfree_1,hypothesis,
class_Rings_Oidom(t_a) ).
fof(subgoal_0,plain,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(strip,[],[conj_0]) ).
fof(negate_0_0,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
class_Int_Oring__char__0(t_a),
inference(canonicalize,[],[tfree_0]) ).
fof(normalize_0_1,plain,
! [T] :
( ~ class_Int_Oring__char__0(T)
| class_Groups_Ozero(T) ),
inference(canonicalize,[],[clrel_Int_Oring__char__0__Groups_Ozero]) ).
fof(normalize_0_2,plain,
! [T] :
( ~ class_Int_Oring__char__0(T)
| class_Groups_Ozero(T) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [T_a,V_a] :
( ~ class_Groups_Ozero(T_a)
| c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(canonicalize,[],[fact_degree__pCons__0]) ).
fof(normalize_0_4,plain,
! [T_a,V_a] :
( ~ class_Groups_Ozero(T_a)
| c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
inference(canonicalize,[],[fact__096p_A_061_A_091_058poly_Ap_A_I0_058_058_Ha_J_058_093_096]) ).
fof(normalize_0_6,plain,
class_Rings_Oidom(t_a),
inference(canonicalize,[],[tfree_1]) ).
fof(normalize_0_7,plain,
( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| ! [V_x] : hAPP(c_Polynomial_Opoly(t_a,v_p),V_x) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) ),
inference(canonicalize,[],[fact__096_B_Bx_O_Apoly_Ap_Ax_A_061_Apoly_Ap_A_I0_058_058_Ha_J_096]) ).
fof(normalize_0_8,plain,
! [V_x] :
( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_p),V_x) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
class_Int_Oring__char__0(t_a),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ class_Int_Oring__char__0(T)
| class_Groups_Ozero(T) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ class_Int_Oring__char__0(t_a)
| class_Groups_Ozero(t_a) ),
inference(subst,[],[refute_0_1:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_3,plain,
class_Groups_Ozero(t_a),
inference(resolve,[$cnf( class_Int_Oring__char__0(t_a) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ class_Groups_Ozero(T_a)
| c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_5,plain,
( ~ class_Groups_Ozero(t_a)
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,X_1209,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(subst,[],[refute_0_4:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_1209))]]) ).
cnf(refute_0_6,plain,
c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,X_1209,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(resolve,[$cnf( class_Groups_Ozero(t_a) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(subst,[],[refute_0_6:[bind(X_1209,$fot(hAPP(c_Polynomial_Opoly(t_a,v_p),X_150)))]]) ).
cnf(refute_0_8,plain,
( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_9,plain,
( ~ class_Rings_Oidom(t_a)
| v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
inference(resolve,[$cnf( class_Int_Oring__char__0(t_a) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
class_Rings_Oidom(t_a),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_11,plain,
v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(resolve,[$cnf( class_Rings_Oidom(t_a) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( ~ class_Int_Oring__char__0(t_a)
| ~ class_Rings_Oidom(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_p),V_x) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_13,plain,
( ~ class_Rings_Oidom(t_a)
| hAPP(c_Polynomial_Opoly(t_a,v_p),V_x) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) ),
inference(resolve,[$cnf( class_Int_Oring__char__0(t_a) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
hAPP(c_Polynomial_Opoly(t_a,v_p),V_x) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),
inference(resolve,[$cnf( class_Rings_Oidom(t_a) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
hAPP(c_Polynomial_Opoly(t_a,v_p),X_150) = hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),
inference(subst,[],[refute_0_14:[bind(V_x,$fot(X_150))]]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( hAPP(c_Polynomial_Opoly(t_a,v_p),X_150) != hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a))
| hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) = hAPP(c_Polynomial_Opoly(t_a,v_p),X_150) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(c_Polynomial_Opoly(t_a,v_p),X_150))),bind(Y,$fot(hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a))))]]) ).
cnf(refute_0_20,plain,
hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) = hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),
inference(resolve,[$cnf( $equal(hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a))) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)) != hAPP(c_Polynomial_Opoly(t_a,v_p),X_150)
| v_p != c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
introduced(tautology,[equality,[$cnf( $equal(v_p,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),[1,1],$fot(hAPP(c_Polynomial_Opoly(t_a,v_p),X_150))]]) ).
cnf(refute_0_22,plain,
( v_p != c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
inference(resolve,[$cnf( $equal(hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),hAPP(c_Polynomial_Opoly(t_a,v_p),X_150)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(resolve,[$cnf( $equal(v_p,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )],[refute_0_11,refute_0_22]) ).
cnf(refute_0_24,plain,
( v_p != c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = v_p ),
inference(subst,[],[refute_0_18:[bind(X,$fot(v_p)),bind(Y,$fot(c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))]]) ).
cnf(refute_0_25,plain,
c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = v_p,
inference(resolve,[$cnf( $equal(v_p,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != v_p
| c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(tautology,[equality,[$cnf( $equal(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),[0,1],$fot(v_p)]]) ).
cnf(refute_0_27,plain,
( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(resolve,[$cnf( $equal(c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),v_p) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(resolve,[$cnf( $equal(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),X_150),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )],[refute_0_7,refute_0_27]) ).
cnf(refute_0_29,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( $equal(c_Polynomial_Odegree(t_a,v_p),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )],[refute_0_28,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW288+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.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 : Sat Jun 4 11:26:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.51/6.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.51/6.75
% 6.51/6.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.51/6.75
%------------------------------------------------------------------------------