TSTP Solution File: SWW196+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWW196+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 00:59:19 EDT 2022
% Result : Theorem 38.74s 38.95s
% Output : CNFRefutation 38.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 69 ( 40 unt; 0 def)
% Number of atoms : 110 ( 99 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 89 ( 48 ~; 40 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 41 ( 4 sgn 5 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096EX_Am_O_An_A_061_A2_A_K_Am_096,axiom,
? [B_m] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) ).
fof(fact_nat__mult__2,axiom,
! [V_z] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z) ).
fof(fact_numeral__2__eq__2,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
fof(conj_0,hypothesis,
( ? [B_m] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)
=> v_thesis____ ) ).
fof(conj_1,conjecture,
v_thesis____ ).
fof(subgoal_0,plain,
v_thesis____,
inference(strip,[],[conj_1]) ).
fof(negate_0_0,plain,
~ v_thesis____,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( v_thesis____
| ! [B_m] : v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) ),
inference(canonicalize,[],[conj_0]) ).
fof(normalize_0_1,plain,
! [B_m] :
( v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)
| v_thesis____ ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(canonicalize,[],[fact_One__nat__def]) ).
fof(normalize_0_3,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(canonicalize,[],[fact_numeral__2__eq__2]) ).
fof(normalize_0_4,plain,
~ v_thesis____,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [V_z] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(canonicalize,[],[fact_nat__mult__2]) ).
fof(normalize_0_6,plain,
! [V_z] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [B_m] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m),
inference(canonicalize,[],[fact__096EX_Am_O_An_A_061_A2_A_K_Am_096]) ).
fof(normalize_0_8,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m),
inference(skolemize,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)
| v_thesis____ ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(c_Groups_Oone__class_Oone(tc_Nat_Onat))),bind(Y,$fot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]) ).
cnf(refute_0_6,plain,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(resolve,[$cnf( $equal(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
introduced(tautology,[refl,[$fot(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]) ).
cnf(refute_0_8,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),[1,0],$fot(c_Groups_Oone__class_Oone(tc_Nat_Onat))]]) ).
cnf(refute_0_9,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(resolve,[$cnf( $equal(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(resolve,[$cnf( $equal(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_12,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) != c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),bind(Y,$fot(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),bind(Z,$fot(c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))))]]) ).
cnf(refute_0_15,plain,
( c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(resolve,[$cnf( $equal(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(resolve,[$cnf( $equal(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m),
introduced(tautology,[refl,[$fot(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m))]]) ).
cnf(refute_0_18,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) != c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m) ),
introduced(tautology,[equality,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)) ),[1,1],$fot(c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]) ).
cnf(refute_0_19,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) != c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m) ),
inference(resolve,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m),
inference(resolve,[$cnf( $equal(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m)
| v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m)
| v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_na____,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)) ),[1],$fot(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m))]]) ).
cnf(refute_0_22,plain,
( v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m)
| v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) ),
inference(resolve,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m)
| v_thesis____ ),
inference(resolve,[$cnf( $equal(v_na____,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
~ v_thesis____,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_25,plain,
v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m),
inference(resolve,[$cnf( v_thesis____ )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624),
inference(subst,[],[refute_0_25:[bind(B_m,$fot(X_624))]]) ).
cnf(refute_0_27,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_28,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z),
introduced(tautology,[refl,[$fot(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z))]]) ).
cnf(refute_0_29,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) != c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z) ),
introduced(tautology,[equality,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z)) ),[1,1],$fot(c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]) ).
cnf(refute_0_30,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) != c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z) ),
inference(resolve,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z),
inference(resolve,[$cnf( $equal(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))) )],[refute_0_16,refute_0_30]) ).
cnf(refute_0_32,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z) ),
introduced(tautology,[equality,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)) ),[0],$fot(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z))]]) ).
cnf(refute_0_33,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z) ),
inference(resolve,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(resolve,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z)) )],[refute_0_27,refute_0_33]) ).
cnf(refute_0_35,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X_624,X_624),
inference(subst,[],[refute_0_34:[bind(V_z,$fot(X_624))]]) ).
cnf(refute_0_36,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X_624,X_624)
| v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X_624,X_624)
| v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_na____,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624)) ),[1],$fot(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X_624,X_624))]]) ).
cnf(refute_0_37,plain,
( v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X_624,X_624)
| v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624) ),
inference(resolve,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X_624,X_624)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X_624,X_624),
inference(resolve,[$cnf( $equal(v_na____,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X_624)) )],[refute_0_37,refute_0_26]) ).
cnf(refute_0_39,plain,
v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m),
inference(subst,[],[refute_0_38:[bind(X_624,$fot(skolemFOFtoCNF_B_m))]]) ).
cnf(refute_0_40,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_41,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m),
inference(subst,[],[refute_0_27:[bind(V_z,$fot(skolemFOFtoCNF_B_m))]]) ).
cnf(refute_0_42,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m)
| v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m)
| v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m) ),
introduced(tautology,[equality,[$cnf( $equal(v_na____,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m)) ),[1],$fot(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m))]]) ).
cnf(refute_0_43,plain,
( v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m)
| v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m) ),
inference(resolve,[$cnf( $equal(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m),
inference(resolve,[$cnf( $equal(v_na____,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),skolemFOFtoCNF_B_m)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m) = v_na____ ),
inference(subst,[],[refute_0_4:[bind(X,$fot(v_na____)),bind(Y,$fot(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m)))]]) ).
cnf(refute_0_46,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m) = v_na____,
inference(resolve,[$cnf( $equal(v_na____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m) != v_na____
| v_na____ != v_na____
| v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_na____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m)) ),[1],$fot(v_na____)]]) ).
cnf(refute_0_48,plain,
( v_na____ != v_na____
| v_na____ = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m) ),
inference(resolve,[$cnf( $equal(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m),v_na____) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
v_na____ != v_na____,
inference(resolve,[$cnf( $equal(v_na____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,skolemFOFtoCNF_B_m,skolemFOFtoCNF_B_m)) )],[refute_0_48,refute_0_39]) ).
cnf(refute_0_50,plain,
v_na____ = v_na____,
introduced(tautology,[refl,[$fot(v_na____)]]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(v_na____,v_na____) )],[refute_0_50,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW196+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 6 01:58:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 38.74/38.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.74/38.95
% 38.74/38.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.74/38.96
%------------------------------------------------------------------------------