TSTP Solution File: SWW225+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWW225+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 00:59:22 EDT 2022
% Result : Theorem 179.00s 179.25s
% Output : CNFRefutation 179.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 76 ( 29 unt; 0 def)
% Number of atoms : 140 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 130 ( 66 ~; 47 |; 5 &)
% ( 10 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_fz_I1_J,axiom,
c_SEQ_Osubseq(v_f____) ).
fof(fact_real__of__nat__le__iff,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
fof(fact_seq__suble,axiom,
! [V_n_2,V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ) ).
fof(fact_less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| V_m_2 = V_n_2 ) ) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
| V_m_2 = V_n_2 ) ) ).
fof(fact_Suc__leI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
fof(fact_real__eq__of__nat,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ).
fof(fact_real__of__nat__def,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ).
fof(subgoal_0,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(strip,[],[conj_0]) ).
fof(negate_0_0,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(canonicalize,[],[fact_real__of__nat__def]) ).
fof(normalize_0_2,plain,
c_SEQ_Osubseq(v_f____),
inference(canonicalize,[],[fact_fz_I1_J]) ).
fof(normalize_0_3,plain,
! [V_fa_2,V_n_2] :
( ~ c_SEQ_Osubseq(V_fa_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ),
inference(canonicalize,[],[fact_seq__suble]) ).
fof(normalize_0_4,plain,
! [V_fa_2,V_n_2] :
( ~ c_SEQ_Osubseq(V_fa_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
<=> ( V_m_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(canonicalize,[],[fact_le__eq__less__or__eq]) ).
fof(normalize_0_6,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ( V_m_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(canonicalize,[],[fact_less__Suc__eq]) ).
fof(normalize_0_7,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ( V_m_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
inference(simplify,[],[normalize_0_5,normalize_0_7]) ).
fof(normalize_0_9,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [V_m_2,V_n_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [V_m,V_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(canonicalize,[],[fact_Suc__leI]) ).
fof(normalize_0_13,plain,
! [V_m,V_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),
inference(canonicalize,[],[fact_real__of__nat__le__iff]) ).
fof(normalize_0_15,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
<=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [V_m_2,V_n_2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),
inference(conjunct,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
introduced(tautology,[refl,[$fot(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))]]) ).
cnf(refute_0_3,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),[1,0],$fot(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))]]) ).
cnf(refute_0_4,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(resolve,[$cnf( $equal(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
introduced(tautology,[equality,[$cnf( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),[1],$fot(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))]]) ).
cnf(refute_0_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
introduced(tautology,[refl,[$fot(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))]]) ).
cnf(refute_0_9,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),[1,0],$fot(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))]]) ).
cnf(refute_0_10,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(resolve,[$cnf( $equal(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
introduced(tautology,[equality,[$cnf( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),[2],$fot(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))]]) ).
cnf(refute_0_13,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) )],[refute_0_13,refute_0_7]) ).
cnf(refute_0_15,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
c_SEQ_Osubseq(v_f____),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_17,plain,
( ~ c_SEQ_Osubseq(V_fa_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_18,plain,
( ~ c_SEQ_Osubseq(v_f____)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X_1395,hAPP(v_f____,X_1395)) ),
inference(subst,[],[refute_0_17:[bind(V_fa_2,$fot(v_f____)),bind(V_n_2,$fot(X_1395))]]) ).
cnf(refute_0_19,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X_1395,hAPP(v_f____,X_1395)),
inference(resolve,[$cnf( c_SEQ_Osubseq(v_f____) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X_2552,hAPP(v_f____,X_2552)),
inference(subst,[],[refute_0_19:[bind(X_1395,$fot(X_2552))]]) ).
cnf(refute_0_21,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_22,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X_2552,hAPP(v_f____,X_2552))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X_2552,c_Nat_OSuc(hAPP(v_f____,X_2552))) ),
inference(subst,[],[refute_0_21:[bind(V_m_2,$fot(X_2552)),bind(V_n_2,$fot(hAPP(v_f____,X_2552)))]]) ).
cnf(refute_0_23,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X_2552,c_Nat_OSuc(hAPP(v_f____,X_2552))),
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X_2552,hAPP(v_f____,X_2552)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X_2616,c_Nat_OSuc(hAPP(v_f____,X_2616))),
inference(subst,[],[refute_0_23:[bind(X_2552,$fot(X_2616))]]) ).
cnf(refute_0_25,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_26,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X_2616,c_Nat_OSuc(hAPP(v_f____,X_2616)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X_2616),c_Nat_OSuc(hAPP(v_f____,X_2616))) ),
inference(subst,[],[refute_0_25:[bind(V_m,$fot(X_2616)),bind(V_n,$fot(c_Nat_OSuc(hAPP(v_f____,X_2616))))]]) ).
cnf(refute_0_27,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X_2616),c_Nat_OSuc(hAPP(v_f____,X_2616))),
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X_2616,c_Nat_OSuc(hAPP(v_f____,X_2616))) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_29,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),
introduced(tautology,[refl,[$fot(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2))]]) ).
cnf(refute_0_30,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)) ),[1,0],$fot(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))]]) ).
cnf(refute_0_31,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),
inference(resolve,[$cnf( $equal(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)) )],[refute_0_1,refute_0_31]) ).
cnf(refute_0_33,plain,
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),
introduced(tautology,[equality,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),[1],$fot(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2))]]) ).
cnf(refute_0_34,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),
introduced(tautology,[refl,[$fot(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))]]) ).
cnf(refute_0_36,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),[1,0],$fot(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))]]) ).
cnf(refute_0_37,plain,
( c_RealDef_Oreal(tc_Nat_Onat) != c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2),
inference(resolve,[$cnf( $equal(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal)) )],[refute_0_1,refute_0_37]) ).
cnf(refute_0_39,plain,
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2)) ),
introduced(tautology,[equality,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ),[2],$fot(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2))]]) ).
cnf(refute_0_40,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2)) ),
inference(resolve,[$cnf( $equal(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2)) ),
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) )],[refute_0_34,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2)) ),
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) )],[refute_0_28,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X_2616),c_Nat_OSuc(hAPP(v_f____,X_2616)))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(X_2616)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,X_2616)))) ),
inference(subst,[],[refute_0_42:[bind(V_m_2,$fot(c_Nat_OSuc(hAPP(v_f____,X_2616)))),bind(V_n_2,$fot(c_Nat_OSuc(X_2616)))]]) ).
cnf(refute_0_44,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(X_2616)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,X_2616)))),
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X_2616),c_Nat_OSuc(hAPP(v_f____,X_2616))) )],[refute_0_27,refute_0_43]) ).
cnf(refute_0_45,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(subst,[],[refute_0_44:[bind(X_2616,$fot(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))]]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) )],[refute_0_45,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWW225+1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sat Jun 4 21:21:48 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.14/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 179.00/179.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 179.00/179.25
% 179.00/179.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 179.00/179.26
%------------------------------------------------------------------------------