TSTP Solution File: NUM924+7 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 : Mon Jul 18 12:31:36 EDT 2022
% Result : Theorem 2.59s 2.83s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 85
% Syntax : Number of formulae : 302 ( 160 unt; 0 def)
% Number of atoms : 509 ( 485 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 418 ( 211 ~; 207 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 8 con; 0-5 aty)
% Number of variables : 97 ( 1 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Int_OBit0_res,hypothesis,
! [B_1_1] : ti(int,bit0(B_1_1)) = bit0(B_1_1) ).
fof(tsy_c_Int_OBit1_res,hypothesis,
! [B_1_1] : ti(int,bit1(B_1_1)) = bit1(B_1_1) ).
fof(tsy_c_Int_OMin_res,axiom,
ti(int,min) = min ).
fof(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))) ).
fof(fact_3_t,axiom,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) ).
fof(fact_22_number__of__is__id,axiom,
! [K_1] : number_number_of(int,K_1) = ti(int,K_1) ).
fof(fact_23_zmult__commute,axiom,
! [Z_1,W] : hAPP(int,int,times_times(int,Z_1),W) = hAPP(int,int,times_times(int,W),Z_1) ).
fof(fact_62_mult__Pls,axiom,
! [W] : hAPP(int,int,times_times(int,pls),W) = pls ).
fof(fact_98_zadd__commute,axiom,
! [Z_1,W] : hAPP(int,int,plus_plus(int,Z_1),W) = hAPP(int,int,plus_plus(int,W),Z_1) ).
fof(fact_111_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)) ).
fof(fact_122_Pls__def,axiom,
pls = zero_zero(int) ).
fof(fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) ).
fof(fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096,axiom,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) ).
fof(help_COMBC_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) ).
fof(conj_0,conjecture,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))) ).
fof(subgoal_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(strip,[],[conj_0]) ).
fof(negate_0_0,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))),
inference(canonicalize,[],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
fof(normalize_0_1,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
inference(canonicalize,[],[fact_751__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096]) ).
fof(normalize_0_2,plain,
! [W,Z_1] : hAPP(int,int,times_times(int,Z_1),W) = hAPP(int,int,times_times(int,W),Z_1),
inference(canonicalize,[],[fact_23_zmult__commute]) ).
fof(normalize_0_3,plain,
! [W,Z_1] : hAPP(int,int,times_times(int,Z_1),W) = hAPP(int,int,times_times(int,W),Z_1),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W,Z_1] : hAPP(int,int,plus_plus(int,Z_1),W) = hAPP(int,int,plus_plus(int,W),Z_1),
inference(canonicalize,[],[fact_98_zadd__commute]) ).
fof(normalize_0_5,plain,
! [W,Z_1] : hAPP(int,int,plus_plus(int,Z_1),W) = hAPP(int,int,plus_plus(int,W),Z_1),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W] : hAPP(int,int,times_times(int,pls),W) = pls,
inference(canonicalize,[],[fact_62_mult__Pls]) ).
fof(normalize_0_7,plain,
! [W] : hAPP(int,int,times_times(int,pls),W) = pls,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
pls = zero_zero(int),
inference(canonicalize,[],[fact_122_Pls__def]) ).
fof(normalize_0_9,plain,
! [P,Q,R,X_a,X_b,X_c] : hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q),
inference(canonicalize,[],[help_COMBC_1_1_U]) ).
fof(normalize_0_10,plain,
! [P,Q,R,X_a,X_b,X_c] : hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(canonicalize,[],[fact_111_one__is__num__one]) ).
fof(normalize_0_12,plain,
! [B_1_1] : ti(int,bit1(B_1_1)) = bit1(B_1_1),
inference(canonicalize,[],[tsy_c_Int_OBit1_res]) ).
fof(normalize_0_13,plain,
! [B_1_1] : ti(int,bit1(B_1_1)) = bit1(B_1_1),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [K_1] : number_number_of(int,K_1) = ti(int,K_1),
inference(canonicalize,[],[fact_22_number__of__is__id]) ).
fof(normalize_0_15,plain,
! [K_1] : number_number_of(int,K_1) = ti(int,K_1),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_17,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
inference(canonicalize,[],[fact_466__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096]) ).
fof(normalize_0_18,plain,
ti(int,min) = min,
inference(canonicalize,[],[tsy_c_Int_OMin_res]) ).
fof(normalize_0_19,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
inference(canonicalize,[],[fact_3_t]) ).
fof(normalize_0_20,plain,
! [B_1_1] : ti(int,bit0(B_1_1)) = bit0(B_1_1),
inference(canonicalize,[],[tsy_c_Int_OBit0_res]) ).
fof(normalize_0_21,plain,
! [B_1_1] : ti(int,bit0(B_1_1)) = bit0(B_1_1),
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
hAPP(int,int,times_times(int,Z_1),W) = hAPP(int,int,times_times(int,W),Z_1),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( hAPP(int,int,times_times(int,Z_1),W) != hAPP(int,int,times_times(int,W),Z_1)
| hAPP(int,int,times_times(int,W),Z_1) = hAPP(int,int,times_times(int,Z_1),W) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(hAPP(int,int,times_times(int,Z_1),W))),bind(Y,$fot(hAPP(int,int,times_times(int,W),Z_1)))]]) ).
cnf(refute_0_7,plain,
hAPP(int,int,times_times(int,W),Z_1) = hAPP(int,int,times_times(int,Z_1),W),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,Z_1),W),hAPP(int,int,times_times(int,W),Z_1)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) = hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))),
inference(subst,[],[refute_0_7:[bind(W,$fot(number_number_of(int,bit0(bit0(bit1(pls)))))),bind(Z_1,$fot(m))]]) ).
cnf(refute_0_9,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),
introduced(tautology,[refl,[$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)))]]) ).
cnf(refute_0_10,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))
| hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) != hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))) ),[1,3],$fot(hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_11,plain,
( hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) != hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
hAPP(int,int,plus_plus(int,Z_1),W) = hAPP(int,int,plus_plus(int,W),Z_1),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_14,plain,
( hAPP(int,int,plus_plus(int,Z_1),W) != hAPP(int,int,plus_plus(int,W),Z_1)
| hAPP(int,int,plus_plus(int,W),Z_1) = hAPP(int,int,plus_plus(int,Z_1),W) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(hAPP(int,int,plus_plus(int,Z_1),W))),bind(Y,$fot(hAPP(int,int,plus_plus(int,W),Z_1)))]]) ).
cnf(refute_0_15,plain,
hAPP(int,int,plus_plus(int,W),Z_1) = hAPP(int,int,plus_plus(int,Z_1),W),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,Z_1),W),hAPP(int,int,plus_plus(int,W),Z_1)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),
inference(subst,[],[refute_0_15:[bind(W,$fot(hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))),bind(Z_1,$fot(one_one(int)))]]) ).
cnf(refute_0_17,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_5,refute_0_17]) ).
cnf(refute_0_19,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))),bind(Y,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)))),bind(Z,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_20,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))]]) ).
cnf(refute_0_23,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) ),[1,3],$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_24,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),
inference(subst,[],[refute_0_7:[bind(W,$fot(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))),bind(Z_1,$fot(t))]]) ).
cnf(refute_0_27,plain,
( hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))),bind(Y,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Z,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))))]]) ).
cnf(refute_0_28,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
introduced(tautology,[equality,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) ),[1],$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_31,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) )],[refute_0_1,refute_0_31]) ).
cnf(refute_0_33,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))),bind(Y,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))))]]) ).
cnf(refute_0_34,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Y,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))))),bind(Z,$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))))]]) ).
cnf(refute_0_36,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_25,refute_0_35]) ).
cnf(refute_0_37,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))),bind(Y,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Z,$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))))]]) ).
cnf(refute_0_39,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_26,refute_0_38]) ).
cnf(refute_0_40,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),
introduced(tautology,[refl,[$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)))]]) ).
cnf(refute_0_42,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) != twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) ),[1,3],$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))]]) ).
cnf(refute_0_43,plain,
( hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) != twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
hAPP(int,int,times_times(int,pls),W) = pls,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_46,plain,
hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = pls,
inference(subst,[],[refute_0_45:[bind(W,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_47,plain,
hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))]]) ).
cnf(refute_0_48,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) ),[1,3],$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_49,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) )],[refute_0_21,refute_0_49]) ).
cnf(refute_0_51,plain,
pls = zero_zero(int),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_52,plain,
( pls != zero_zero(int)
| zero_zero(int) = pls ),
inference(subst,[],[refute_0_5:[bind(X,$fot(pls)),bind(Y,$fot(zero_zero(int)))]]) ).
cnf(refute_0_53,plain,
zero_zero(int) = pls,
inference(resolve,[$cnf( $equal(pls,zero_zero(int)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
times_times(int,zero_zero(int)) = times_times(int,zero_zero(int)),
introduced(tautology,[refl,[$fot(times_times(int,zero_zero(int)))]]) ).
cnf(refute_0_55,plain,
( times_times(int,zero_zero(int)) != times_times(int,zero_zero(int))
| zero_zero(int) != pls
| times_times(int,zero_zero(int)) = times_times(int,pls) ),
introduced(tautology,[equality,[$cnf( $equal(times_times(int,zero_zero(int)),times_times(int,zero_zero(int))) ),[1,1],$fot(pls)]]) ).
cnf(refute_0_56,plain,
( zero_zero(int) != pls
| times_times(int,zero_zero(int)) = times_times(int,pls) ),
inference(resolve,[$cnf( $equal(times_times(int,zero_zero(int)),times_times(int,zero_zero(int))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
times_times(int,zero_zero(int)) = times_times(int,pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))]]) ).
cnf(refute_0_59,plain,
( hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| times_times(int,zero_zero(int)) != times_times(int,pls)
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) ),[1,2],$fot(times_times(int,pls))]]) ).
cnf(refute_0_60,plain,
( times_times(int,zero_zero(int)) != times_times(int,pls)
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),
inference(resolve,[$cnf( $equal(times_times(int,zero_zero(int)),times_times(int,pls)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Y,$fot(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Z,$fot(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))))]]) ).
cnf(refute_0_63,plain,
( hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_50,refute_0_63]) ).
cnf(refute_0_65,plain,
( hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) != pls
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = pls ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Y,$fot(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))))),bind(Z,$fot(pls))]]) ).
cnf(refute_0_66,plain,
( hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) != pls
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = pls ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = pls,
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),pls) )],[refute_0_46,refute_0_66]) ).
cnf(refute_0_68,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)) = hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),
inference(subst,[],[refute_0_7:[bind(W,$fot(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))),bind(Z_1,$fot(zero_zero(int)))]]) ).
cnf(refute_0_69,plain,
( hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)) != hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != pls
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)) = pls ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))),bind(Y,$fot(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Z,$fot(pls))]]) ).
cnf(refute_0_70,plain,
( hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != pls
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)) = pls ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)),hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)) = pls,
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),pls) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),
introduced(tautology,[refl,[$fot(combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))))]]) ).
cnf(refute_0_73,plain,
( combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) != combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)) != pls
| combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = combc(int,int,bool,ord_less(int),pls) ),
introduced(tautology,[equality,[$cnf( $equal(combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))) ),[1,4],$fot(pls)]]) ).
cnf(refute_0_74,plain,
( hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)) != pls
| combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = combc(int,int,bool,ord_less(int),pls) ),
inference(resolve,[$cnf( $equal(combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = combc(int,int,bool,ord_less(int),pls),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)),pls) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),
introduced(tautology,[refl,[$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)))]]) ).
cnf(refute_0_77,plain,
( combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) != combc(int,int,bool,ord_less(int),pls)
| hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) ),[1,2],$fot(combc(int,int,bool,ord_less(int),pls))]]) ).
cnf(refute_0_78,plain,
( combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) != combc(int,int,bool,ord_less(int),pls)
| hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),
inference(resolve,[$cnf( $equal(combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),combc(int,int,bool,ord_less(int),pls)) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)))),bind(Y,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)))),bind(Z,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))))]]) ).
cnf(refute_0_81,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) )],[refute_0_44,refute_0_81]) ).
cnf(refute_0_83,plain,
hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_84,plain,
( hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R) != hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)
| hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) = hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R))),bind(Y,$fot(hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)))]]) ).
cnf(refute_0_85,plain,
hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) = hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R),
inference(resolve,[$cnf( $equal(hAPP(X_a,X_c,combc(X_a,X_b,X_c,P,Q),R),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),
inference(subst,[],[refute_0_85:[bind(P,$fot(ord_less(int))),bind(Q,$fot(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))),bind(R,$fot(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))),bind(X_a,$fot(int)),bind(X_b,$fot(int)),bind(X_c,$fot(bool))]]) ).
cnf(refute_0_87,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))))),bind(Y,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)))),bind(Z,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))))]]) ).
cnf(refute_0_88,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) )],[refute_0_82,refute_0_88]) ).
cnf(refute_0_90,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))))
| hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))) ),[0],$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))))]]) ).
cnf(refute_0_91,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))))
| hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),zero_zero(int)))) )],[refute_0_0,refute_0_91]) ).
cnf(refute_0_93,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_94,plain,
ti(int,bit1(B_1_1)) = bit1(B_1_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_95,plain,
number_number_of(int,K_1) = ti(int,K_1),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_96,plain,
( number_number_of(int,K_1) != ti(int,K_1)
| ti(int,K_1) = number_number_of(int,K_1) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(number_number_of(int,K_1))),bind(Y,$fot(ti(int,K_1)))]]) ).
cnf(refute_0_97,plain,
ti(int,K_1) = number_number_of(int,K_1),
inference(resolve,[$cnf( $equal(number_number_of(int,K_1),ti(int,K_1)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
ti(int,bit1(B_1_1)) = number_number_of(int,bit1(B_1_1)),
inference(subst,[],[refute_0_97:[bind(K_1,$fot(bit1(B_1_1)))]]) ).
cnf(refute_0_99,plain,
( ti(int,bit1(B_1_1)) != bit1(B_1_1)
| ti(int,bit1(B_1_1)) != number_number_of(int,bit1(B_1_1))
| number_number_of(int,bit1(B_1_1)) = bit1(B_1_1) ),
introduced(tautology,[equality,[$cnf( $equal(ti(int,bit1(B_1_1)),bit1(B_1_1)) ),[0],$fot(number_number_of(int,bit1(B_1_1)))]]) ).
cnf(refute_0_100,plain,
( ti(int,bit1(B_1_1)) != bit1(B_1_1)
| number_number_of(int,bit1(B_1_1)) = bit1(B_1_1) ),
inference(resolve,[$cnf( $equal(ti(int,bit1(B_1_1)),number_number_of(int,bit1(B_1_1))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
number_number_of(int,bit1(B_1_1)) = bit1(B_1_1),
inference(resolve,[$cnf( $equal(ti(int,bit1(B_1_1)),bit1(B_1_1)) )],[refute_0_94,refute_0_100]) ).
cnf(refute_0_102,plain,
number_number_of(int,bit1(pls)) = bit1(pls),
inference(subst,[],[refute_0_101:[bind(B_1_1,$fot(pls))]]) ).
cnf(refute_0_103,plain,
( number_number_of(int,bit1(pls)) != bit1(pls)
| one_one(int) != number_number_of(int,bit1(pls))
| one_one(int) = bit1(pls) ),
introduced(tautology,[equality,[$cnf( $equal(one_one(int),number_number_of(int,bit1(pls))) ),[1],$fot(bit1(pls))]]) ).
cnf(refute_0_104,plain,
( one_one(int) != number_number_of(int,bit1(pls))
| one_one(int) = bit1(pls) ),
inference(resolve,[$cnf( $equal(number_number_of(int,bit1(pls)),bit1(pls)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
one_one(int) = bit1(pls),
inference(resolve,[$cnf( $equal(one_one(int),number_number_of(int,bit1(pls))) )],[refute_0_93,refute_0_104]) ).
cnf(refute_0_106,plain,
product_Pair(int,int,s,one_one(int)) = product_Pair(int,int,s,one_one(int)),
introduced(tautology,[refl,[$fot(product_Pair(int,int,s,one_one(int)))]]) ).
cnf(refute_0_107,plain,
( one_one(int) != bit1(pls)
| product_Pair(int,int,s,one_one(int)) != product_Pair(int,int,s,one_one(int))
| product_Pair(int,int,s,one_one(int)) = product_Pair(int,int,s,bit1(pls)) ),
introduced(tautology,[equality,[$cnf( $equal(product_Pair(int,int,s,one_one(int)),product_Pair(int,int,s,one_one(int))) ),[1,3],$fot(bit1(pls))]]) ).
cnf(refute_0_108,plain,
( one_one(int) != bit1(pls)
| product_Pair(int,int,s,one_one(int)) = product_Pair(int,int,s,bit1(pls)) ),
inference(resolve,[$cnf( $equal(product_Pair(int,int,s,one_one(int)),product_Pair(int,int,s,one_one(int))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
product_Pair(int,int,s,one_one(int)) = product_Pair(int,int,s,bit1(pls)),
inference(resolve,[$cnf( $equal(one_one(int),bit1(pls)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),
introduced(tautology,[refl,[$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))]]) ).
cnf(refute_0_111,plain,
( product_Pair(int,int,s,one_one(int)) != product_Pair(int,int,s,bit1(pls))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
introduced(tautology,[equality,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) ),[1,0],$fot(product_Pair(int,int,s,bit1(pls)))]]) ).
cnf(refute_0_112,plain,
( product_Pair(int,int,s,one_one(int)) != product_Pair(int,int,s,bit1(pls))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(resolve,[$cnf( $equal(product_Pair(int,int,s,one_one(int)),product_Pair(int,int,s,bit1(pls))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))))]]) ).
cnf(refute_0_115,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) ),[1,3],$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))]]) ).
cnf(refute_0_116,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))
| ~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))))
| hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) ),[0],$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))))]]) ).
cnf(refute_0_119,plain,
( ~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))))
| hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int)))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))))) )],[refute_0_92,refute_0_119]) ).
cnf(refute_0_121,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_122,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_123,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),
inference(subst,[],[refute_0_15:[bind(W,$fot(hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))),bind(Z_1,$fot(one_one(int)))]]) ).
cnf(refute_0_124,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) != hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))
| hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) ),[0],$fot(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))]]) ).
cnf(refute_0_125,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) != hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
ti(int,min) = min,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_128,plain,
ti(int,min) = number_number_of(int,min),
inference(subst,[],[refute_0_97:[bind(K_1,$fot(min))]]) ).
cnf(refute_0_129,plain,
( ti(int,min) != min
| ti(int,min) != number_number_of(int,min)
| number_number_of(int,min) = min ),
introduced(tautology,[equality,[$cnf( $equal(ti(int,min),min) ),[0],$fot(number_number_of(int,min))]]) ).
cnf(refute_0_130,plain,
( ti(int,min) != min
| number_number_of(int,min) = min ),
inference(resolve,[$cnf( $equal(ti(int,min),number_number_of(int,min)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
number_number_of(int,min) = min,
inference(resolve,[$cnf( $equal(ti(int,min),min) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),
introduced(tautology,[refl,[$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)))]]) ).
cnf(refute_0_133,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) != hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min))
| number_number_of(int,min) != min
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min))) ),[1,3],$fot(min)]]) ).
cnf(refute_0_134,plain,
( number_number_of(int,min) != min
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),
inference(resolve,[$cnf( $equal(number_number_of(int,min),min) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) != hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) ),[0],$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min))]]) ).
cnf(refute_0_137,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
plus_plus(int,one_one(int)) = plus_plus(int,one_one(int)),
introduced(tautology,[refl,[$fot(plus_plus(int,one_one(int)))]]) ).
cnf(refute_0_139,plain,
( one_one(int) != bit1(pls)
| plus_plus(int,one_one(int)) != plus_plus(int,one_one(int))
| plus_plus(int,one_one(int)) = plus_plus(int,bit1(pls)) ),
introduced(tautology,[equality,[$cnf( $equal(plus_plus(int,one_one(int)),plus_plus(int,one_one(int))) ),[1,1],$fot(bit1(pls))]]) ).
cnf(refute_0_140,plain,
( one_one(int) != bit1(pls)
| plus_plus(int,one_one(int)) = plus_plus(int,bit1(pls)) ),
inference(resolve,[$cnf( $equal(plus_plus(int,one_one(int)),plus_plus(int,one_one(int))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
plus_plus(int,one_one(int)) = plus_plus(int,bit1(pls)),
inference(resolve,[$cnf( $equal(one_one(int),bit1(pls)) )],[refute_0_105,refute_0_140]) ).
cnf(refute_0_142,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))]]) ).
cnf(refute_0_143,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| plus_plus(int,one_one(int)) != plus_plus(int,bit1(pls))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) ),[1,2],$fot(plus_plus(int,bit1(pls)))]]) ).
cnf(refute_0_144,plain,
( plus_plus(int,one_one(int)) != plus_plus(int,bit1(pls))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(plus_plus(int,one_one(int)),plus_plus(int,bit1(pls))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) ),[0],$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))]]) ).
cnf(refute_0_147,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_137,refute_0_147]) ).
cnf(refute_0_149,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),number_number_of(int,min)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_126,refute_0_148]) ).
cnf(refute_0_150,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
introduced(tautology,[equality,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) ),[0],$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))]]) ).
cnf(refute_0_151,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) )],[refute_0_113,refute_0_150]) ).
cnf(refute_0_152,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_153,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) ),[0],$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))]]) ).
cnf(refute_0_154,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_123,refute_0_153]) ).
cnf(refute_0_155,plain,
ti(int,bit0(B_1_1)) = bit0(B_1_1),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_156,plain,
ti(int,bit0(B_1_1)) = number_number_of(int,bit0(B_1_1)),
inference(subst,[],[refute_0_97:[bind(K_1,$fot(bit0(B_1_1)))]]) ).
cnf(refute_0_157,plain,
( ti(int,bit0(B_1_1)) != bit0(B_1_1)
| ti(int,bit0(B_1_1)) != number_number_of(int,bit0(B_1_1))
| number_number_of(int,bit0(B_1_1)) = bit0(B_1_1) ),
introduced(tautology,[equality,[$cnf( $equal(ti(int,bit0(B_1_1)),bit0(B_1_1)) ),[0],$fot(number_number_of(int,bit0(B_1_1)))]]) ).
cnf(refute_0_158,plain,
( ti(int,bit0(B_1_1)) != bit0(B_1_1)
| number_number_of(int,bit0(B_1_1)) = bit0(B_1_1) ),
inference(resolve,[$cnf( $equal(ti(int,bit0(B_1_1)),number_number_of(int,bit0(B_1_1))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
number_number_of(int,bit0(B_1_1)) = bit0(B_1_1),
inference(resolve,[$cnf( $equal(ti(int,bit0(B_1_1)),bit0(B_1_1)) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
number_number_of(int,bit0(bit0(bit1(pls)))) = bit0(bit0(bit1(pls))),
inference(subst,[],[refute_0_159:[bind(B_1_1,$fot(bit0(bit1(pls))))]]) ).
cnf(refute_0_161,plain,
hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) = hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_162,plain,
( hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) != hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))
| number_number_of(int,bit0(bit0(bit1(pls)))) != bit0(bit0(bit1(pls)))
| hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) = hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) ),[1,3],$fot(bit0(bit0(bit1(pls))))]]) ).
cnf(refute_0_163,plain,
( number_number_of(int,bit0(bit0(bit1(pls)))) != bit0(bit0(bit1(pls)))
| hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) = hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) = hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))),
inference(resolve,[$cnf( $equal(number_number_of(int,bit0(bit0(bit1(pls)))),bit0(bit0(bit1(pls)))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
( hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) != hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))
| hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) != hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))
| hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) = hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))),bind(Y,$fot(hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),bind(Z,$fot(hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_166,plain,
( hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) != hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))
| hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) = hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) )],[refute_0_8,refute_0_165]) ).
cnf(refute_0_167,plain,
hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) = hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) )],[refute_0_164,refute_0_166]) ).
cnf(refute_0_168,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))
| hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) != hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))) ),[1,3],$fot(hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))]]) ).
cnf(refute_0_169,plain,
( hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m) != hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))) )],[refute_0_9,refute_0_168]) ).
cnf(refute_0_170,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) )],[refute_0_167,refute_0_169]) ).
cnf(refute_0_171,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))),bind(Y,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)))),bind(Z,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_172,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m))) )],[refute_0_16,refute_0_171]) ).
cnf(refute_0_173,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) )],[refute_0_170,refute_0_172]) ).
cnf(refute_0_174,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) ),[1,3],$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_175,plain,
( hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_22,refute_0_174]) ).
cnf(refute_0_176,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) )],[refute_0_173,refute_0_175]) ).
cnf(refute_0_177,plain,
( hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))),bind(Y,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))))),bind(Z,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_178,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int)))) )],[refute_0_26,refute_0_177]) ).
cnf(refute_0_179,plain,
hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_176,refute_0_178]) ).
cnf(refute_0_180,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)
| hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) ),[0],$fot(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t))]]) ).
cnf(refute_0_181,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) )],[refute_0_154,refute_0_181]) ).
cnf(refute_0_183,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),hAPP(int,int,times_times(int,hAPP(int,int,plus_plus(int,hAPP(int,int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls))))),m)),one_one(int))),t)) )],[refute_0_152,refute_0_182]) ).
cnf(refute_0_184,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) ),[0],$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))]]) ).
cnf(refute_0_185,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_145,refute_0_184]) ).
cnf(refute_0_186,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_187,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| plus_plus(int,one_one(int)) != plus_plus(int,bit1(pls))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),[1,2],$fot(plus_plus(int,bit1(pls)))]]) ).
cnf(refute_0_188,plain,
( plus_plus(int,one_one(int)) != plus_plus(int,bit1(pls))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(plus_plus(int,one_one(int)),plus_plus(int,bit1(pls))) )],[refute_0_141,refute_0_188]) ).
cnf(refute_0_190,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_191,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) ),[1,3],$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_192,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) ),[0],$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_195,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_185,refute_0_195]) ).
cnf(refute_0_197,plain,
hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_183,refute_0_196]) ).
cnf(refute_0_198,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min))),bind(Y,$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))))]]) ).
cnf(refute_0_199,plain,
hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_149,refute_0_198]) ).
cnf(refute_0_200,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) ),[0],$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min))]]) ).
cnf(refute_0_201,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_197,refute_0_201]) ).
cnf(refute_0_203,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min))),bind(Y,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_204,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_206,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) != hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),[1,3],$fot(hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))]]) ).
cnf(refute_0_207,plain,
( hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))) != hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) )],[refute_0_164,refute_0_207]) ).
cnf(refute_0_209,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_210,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| plus_plus(int,one_one(int)) != plus_plus(int,bit1(pls))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) ),[1,2],$fot(plus_plus(int,bit1(pls)))]]) ).
cnf(refute_0_211,plain,
( plus_plus(int,one_one(int)) != plus_plus(int,bit1(pls))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(plus_plus(int,one_one(int)),plus_plus(int,bit1(pls))) )],[refute_0_141,refute_0_211]) ).
cnf(refute_0_213,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))),bind(Y,$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))),bind(Z,$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_214,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) )],[refute_0_208,refute_0_214]) ).
cnf(refute_0_216,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_217,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) ),[1,3],$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_218,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) != hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))))),bind(Y,$fot(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))))),bind(Z,$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)))]]) ).
cnf(refute_0_221,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))) != hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)
| hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls))))))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(int,int,times_times(int,m),bit0(bit0(bit1(pls)))))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)) )],[refute_0_204,refute_0_221]) ).
cnf(refute_0_223,plain,
( hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))) != hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
introduced(tautology,[equality,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) ),[1],$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min))]]) ).
cnf(refute_0_224,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls))))))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))) != hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) ),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_151,refute_0_224]) ).
cnf(refute_0_226,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,one_one(int))),hAPP(int,int,times_times(int,t),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(int,int,times_times(int,m),number_number_of(int,bit0(bit0(bit1(pls)))))))) )],[refute_0_32,refute_0_225]) ).
cnf(refute_0_227,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) != hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))),bind(Y,$fot(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)))]]) ).
cnf(refute_0_228,plain,
hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min)) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) ),[0],$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))]]) ).
cnf(refute_0_230,plain,
( hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) = hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,minus_minus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),min),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_149,refute_0_230]) ).
cnf(refute_0_232,plain,
( twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))),bind(Y,$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))))]]) ).
cnf(refute_0_233,plain,
hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(resolve,[$cnf( $equal(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))),bind(Y,$fot(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))),bind(Z,$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))))]]) ).
cnf(refute_0_235,plain,
( hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_145,refute_0_234]) ).
cnf(refute_0_236,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,bit1(pls)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) )],[refute_0_233,refute_0_235]) ).
cnf(refute_0_237,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))),bind(Y,$fot(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))))),bind(Z,$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))))]]) ).
cnf(refute_0_238,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls)))))) )],[refute_0_123,refute_0_237]) ).
cnf(refute_0_239,plain,
hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) = twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) )],[refute_0_236,refute_0_238]) ).
cnf(refute_0_240,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))))]]) ).
cnf(refute_0_241,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))
| hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))) ),[1,3],$fot(twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))]]) ).
cnf(refute_0_242,plain,
( hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)) != twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) )],[refute_0_239,refute_0_242]) ).
cnf(refute_0_244,plain,
combc(int,int,bool,ord_less(int),zero_zero(int)) = combc(int,int,bool,ord_less(int),zero_zero(int)),
introduced(tautology,[refl,[$fot(combc(int,int,bool,ord_less(int),zero_zero(int)))]]) ).
cnf(refute_0_245,plain,
( combc(int,int,bool,ord_less(int),zero_zero(int)) != combc(int,int,bool,ord_less(int),zero_zero(int))
| zero_zero(int) != pls
| combc(int,int,bool,ord_less(int),zero_zero(int)) = combc(int,int,bool,ord_less(int),pls) ),
introduced(tautology,[equality,[$cnf( $equal(combc(int,int,bool,ord_less(int),zero_zero(int)),combc(int,int,bool,ord_less(int),zero_zero(int))) ),[1,4],$fot(pls)]]) ).
cnf(refute_0_246,plain,
( zero_zero(int) != pls
| combc(int,int,bool,ord_less(int),zero_zero(int)) = combc(int,int,bool,ord_less(int),pls) ),
inference(resolve,[$cnf( $equal(combc(int,int,bool,ord_less(int),zero_zero(int)),combc(int,int,bool,ord_less(int),zero_zero(int))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
combc(int,int,bool,ord_less(int),zero_zero(int)) = combc(int,int,bool,ord_less(int),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_53,refute_0_246]) ).
cnf(refute_0_248,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))))]]) ).
cnf(refute_0_249,plain,
( combc(int,int,bool,ord_less(int),zero_zero(int)) != combc(int,int,bool,ord_less(int),pls)
| hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))) ),[1,2],$fot(combc(int,int,bool,ord_less(int),pls))]]) ).
cnf(refute_0_250,plain,
( combc(int,int,bool,ord_less(int),zero_zero(int)) != combc(int,int,bool,ord_less(int),pls)
| hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),
inference(resolve,[$cnf( $equal(combc(int,int,bool,ord_less(int),zero_zero(int)),combc(int,int,bool,ord_less(int),pls)) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))))),bind(Y,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))))),bind(Z,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))))]]) ).
cnf(refute_0_253,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))
| hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))) )],[refute_0_243,refute_0_253]) ).
cnf(refute_0_255,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),
inference(subst,[],[refute_0_85:[bind(P,$fot(ord_less(int))),bind(Q,$fot(zero_zero(int))),bind(R,$fot(hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))),bind(X_a,$fot(int)),bind(X_b,$fot(int)),bind(X_c,$fot(bool))]]) ).
cnf(refute_0_256,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)))),bind(Y,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))))),bind(Z,$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))))]]) ).
cnf(refute_0_257,plain,
( hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)),hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))),
inference(resolve,[$cnf( $equal(hAPP(int,bool,combc(int,int,bool,ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)) != hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))
| ~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))) ),
introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))) ),[0],$fot(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))))]]) ).
cnf(refute_0_260,plain,
( ~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls)))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int)),hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
~ hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,plus_plus(int,hAPP(nat,int,power_power(int,s),number_number_of(nat,bit0(bit1(pls))))),one_one(int))),zero_zero(int))) )],[refute_0_260,refute_0_121]) ).
cnf(refute_0_262,plain,
$false,
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,combc(int,int,bool,ord_less(int),pls),twoSqu1929807760sum2sq(product_Pair(int,int,s,bit1(pls))))) )],[refute_0_120,refute_0_261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM924+7 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 15:33:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.59/2.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/2.83
% 2.59/2.83 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.73/2.89
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