%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 12:31:29 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 34
% Syntax : Number of formulae : 128 ( 73 unt; 0 def)
% Number of atoms : 208 ( 172 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 164 ( 84 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 1 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ).
fof(fact_3_t,axiom,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) ).
fof(fact_24_number__of__is__id,axiom,
! [K_1] : number_number_of_int(K_1) = K_1 ).
fof(fact_25_zmult__commute,axiom,
! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z) ).
fof(fact_65_nat__1__add__1,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))) ).
fof(fact_66_mult__Pls,axiom,
! [W] : times_times_int(pls,W) = pls ).
fof(fact_104_zadd__commute,axiom,
! [Z,W] : plus_plus_int(Z,W) = plus_plus_int(W,Z) ).
fof(fact_105_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls) ).
fof(conj_0,conjecture,
ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ).
fof(subgoal_0,plain,
ord_less_int(plus_plus_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,
~ ord_less_int(plus_plus_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,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_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,
! [K_1] : number_number_of_int(K_1) = K_1,
inference(canonicalize,[],[fact_24_number__of__is__id]) ).
fof(normalize_0_2,plain,
! [K_1] : number_number_of_int(K_1) = K_1,
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W,Z] : times_times_int(Z,W) = times_times_int(W,Z),
inference(canonicalize,[],[fact_25_zmult__commute]) ).
fof(normalize_0_4,plain,
! [W,Z] : times_times_int(Z,W) = times_times_int(W,Z),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W,Z] : plus_plus_int(Z,W) = plus_plus_int(W,Z),
inference(canonicalize,[],[fact_104_zadd__commute]) ).
fof(normalize_0_6,plain,
! [W,Z] : plus_plus_int(Z,W) = plus_plus_int(W,Z),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W] : times_times_int(pls,W) = pls,
inference(canonicalize,[],[fact_66_mult__Pls]) ).
fof(normalize_0_8,plain,
! [W] : times_times_int(pls,W) = pls,
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
zero_zero_int = number_number_of_int(pls),
inference(canonicalize,[],[fact_105_zero__is__num__zero]) ).
fof(normalize_0_10,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_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_11,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(canonicalize,[],[fact_65_nat__1__add__1]) ).
fof(normalize_0_12,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_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,
number_number_of_int(K_1) = K_1,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
number_number_of_int(bit0(bit0(bit1(pls)))) = bit0(bit0(bit1(pls))),
inference(subst,[],[refute_0_1:[bind(K_1,$fot(bit0(bit0(bit1(pls)))))]]) ).
cnf(refute_0_3,plain,
times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))) = times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))),
introduced(tautology,[refl,[$fot(times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_4,plain,
( number_number_of_int(bit0(bit0(bit1(pls)))) != bit0(bit0(bit1(pls)))
| times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))) != times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))
| times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))) = times_times_int(m,bit0(bit0(bit1(pls)))) ),
introduced(tautology,[equality,[$cnf( $equal(times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))),times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))) ),[1,1],$fot(bit0(bit0(bit1(pls))))]]) ).
cnf(refute_0_5,plain,
( number_number_of_int(bit0(bit0(bit1(pls)))) != bit0(bit0(bit1(pls)))
| times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))) = times_times_int(m,bit0(bit0(bit1(pls)))) ),
inference(resolve,[$cnf( $equal(times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))),times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))) = times_times_int(m,bit0(bit0(bit1(pls)))),
inference(resolve,[$cnf( $equal(number_number_of_int(bit0(bit0(bit1(pls)))),bit0(bit0(bit1(pls)))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
times_times_int(Z,W) = times_times_int(W,Z),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( times_times_int(Z,W) != times_times_int(W,Z)
| times_times_int(W,Z) = times_times_int(Z,W) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(times_times_int(Z,W))),bind(Y,$fot(times_times_int(W,Z)))]]) ).
cnf(refute_0_12,plain,
times_times_int(W,Z) = times_times_int(Z,W),
inference(resolve,[$cnf( $equal(times_times_int(Z,W),times_times_int(W,Z)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m) = times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))),
inference(subst,[],[refute_0_12:[bind(W,$fot(number_number_of_int(bit0(bit0(bit1(pls)))))),bind(Z,$fot(m))]]) ).
cnf(refute_0_14,plain,
( Y != X
| Y != Z0
| X = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z0) ),[0],$fot(X)]]) ).
cnf(refute_0_15,plain,
( X != Y
| Y != Z0
| X = Z0 ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))) != times_times_int(m,bit0(bit0(bit1(pls))))
| times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m) != times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))
| times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m) = times_times_int(m,bit0(bit0(bit1(pls)))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))),bind(Y,$fot(times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))))),bind(Z0,$fot(times_times_int(m,bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_17,plain,
( times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))) != times_times_int(m,bit0(bit0(bit1(pls))))
| times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m) = times_times_int(m,bit0(bit0(bit1(pls)))) ),
inference(resolve,[$cnf( $equal(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls)))))) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m) = times_times_int(m,bit0(bit0(bit1(pls)))),
inference(resolve,[$cnf( $equal(times_times_int(m,number_number_of_int(bit0(bit0(bit1(pls))))),times_times_int(m,bit0(bit0(bit1(pls))))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)) = plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)),
introduced(tautology,[refl,[$fot(plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)))]]) ).
cnf(refute_0_20,plain,
( plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)) != plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))
| times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m) != times_times_int(m,bit0(bit0(bit1(pls))))
| plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)) = plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))) ),
introduced(tautology,[equality,[$cnf( $equal(plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)),plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))) ),[1,1],$fot(times_times_int(m,bit0(bit0(bit1(pls)))))]]) ).
cnf(refute_0_21,plain,
( times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m) != times_times_int(m,bit0(bit0(bit1(pls))))
| plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)) = plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)),plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)) = plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),times_times_int(m,bit0(bit0(bit1(pls))))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
plus_plus_int(Z,W) = plus_plus_int(W,Z),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_24,plain,
( plus_plus_int(Z,W) != plus_plus_int(W,Z)
| plus_plus_int(W,Z) = plus_plus_int(Z,W) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(plus_plus_int(Z,W))),bind(Y,$fot(plus_plus_int(W,Z)))]]) ).
cnf(refute_0_25,plain,
plus_plus_int(W,Z) = plus_plus_int(Z,W),
inference(resolve,[$cnf( $equal(plus_plus_int(Z,W),plus_plus_int(W,Z)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)),
inference(subst,[],[refute_0_25:[bind(W,$fot(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))),bind(Z,$fot(one_one_int))]]) ).
cnf(refute_0_27,plain,
( plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)) != plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))
| plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) != plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))
| plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))),bind(Y,$fot(plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)))),bind(Z0,$fot(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_28,plain,
( plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)) != plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))
| plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))) ),
inference(resolve,[$cnf( $equal(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))),
inference(resolve,[$cnf( $equal(plus_plus_int(one_one_int,times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m)),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) )],[refute_0_22,refute_0_28]) ).
cnf(refute_0_30,plain,
times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
introduced(tautology,[refl,[$fot(times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))]]) ).
cnf(refute_0_31,plain,
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) != plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))
| times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) ),[1,1],$fot(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_32,plain,
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) != plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))
| times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(subst,[],[refute_0_12:[bind(W,$fot(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))),bind(Z,$fot(t))]]) ).
cnf(refute_0_35,plain,
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) != times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t))),bind(Y,$fot(times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))),bind(Z0,$fot(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_36,plain,
( times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(times_times_int(t,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) != times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| ~ ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
| ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),
introduced(tautology,[equality,[$cnf( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),[0],$fot(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_39,plain,
( ~ ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
| ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),
inference(resolve,[$cnf( $equal(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
times_times_int(pls,W) = pls,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_41,plain,
times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) = pls,
inference(subst,[],[refute_0_40:[bind(W,$fot(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))))]]) ).
cnf(refute_0_42,plain,
times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
introduced(tautology,[refl,[$fot(times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))]]) ).
cnf(refute_0_43,plain,
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) != plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))
| times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( $equal(times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) ),[1,1],$fot(plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))]]) ).
cnf(refute_0_44,plain,
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) != plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))
| times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) )],[refute_0_29,refute_0_44]) ).
cnf(refute_0_46,plain,
zero_zero_int = number_number_of_int(pls),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_47,plain,
number_number_of_int(pls) = pls,
inference(subst,[],[refute_0_1:[bind(K_1,$fot(pls))]]) ).
cnf(refute_0_48,plain,
( number_number_of_int(pls) != pls
| zero_zero_int != number_number_of_int(pls)
| zero_zero_int = pls ),
introduced(tautology,[equality,[$cnf( $equal(zero_zero_int,number_number_of_int(pls)) ),[1],$fot(pls)]]) ).
cnf(refute_0_49,plain,
( zero_zero_int != number_number_of_int(pls)
| zero_zero_int = pls ),
inference(resolve,[$cnf( $equal(number_number_of_int(pls),pls) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
zero_zero_int = pls,
inference(resolve,[$cnf( $equal(zero_zero_int,number_number_of_int(pls)) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
introduced(tautology,[refl,[$fot(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))]]) ).
cnf(refute_0_52,plain,
( times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| zero_zero_int != pls
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) ),[1,0],$fot(pls)]]) ).
cnf(refute_0_53,plain,
( zero_zero_int != pls
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) ),
inference(resolve,[$cnf( $equal(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(resolve,[$cnf( $equal(zero_zero_int,pls) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))),bind(Y,$fot(times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))),bind(Z0,$fot(times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_56,plain,
( times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(times_times_int(pls,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))) )],[refute_0_45,refute_0_56]) ).
cnf(refute_0_58,plain,
( times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) != pls
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = pls ),
inference(subst,[],[refute_0_15:[bind(X,$fot(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))),bind(Y,$fot(times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))))),bind(Z0,$fot(pls))]]) ).
cnf(refute_0_59,plain,
( times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) != pls
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = pls ),
inference(resolve,[$cnf( $equal(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) = pls,
inference(resolve,[$cnf( $equal(times_times_int(pls,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls) )],[refute_0_41,refute_0_59]) ).
cnf(refute_0_61,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),
inference(subst,[],[refute_0_12:[bind(W,$fot(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))),bind(Z,$fot(zero_zero_int))]]) ).
cnf(refute_0_62,plain,
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) != times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))
| times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != pls
| times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = pls ),
inference(subst,[],[refute_0_15:[bind(X,$fot(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))),bind(Y,$fot(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)))),bind(Z0,$fot(pls))]]) ).
cnf(refute_0_63,plain,
( times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)) != pls
| times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = pls ),
inference(resolve,[$cnf( $equal(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int),times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) = pls,
inference(resolve,[$cnf( $equal(times_times_int(zero_zero_int,plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)),pls) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int) != pls
| ~ ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
| ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls) ),
introduced(tautology,[equality,[$cnf( ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) ),[1],$fot(pls)]]) ).
cnf(refute_0_66,plain,
( ~ ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
| ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls) ),
inference(resolve,[$cnf( $equal(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int),pls) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int))
| ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls) ),
inference(resolve,[$cnf( ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) )],[refute_0_39,refute_0_66]) ).
cnf(refute_0_68,plain,
ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls),
inference(resolve,[$cnf( ord_less_int(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),zero_zero_int)) )],[refute_0_0,refute_0_67]) ).
cnf(refute_0_69,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_70,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_71,plain,
( plus_plus_nat(one_one_nat,one_one_nat) != number_number_of_nat(bit0(bit1(pls)))
| number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(plus_plus_nat(one_one_nat,one_one_nat))),bind(Y,$fot(number_number_of_nat(bit0(bit1(pls)))))]]) ).
cnf(refute_0_72,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(resolve,[$cnf( $equal(plus_plus_nat(one_one_nat,one_one_nat),number_number_of_nat(bit0(bit1(pls)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
power_power_int(s,number_number_of_nat(bit0(bit1(pls)))) = power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),
introduced(tautology,[refl,[$fot(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))))]]) ).
cnf(refute_0_74,plain,
( number_number_of_nat(bit0(bit1(pls))) != plus_plus_nat(one_one_nat,one_one_nat)
| power_power_int(s,number_number_of_nat(bit0(bit1(pls)))) != power_power_int(s,number_number_of_nat(bit0(bit1(pls))))
| power_power_int(s,number_number_of_nat(bit0(bit1(pls)))) = power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) ),[1,1],$fot(plus_plus_nat(one_one_nat,one_one_nat))]]) ).
cnf(refute_0_75,plain,
( number_number_of_nat(bit0(bit1(pls))) != plus_plus_nat(one_one_nat,one_one_nat)
| power_power_int(s,number_number_of_nat(bit0(bit1(pls)))) = power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)) ),
inference(resolve,[$cnf( $equal(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
power_power_int(s,number_number_of_nat(bit0(bit1(pls)))) = power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),
inference(resolve,[$cnf( $equal(number_number_of_nat(bit0(bit1(pls))),plus_plus_nat(one_one_nat,one_one_nat)) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),
introduced(tautology,[refl,[$fot(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))))]]) ).
cnf(refute_0_78,plain,
( plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls)))))
| power_power_int(s,number_number_of_nat(bit0(bit1(pls)))) != power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))
| plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) ),
introduced(tautology,[equality,[$cnf( $equal(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls)))))) ),[1,1],$fot(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))]]) ).
cnf(refute_0_79,plain,
( power_power_int(s,number_number_of_nat(bit0(bit1(pls)))) != power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))
| plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) ),
inference(resolve,[$cnf( $equal(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls)))))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),
inference(resolve,[$cnf( $equal(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),
inference(subst,[],[refute_0_25:[bind(W,$fot(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))))),bind(Z,$fot(one_one_int))]]) ).
cnf(refute_0_82,plain,
( plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))
| plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls)))))
| plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int))),bind(Y,$fot(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))))),bind(Z0,$fot(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))))]]) ).
cnf(refute_0_83,plain,
( plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))
| plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) ),
inference(resolve,[$cnf( $equal(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls)))))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),
inference(resolve,[$cnf( $equal(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))
| plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)
| plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) ),
introduced(tautology,[equality,[$cnf( $equal(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) ),[0],$fot(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))))]]) ).
cnf(refute_0_86,plain,
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)
| plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) ),
inference(resolve,[$cnf( $equal(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)
| times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t) != times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))) ),[0],$fot(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t))]]) ).
cnf(refute_0_88,plain,
( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)
| plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t),times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))) )],[refute_0_37,refute_0_87]) ).
cnf(refute_0_89,plain,
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)
| plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) ),
inference(resolve,[$cnf( $equal(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) )],[refute_0_86,refute_0_88]) ).
cnf(refute_0_90,plain,
plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) = times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),
inference(resolve,[$cnf( $equal(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),times_times_int(plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int),t)) )],[refute_0_69,refute_0_89]) ).
cnf(refute_0_91,plain,
( plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) != times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))
| times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))))),bind(Y,$fot(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))))]]) ).
cnf(refute_0_92,plain,
times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) = plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),
inference(resolve,[$cnf( $equal(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls))))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))) != plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))
| ~ ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls)
| ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls) ),
introduced(tautology,[equality,[$cnf( ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls) ),[0],$fot(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))))]]) ).
cnf(refute_0_94,plain,
( ~ ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls)
| ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls) ),
inference(resolve,[$cnf( $equal(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls),
inference(resolve,[$cnf( ord_less_int(times_times_int(t,plus_plus_int(one_one_int,times_times_int(m,bit0(bit0(bit1(pls)))))),pls) )],[refute_0_68,refute_0_94]) ).
cnf(refute_0_96,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_97,plain,
( plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int) != plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))
| ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int)
| ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
introduced(tautology,[equality,[$cnf( ~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),[0],$fot(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))))]]) ).
cnf(refute_0_98,plain,
( ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int)
| ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
inference(resolve,[$cnf( $equal(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)))) )],[refute_0_84,refute_0_97]) ).
cnf(refute_0_99,plain,
( zero_zero_int != pls
| ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls)
| ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int) ),
introduced(tautology,[equality,[$cnf( ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int) ),[1],$fot(pls)]]) ).
cnf(refute_0_100,plain,
( ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls)
| ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int) ),
inference(resolve,[$cnf( $equal(zero_zero_int,pls) )],[refute_0_50,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls)
| ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) ),
inference(resolve,[$cnf( ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),zero_zero_int) )],[refute_0_100,refute_0_98]) ).
cnf(refute_0_102,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls),
inference(resolve,[$cnf( ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int) )],[refute_0_101,refute_0_96]) ).
cnf(refute_0_103,plain,
$false,
inference(resolve,[$cnf( ord_less_int(plus_plus_int(one_one_int,power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat))),pls) )],[refute_0_95,refute_0_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM924+1 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 00:34:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------