%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM925+6 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %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 : 300s
% DateTime : Wed Apr 9 07:57:37 PM UTC 2025
% Result : Theorem 34.77s 11.61s
% Output : CNFRefutation 34.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 101 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 86 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 43 ~; 44 |; 0 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-2 aty)
% Number of functors : 75 ( 75 usr; 15 con; 0-6 aty)
% Number of variables : 117 ( 117 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ zero_neq_one > zero > semiring_char_0 > semiring_1 > semiring_0 > semiri456707255roduct > ring_char_0 > ring_11004092258visors > preorder > power > ordere779506340up_add > ordere236663937imp_le > ordere223160158up_add > ordere216010020id_add > order > ord > one > number_semiring > number_ring > number > no_zero_divisors > mult_zero > monoid_mult > monoid_add > linordered_semiring > linordered_semidom > linordered_ring > linordered_idom > linorder > linord893533164strict > linord581940658strict > linord219039673up_add > linord20386208strict > hBOOL > dense_linorder > comm_semiring_1 > comm_monoid_add > cancel_semigroup_add > cancel146912293up_add > ab_semigroup_add > hAPP > ti > power_power > plus_plus > number_number_of > fun > #nlpp > zero_zero > undefined > times_times > semiring_1_of_nat > ord_less_eq > ord_less > one_one > if > tn > t > succ > sqrt > real > pls > nat > n > m1 > int > fTrue > fFalse > bool > bit1 > bit0 > #skF_35 > #skF_29 > #skF_9 > #skF_7 > #skF_24 > #skF_28 > #skF_17 > #skF_1 > #skF_2 > #skF_39 > #skF_45 > #skF_26 > #skF_27 > #skF_30 > #skF_18 > #skF_34 > #skF_42 > #skF_8 > #skF_31 > #skF_3 > #skF_13 > #skF_14 > #skF_15 > #skF_25 > #skF_19 > #skF_41 > #skF_46 > #skF_44 > #skF_10 > #skF_40 > #skF_36 > #skF_20 > #skF_23 > #skF_38 > #skF_11 > #skF_43 > #skF_12 > #skF_37 > #skF_21 > #skF_5 > #skF_22 > #skF_6 > #skF_33 > #skF_4 > #skF_16 > #skF_32
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(tn,type,
tn: $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': $i > $i ).
tff(hAPP,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(semiring_1,type,
semiring_1: $i > $o ).
tff(power,type,
power: $i > $o ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i ) > $i ).
tff(semiri456707255roduct,type,
semiri456707255roduct: $i > $o ).
tff(ord_less_eq,type,
ord_less_eq: $i > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(linord581940658strict,type,
linord581940658strict: $i > $o ).
tff(one_one,type,
one_one: $i > $i ).
tff(number,type,
number: $i > $o ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(t,type,
t: $i ).
tff(pls,type,
pls: $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(monoid_add,type,
monoid_add: $i > $o ).
tff(linordered_ring,type,
linordered_ring: $i > $o ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff(ring_11004092258visors,type,
ring_11004092258visors: $i > $o ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i ) > $i ).
tff(linordered_semidom,type,
linordered_semidom: $i > $o ).
tff(ab_semigroup_add,type,
ab_semigroup_add: $i > $o ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(no_zero_divisors,type,
no_zero_divisors: $i > $o ).
tff(sqrt,type,
sqrt: $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(ord,type,
ord: $i > $o ).
tff(if,type,
if: $i > $i ).
tff(zero_neq_one,type,
zero_neq_one: $i > $o ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff(bool,type,
bool: $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff(number_ring,type,
number_ring: $i > $o ).
tff(linord219039673up_add,type,
linord219039673up_add: $i > $o ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff(semiring_1_of_nat,type,
semiring_1_of_nat: $i > $i ).
tff(nat,type,
nat: $i ).
tff('#skF_15',type,
'#skF_15': $i > $i ).
tff(fun,type,
fun: ( $i * $i ) > $i ).
tff(ordere779506340up_add,type,
ordere779506340up_add: $i > $o ).
tff(bit1,type,
bit1: $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i * $i ) > $i ).
tff(linordered_semiring,type,
linordered_semiring: $i > $o ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff('#skF_41',type,
'#skF_41': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(ordere236663937imp_le,type,
ordere236663937imp_le: $i > $o ).
tff('#skF_44',type,
'#skF_44': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(cancel146912293up_add,type,
cancel146912293up_add: $i > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff(undefined,type,
undefined: $i > $i ).
tff(plus_plus,type,
plus_plus: ( $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(comm_monoid_add,type,
comm_monoid_add: $i > $o ).
tff(ordere223160158up_add,type,
ordere223160158up_add: $i > $o ).
tff(comm_semiring_1,type,
comm_semiring_1: $i > $o ).
tff('#skF_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff(int,type,
int: $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff(ti,type,
ti: ( $i * $i ) > $i ).
tff(semiring_0,type,
semiring_0: $i > $o ).
tff('#skF_38',type,
'#skF_38': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(n,type,
n: $i ).
tff(fTrue,type,
fTrue: $i ).
tff(linord20386208strict,type,
linord20386208strict: $i > $o ).
tff(linordered_idom,type,
linordered_idom: $i > $o ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_43',type,
'#skF_43': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(ordere216010020id_add,type,
ordere216010020id_add: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(mult_zero,type,
mult_zero: $i > $o ).
tff(number_number_of,type,
number_number_of: ( $i * $i ) > $i ).
tff(cancel_semigroup_add,type,
cancel_semigroup_add: $i > $o ).
tff(ring_char_0,type,
ring_char_0: $i > $o ).
tff(power_power,type,
power_power: ( $i * $i ) > $i ).
tff(semiring_char_0,type,
semiring_char_0: $i > $o ).
tff(zero_zero,type,
zero_zero: $i > $i ).
tff(preorder,type,
preorder: $i > $o ).
tff(number_semiring,type,
number_semiring: $i > $o ).
tff(monoid_mult,type,
monoid_mult: $i > $o ).
tff(dense_linorder,type,
dense_linorder: $i > $o ).
tff(bit0,type,
bit0: $i ).
tff(ord_less,type,
ord_less: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(real,type,
real: $i ).
tff(one,type,
one: $i > $o ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff(fFalse,type,
fFalse: $i ).
tff(order,type,
order: $i > $o ).
tff(times_times,type,
times_times: $i > $i ).
tff(m1,type,
m1: $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(zero,type,
zero: $i > $o ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(linord893533164strict,type,
linord893533164strict: $i > $o ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(succ,type,
succ: $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(linorder,type,
linorder: $i > $o ).
tff(f_3394,axiom,
! [P] :
( ( ti(bool,P) = fTrue )
| ( ti(bool,P) = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
tff(f_149,axiom,
! [B_1_1] :
( hBOOL(ti(bool,B_1_1))
<=> hBOOL(B_1_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
tff(f_3282,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(f_3299,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f_457,axiom,
! [K] : ( hAPP(int,int,plus_plus(int,K),pls) = K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
tff(f_36,axiom,
! [B_1_1,X_a] :
( monoid_add(X_a)
=> ( plus_plus(X_a,ti(X_a,B_1_1)) = plus_plus(X_a,B_1_1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
tff(f_453,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
tff(f_340,axiom,
! [Z_1,W_1] : ( hAPP(int,int,plus_plus(int,Z_1),W_1) = hAPP(int,int,plus_plus(int,W_1),Z_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
tff(f_1861,axiom,
! [K] : ( hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,K),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_succ__def) ).
tff(f_301,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
tff(f_670,axiom,
! [K] : ( number_number_of(int,K) = K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_number__of__is__id) ).
tff(f_3398,negated_conjecture,
~ ( ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_902,axiom,
! [X_a] :
( ring_11004092258visors(X_a)
=> ! [N,A_1] :
( ( ti(X_a,A_1) != zero_zero(X_a) )
=> ( hAPP(nat,X_a,power_power(X_a,A_1),N) != zero_zero(X_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_field__power__not__zero) ).
tff(f_399,axiom,
! [Wa,Z_2] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),hAPP(int,int,plus_plus(int,Z_2),one_one(int))))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_2))
| ( Wa = Z_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_zless__add1__eq) ).
tff(f_3342,axiom,
preorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
tff(f_145,axiom,
! [X_a,B_1_1,B_2] : ( ti(X_a,hAPP(X_a,X_a,B_1_1,B_2)) = hAPP(X_a,X_a,B_1_1,B_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_4_res) ).
tff(f_2585,axiom,
! [X_a] :
( preorder(X_a)
=> ! [X] : ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_order__less__irrefl) ).
tff(f_3344,axiom,
ord(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
tff(f_115,axiom,
! [X_a,B_1_1,B_2,X_b] :
( ord(X_b)
=> ( ti(X_b,hAPP(X_a,X_b,B_1_1,B_2)) = hAPP(X_a,X_b,B_1_1,B_2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_0_res) ).
tff(f_402,axiom,
! [K] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K)),zero_zero(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).
tff(f_2044,axiom,
! [M_1,N] :
( ( M_1 = N )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_1),N)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_eq__imp__le) ).
tff(c_2149,plain,
! [P_1977] :
( ( ti(bool,P_1977) = fFalse )
| ( ti(bool,P_1977) = fTrue ) ),
inference(cnfTransformation,[status(thm)],[f_3394]) ).
tff(c_84,plain,
! [B_1_1_77] :
( hBOOL(ti(bool,B_1_1_77))
| ~ hBOOL(B_1_1_77) ),
inference(cnfTransformation,[status(thm)],[f_149]) ).
tff(c_2162,plain,
! [P_1977] :
( hBOOL(fTrue)
| ~ hBOOL(P_1977)
| ( ti(bool,P_1977) = fFalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_2149,c_84]) ).
tff(c_2363,plain,
hBOOL(fTrue),
inference(splitLeft,[status(thm)],[c_2162]) ).
tff(c_1637,plain,
ring_11004092258visors(int),
inference(cnfTransformation,[status(thm)],[f_3282]) ).
tff(c_1671,plain,
monoid_add(int),
inference(cnfTransformation,[status(thm)],[f_3299]) ).
tff(c_320,plain,
! [K_199] : ( hAPP(int,int,plus_plus(int,K_199),pls) = K_199 ),
inference(cnfTransformation,[status(thm)],[f_457]) ).
tff(c_2429,plain,
! [X_a_1985,B_1_1_1986] :
( ( plus_plus(X_a_1985,ti(X_a_1985,B_1_1_1986)) = plus_plus(X_a_1985,B_1_1_1986) )
| ~ monoid_add(X_a_1985) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_2440,plain,
! [B_1_1_1986] :
( ( hAPP(int,int,plus_plus(int,B_1_1_1986),pls) = ti(int,B_1_1_1986) )
| ~ monoid_add(int) ),
inference(superposition,[status(thm),theory(equality)],[c_2429,c_320]) ).
tff(c_2496,plain,
! [B_1_1_1986] : ( ti(int,B_1_1_1986) = B_1_1_1986 ),
inference(demodulation,[status(thm),theory(equality)],[c_1671,c_320,c_2440]) ).
tff(c_316,plain,
zero_zero(int) = pls,
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_7003,plain,
! [Z_1_2096,W_1_2097] : ( hAPP(int,int,plus_plus(int,Z_1_2096),W_1_2097) = hAPP(int,int,plus_plus(int,W_1_2097),Z_1_2096) ),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_1041,plain,
! [K_1021] : ( hAPP(int,int,plus_plus(int,K_1021),one_one(int)) = hAPP(int,int,succ,K_1021) ),
inference(cnfTransformation,[status(thm)],[f_1861]) ).
tff(c_7059,plain,
! [W_1_2097] : ( hAPP(int,int,plus_plus(int,one_one(int)),W_1_2097) = hAPP(int,int,succ,W_1_2097) ),
inference(superposition,[status(thm),theory(equality)],[c_7003,c_1041]) ).
tff(c_194,plain,
number_number_of(int,hAPP(int,int,bit1,pls)) = one_one(int),
inference(cnfTransformation,[status(thm)],[f_301]) ).
tff(c_430,plain,
! [K_303] : ( number_number_of(int,K_303) = K_303 ),
inference(cnfTransformation,[status(thm)],[f_670]) ).
tff(c_2402,plain,
hAPP(int,int,bit1,pls) = one_one(int),
inference(superposition,[status(thm),theory(equality)],[c_194,c_430]) ).
tff(c_1849,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(cnfTransformation,[status(thm)],[f_3398]) ).
tff(c_1904,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_316,c_1849]) ).
tff(c_2411,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_2402,c_1904]) ).
tff(c_7340,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_7059,c_2411]) ).
tff(c_14364,plain,
! [X_a_2196,A_1_2197,N_2198] :
( ( hAPP(nat,X_a_2196,power_power(X_a_2196,A_1_2197),N_2198) != zero_zero(X_a_2196) )
| ( ti(X_a_2196,A_1_2197) = zero_zero(X_a_2196) )
| ~ ring_11004092258visors(X_a_2196) ),
inference(cnfTransformation,[status(thm)],[f_902]) ).
tff(c_14383,plain,
( ( zero_zero(int) != pls )
| ( ti(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) )
| ~ ring_11004092258visors(int) ),
inference(superposition,[status(thm),theory(equality)],[c_7340,c_14364]) ).
tff(c_14419,plain,
hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_1637,c_2496,c_316,c_316,c_14383]) ).
tff(c_276,plain,
! [Z_2_179] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2_179),hAPP(int,int,plus_plus(int,Z_2_179),one_one(int)))),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_15885,plain,
! [Z_2_2218] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2_2218),hAPP(int,int,succ,Z_2_2218))),
inference(demodulation,[status(thm),theory(equality)],[c_1041,c_276]) ).
tff(c_15893,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),n)),pls)),
inference(superposition,[status(thm),theory(equality)],[c_14419,c_15885]) ).
tff(c_1757,plain,
preorder(bool),
inference(cnfTransformation,[status(thm)],[f_3342]) ).
tff(c_80,plain,
! [X_a_74,B_1_1_75,B_2_76] : ( ti(X_a_74,hAPP(X_a_74,X_a_74,B_1_1_75,B_2_76)) = hAPP(X_a_74,X_a_74,B_1_1_75,B_2_76) ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_1847,plain,
! [P_1959] :
( ( ti(bool,P_1959) = fFalse )
| ( ti(bool,P_1959) = fTrue ) ),
inference(cnfTransformation,[status(thm)],[f_3394]) ).
tff(c_4146,plain,
! [X_a_2047,B_1_1_2048,B_2_2049] : ( ti(X_a_2047,hAPP(X_a_2047,X_a_2047,B_1_1_2048,B_2_2049)) = hAPP(X_a_2047,X_a_2047,B_1_1_2048,B_2_2049) ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_4246,plain,
! [B_1_1_2048,B_2_2049] :
( ( hAPP(bool,bool,B_1_1_2048,B_2_2049) = fTrue )
| ( ti(bool,hAPP(bool,bool,B_1_1_2048,B_2_2049)) = fFalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_1847,c_4146]) ).
tff(c_4287,plain,
! [B_1_1_2048,B_2_2049] :
( ( hAPP(bool,bool,B_1_1_2048,B_2_2049) = fTrue )
| ( hAPP(bool,bool,B_1_1_2048,B_2_2049) = fFalse ) ),
inference(demodulation,[status(thm),theory(equality)],[c_80,c_4246]) ).
tff(c_9211,plain,
! [X_a_2120,X_2121] :
( ~ hBOOL(hAPP(X_a_2120,bool,hAPP(X_a_2120,fun(X_a_2120,bool),ord_less(X_a_2120),X_2121),X_2121))
| ~ preorder(X_a_2120) ),
inference(cnfTransformation,[status(thm)],[f_2585]) ).
tff(c_9223,plain,
! [B_2_2049] :
( ~ hBOOL(fTrue)
| ~ preorder(bool)
| ( hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),B_2_2049),B_2_2049) = fFalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_4287,c_9211]) ).
tff(c_9238,plain,
! [B_2_2122] : ( hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less(bool),B_2_2122),B_2_2122) = fFalse ),
inference(demodulation,[status(thm),theory(equality)],[c_1757,c_2363,c_9223]) ).
tff(c_1399,plain,
! [X_a_1428,X_1430] :
( ~ hBOOL(hAPP(X_a_1428,bool,hAPP(X_a_1428,fun(X_a_1428,bool),ord_less(X_a_1428),X_1430),X_1430))
| ~ preorder(X_a_1428) ),
inference(cnfTransformation,[status(thm)],[f_2585]) ).
tff(c_9243,plain,
( ~ hBOOL(fFalse)
| ~ preorder(bool) ),
inference(superposition,[status(thm),theory(equality)],[c_9238,c_1399]) ).
tff(c_9281,plain,
~ hBOOL(fFalse),
inference(demodulation,[status(thm),theory(equality)],[c_1757,c_9243]) ).
tff(c_1761,plain,
ord(bool),
inference(cnfTransformation,[status(thm)],[f_3344]) ).
tff(c_8611,plain,
! [X_b_2112,X_a_2113,B_1_1_2114,B_2_2115] :
( ( ti(X_b_2112,hAPP(X_a_2113,X_b_2112,B_1_1_2114,B_2_2115)) = hAPP(X_a_2113,X_b_2112,B_1_1_2114,B_2_2115) )
| ~ ord(X_b_2112) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_8804,plain,
! [X_a_2113,B_1_1_2114,B_2_2115] :
( ( hAPP(X_a_2113,bool,B_1_1_2114,B_2_2115) = fTrue )
| ~ ord(bool)
| ( ti(bool,hAPP(X_a_2113,bool,B_1_1_2114,B_2_2115)) = fFalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_1847,c_8611]) ).
tff(c_9300,plain,
! [X_a_2123,B_1_1_2124,B_2_2125] :
( ( hAPP(X_a_2123,bool,B_1_1_2124,B_2_2125) = fTrue )
| ( ti(bool,hAPP(X_a_2123,bool,B_1_1_2124,B_2_2125)) = fFalse ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1761,c_8804]) ).
tff(c_9344,plain,
! [X_a_2123,B_1_1_2124,B_2_2125] :
( hBOOL(fFalse)
| ~ hBOOL(hAPP(X_a_2123,bool,B_1_1_2124,B_2_2125))
| ( hAPP(X_a_2123,bool,B_1_1_2124,B_2_2125) = fTrue ) ),
inference(superposition,[status(thm),theory(equality)],[c_9300,c_84]) ).
tff(c_9446,plain,
! [X_a_2123,B_1_1_2124,B_2_2125] :
( ~ hBOOL(hAPP(X_a_2123,bool,B_1_1_2124,B_2_2125))
| ( hAPP(X_a_2123,bool,B_1_1_2124,B_2_2125) = fTrue ) ),
inference(negUnitSimplification,[status(thm)],[c_9281,c_9344]) ).
tff(c_16448,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),n)),pls) = fTrue,
inference(resolution,[status(thm)],[c_15893,c_9446]) ).
tff(c_280,plain,
! [K_180] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_180)),zero_zero(int))),
inference(cnfTransformation,[status(thm)],[f_402]) ).
tff(c_20195,plain,
! [K_2284] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_2284)),pls)),
inference(demodulation,[status(thm),theory(equality)],[c_316,c_280]) ).
tff(c_20197,plain,
~ hBOOL(fTrue),
inference(superposition,[status(thm),theory(equality)],[c_16448,c_20195]) ).
tff(c_20230,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2363,c_20197]) ).
tff(c_20232,plain,
~ hBOOL(fTrue),
inference(splitRight,[status(thm)],[c_2162]) ).
tff(c_26427,plain,
! [X_b_2412,X_a_2413,B_1_1_2414,B_2_2415] :
( ( ti(X_b_2412,hAPP(X_a_2413,X_b_2412,B_1_1_2414,B_2_2415)) = hAPP(X_a_2413,X_b_2412,B_1_1_2414,B_2_2415) )
| ~ ord(X_b_2412) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_26623,plain,
! [X_a_2413,B_1_1_2414,B_2_2415] :
( ( hAPP(X_a_2413,bool,B_1_1_2414,B_2_2415) = fTrue )
| ~ ord(bool)
| ( ti(bool,hAPP(X_a_2413,bool,B_1_1_2414,B_2_2415)) = fFalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_1847,c_26427]) ).
tff(c_27295,plain,
! [X_a_2424,B_1_1_2425,B_2_2426] :
( ( hAPP(X_a_2424,bool,B_1_1_2425,B_2_2426) = fTrue )
| ( ti(bool,hAPP(X_a_2424,bool,B_1_1_2425,B_2_2426)) = fFalse ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1761,c_26623]) ).
tff(c_56,plain,
! [X_b_40,X_a_37,B_1_1_38,B_2_39] :
( ( ti(X_b_40,hAPP(X_a_37,X_b_40,B_1_1_38,B_2_39)) = hAPP(X_a_37,X_b_40,B_1_1_38,B_2_39) )
| ~ ord(X_b_40) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_27305,plain,
! [X_a_2424,B_1_1_2425,B_2_2426] :
( ( hAPP(X_a_2424,bool,B_1_1_2425,B_2_2426) = fFalse )
| ~ ord(bool)
| ( hAPP(X_a_2424,bool,B_1_1_2425,B_2_2426) = fTrue ) ),
inference(superposition,[status(thm),theory(equality)],[c_27295,c_56]) ).
tff(c_27470,plain,
! [X_a_2427,B_1_1_2428,B_2_2429] :
( ( hAPP(X_a_2427,bool,B_1_1_2428,B_2_2429) = fFalse )
| ( hAPP(X_a_2427,bool,B_1_1_2428,B_2_2429) = fTrue ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1761,c_27305]) ).
tff(c_1125,plain,
! [N_1102] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1102),N_1102)),
inference(cnfTransformation,[status(thm)],[f_2044]) ).
tff(c_27568,plain,
! [B_2_2429] :
( hBOOL(fTrue)
| ( hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B_2_2429),B_2_2429) = fFalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_27470,c_1125]) ).
tff(c_27714,plain,
! [B_2_2429] : ( hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B_2_2429),B_2_2429) = fFalse ),
inference(negUnitSimplification,[status(thm)],[c_20232,c_27568]) ).
tff(c_27807,plain,
hBOOL(fFalse),
inference(demodulation,[status(thm),theory(equality)],[c_27714,c_1125]) ).
tff(c_27441,plain,
! [X_a_2424,B_1_1_2425,B_2_2426] :
( ( hAPP(X_a_2424,bool,B_1_1_2425,B_2_2426) = fFalse )
| ( hAPP(X_a_2424,bool,B_1_1_2425,B_2_2426) = fTrue ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1761,c_27305]) ).
tff(c_20296,plain,
! [X_a_2287,B_1_1_2288] :
( ( plus_plus(X_a_2287,ti(X_a_2287,B_1_1_2288)) = plus_plus(X_a_2287,B_1_1_2288) )
| ~ monoid_add(X_a_2287) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_20307,plain,
! [B_1_1_2288] :
( ( hAPP(int,int,plus_plus(int,B_1_1_2288),pls) = ti(int,B_1_1_2288) )
| ~ monoid_add(int) ),
inference(superposition,[status(thm),theory(equality)],[c_20296,c_320]) ).
tff(c_20363,plain,
! [B_1_1_2288] : ( ti(int,B_1_1_2288) = B_1_1_2288 ),
inference(demodulation,[status(thm),theory(equality)],[c_1671,c_320,c_20307]) ).
tff(c_25916,plain,
! [Z_1_2408,W_1_2409] : ( hAPP(int,int,plus_plus(int,Z_1_2408),W_1_2409) = hAPP(int,int,plus_plus(int,W_1_2409),Z_1_2408) ),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_25972,plain,
! [W_1_2409] : ( hAPP(int,int,plus_plus(int,one_one(int)),W_1_2409) = hAPP(int,int,succ,W_1_2409) ),
inference(superposition,[status(thm),theory(equality)],[c_25916,c_1041]) ).
tff(c_20269,plain,
hAPP(int,int,bit1,pls) = one_one(int),
inference(superposition,[status(thm),theory(equality)],[c_194,c_430]) ).
tff(c_20278,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_20269,c_1904]) ).
tff(c_26277,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_25972,c_20278]) ).
tff(c_30268,plain,
! [X_a_2474,A_1_2475,N_2476] :
( ( hAPP(nat,X_a_2474,power_power(X_a_2474,A_1_2475),N_2476) != zero_zero(X_a_2474) )
| ( ti(X_a_2474,A_1_2475) = zero_zero(X_a_2474) )
| ~ ring_11004092258visors(X_a_2474) ),
inference(cnfTransformation,[status(thm)],[f_902]) ).
tff(c_30279,plain,
( ( zero_zero(int) != pls )
| ( ti(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = zero_zero(int) )
| ~ ring_11004092258visors(int) ),
inference(superposition,[status(thm),theory(equality)],[c_26277,c_30268]) ).
tff(c_30319,plain,
hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_1637,c_20363,c_316,c_316,c_30279]) ).
tff(c_34752,plain,
! [Z_2_2530] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2_2530),hAPP(int,int,succ,Z_2_2530))),
inference(demodulation,[status(thm),theory(equality)],[c_1041,c_276]) ).
tff(c_34758,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),n)),pls)),
inference(superposition,[status(thm),theory(equality)],[c_30319,c_34752]) ).
tff(c_34968,plain,
( hBOOL(fTrue)
| ( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),n)),pls) = fFalse ) ),
inference(superposition,[status(thm),theory(equality)],[c_27441,c_34758]) ).
tff(c_34970,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),n)),pls) = fFalse,
inference(negUnitSimplification,[status(thm)],[c_20232,c_34968]) ).
tff(c_40187,plain,
! [K_2610] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_2610)),pls)),
inference(demodulation,[status(thm),theory(equality)],[c_316,c_280]) ).
tff(c_40189,plain,
~ hBOOL(fFalse),
inference(superposition,[status(thm),theory(equality)],[c_34970,c_40187]) ).
tff(c_40229,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_27807,c_40189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+6 : TPTP v9.0.0. Released v5.3.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 15:51:20 EDT 2025
% 0.14/0.34 % CPUTime :
% 34.77/11.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.77/11.62
% 34.77/11.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------