%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM926+5 : 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 : n017.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 07:57:39 PM UTC 2025
% Result : Theorem 6.66s 2.41s
% Output : CNFRefutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 7 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 11 con; 0-3 aty)
% Number of variables : 28 ( 22 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ord_less_eq > ord_less > zprime > twoSqu33214720sum2sq > semiring_1 > ring_char_0 > number_semiring > number_ring > number > monoid_mult > linordered_idom > linorder > comm_semiring_1 > times_times > power_power > plus_plus > ti > number_number_of > #nlpp > undefined > one_one > bit1 > bit0 > t > s > pls > nat > m > int > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(semiring_1,type,
semiring_1: $i > $o ).
tff(m,type,
m: $i ).
tff(ord_less_eq,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
tff(ord_less,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(one_one,type,
one_one: $i > $i ).
tff(number,type,
number: $i > $o ).
tff(t,type,
t: $i ).
tff(pls,type,
pls: $i ).
tff(zprime,type,
zprime: $i > $o ).
tff(bit0,type,
bit0: $i > $i ).
tff(plus_plus,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(s,type,
s: $i ).
tff(number_ring,type,
number_ring: $i > $o ).
tff(power_power,type,
power_power: ( $i * $i * $i ) > $i ).
tff(nat,type,
nat: $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(twoSqu33214720sum2sq,type,
twoSqu33214720sum2sq: $i > $o ).
tff(undefined,type,
undefined: $i > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(comm_semiring_1,type,
comm_semiring_1: $i > $o ).
tff(int,type,
int: $i ).
tff(ti,type,
ti: ( $i * $i ) > $i ).
tff(linordered_idom,type,
linordered_idom: $i > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(bit1,type,
bit1: $i > $i ).
tff(number_number_of,type,
number_number_of: ( $i * $i ) > $i ).
tff(ring_char_0,type,
ring_char_0: $i > $o ).
tff(times_times,type,
times_times: ( $i * $i * $i ) > $i ).
tff(number_semiring,type,
number_semiring: $i > $o ).
tff(monoid_mult,type,
monoid_mult: $i > $o ).
tff(linorder,type,
linorder: $i > $o ).
tff(f_498,axiom,
! [Z,W] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).
tff(f_500,axiom,
! [K_1] : ( number_number_of(int,K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
tff(f_506,axiom,
! [Z,W] : ( plus_plus(int,Z,W) = plus_plus(int,W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
tff(f_561,negated_conjecture,
~ ? [X,Y] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_136,axiom,
( ( t = one_one(int) )
=> ? [X,Y] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(f_140,axiom,
( ord_less(int,one_one(int),t)
=> ? [X,Y] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
tff(f_132,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
tff(f_212,axiom,
! [Z_1,W_1] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( Z_1 != W_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zless__le) ).
tff(c_299,plain,
! [Z_305,W_306] : ( times_times(int,Z_305,W_306) = times_times(int,W_306,Z_305) ),
inference(cnfTransformation,[status(thm)],[f_498]) ).
tff(c_301,plain,
! [K_1_307] : ( number_number_of(int,K_1_307) = K_1_307 ),
inference(cnfTransformation,[status(thm)],[f_500]) ).
tff(c_307,plain,
! [Z_314,W_315] : ( plus_plus(int,Z_314,W_315) = plus_plus(int,W_315,Z_314) ),
inference(cnfTransformation,[status(thm)],[f_506]) ).
tff(c_373,plain,
! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(cnfTransformation,[status(thm)],[f_561]) ).
tff(c_374,plain,
! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)) ),
inference(demodulation,[status(thm),theory(equality)],[c_307,c_373]) ).
tff(c_375,plain,
! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,bit0(bit0(bit1(pls))),m)) ),
inference(demodulation,[status(thm),theory(equality)],[c_301,c_374]) ).
tff(c_376,plain,
! [X_330,Y_331] : ( plus_plus(int,power_power(int,X_330,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y_331,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) ),
inference(demodulation,[status(thm),theory(equality)],[c_299,c_375]) ).
tff(c_70,plain,
( ( plus_plus(int,power_power(int,'#skF_1',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_2',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) )
| ( one_one(int) != t ) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_394,plain,
( ( plus_plus(int,power_power(int,'#skF_1',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_2',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) )
| ( one_one(int) != t ) ),
inference(demodulation,[status(thm),theory(equality)],[c_299,c_301,c_307,c_70]) ).
tff(c_395,plain,
one_one(int) != t,
inference(negUnitSimplification,[status(thm)],[c_376,c_394]) ).
tff(c_72,plain,
( ( plus_plus(int,power_power(int,'#skF_3',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_4',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) )
| ~ ord_less(int,one_one(int),t) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_392,plain,
( ( plus_plus(int,power_power(int,'#skF_4',number_number_of(nat,bit0(bit1(pls)))),power_power(int,'#skF_3',number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))) )
| ~ ord_less(int,one_one(int),t) ),
inference(demodulation,[status(thm),theory(equality)],[c_299,c_301,c_307,c_307,c_72]) ).
tff(c_393,plain,
~ ord_less(int,one_one(int),t),
inference(negUnitSimplification,[status(thm)],[c_376,c_392]) ).
tff(c_68,plain,
ord_less_eq(int,one_one(int),t),
inference(cnfTransformation,[status(thm)],[f_132]) ).
tff(c_1182,plain,
! [Z_1_409,W_1_410] :
( ord_less(int,Z_1_409,W_1_410)
| ( Z_1_409 = W_1_410 )
| ~ ord_less_eq(int,Z_1_409,W_1_410) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_1218,plain,
( ord_less(int,one_one(int),t)
| ( one_one(int) = t ) ),
inference(resolution,[status(thm)],[c_68,c_1182]) ).
tff(c_1236,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_395,c_393,c_1218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM926+5 : TPTP v9.0.0. Released v5.3.0.
% 0.03/0.11 % 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
% 0.11/0.31 % Computer : n017.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Apr 8 15:51:25 EDT 2025
% 0.11/0.31 % CPUTime :
% 6.66/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.66/2.41
% 6.66/2.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------