%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM924_1 : 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 : n026.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 07:57:33 PM UTC 2025
% Result : Theorem 5.15s 2.15s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
%$ ord_less_nat > ord_less_int > ord_less_eq_nat > ord_less_eq_int > zprime > twoSqu1431725154sum2sq > times_times_nat > times_times_int > power_power_nat > power_power_int > plus_plus_nat > plus_plus_int > #nlpp > number_number_of_nat > number_number_of_int > bit1 > bit0 > zero_zero_nat > zero_zero_int > t > s > pls > one_one_nat > one_one_int > m > #skF_1
%Foreground sorts:
tff(nat,type,
nat: $tType ).
tff(int,type,
int: $tType ).
%Background operators:
%Foreground operators:
tff(twoSqu1431725154sum2sq,type,
twoSqu1431725154sum2sq: int > $o ).
tff(zprime,type,
zprime: int > $o ).
tff(bit1,type,
bit1: int > int ).
tff(times_times_nat,type,
times_times_nat: ( nat * nat ) > nat ).
tff(one_one_int,type,
one_one_int: int ).
tff(power_power_nat,type,
power_power_nat: ( nat * nat ) > nat ).
tff(ord_less_eq_nat,type,
ord_less_eq_nat: ( nat * nat ) > $o ).
tff('#skF_1',type,
'#skF_1': int ).
tff(number_number_of_int,type,
number_number_of_int: int > int ).
tff(s,type,
s: int ).
tff(m,type,
m: int ).
tff(number_number_of_nat,type,
number_number_of_nat: int > nat ).
tff(plus_plus_nat,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(one_one_nat,type,
one_one_nat: nat ).
tff(power_power_int,type,
power_power_int: ( int * nat ) > int ).
tff(ord_less_eq_int,type,
ord_less_eq_int: ( int * int ) > $o ).
tff(ord_less_nat,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(times_times_int,type,
times_times_int: ( int * int ) > int ).
tff(pls,type,
pls: int ).
tff(zero_zero_nat,type,
zero_zero_nat: nat ).
tff(bit0,type,
bit0: int > int ).
tff(ord_less_int,type,
ord_less_int: ( int * int ) > $o ).
tff(plus_plus_int,type,
plus_plus_int: ( int * int ) > int ).
tff(t,type,
t: int ).
tff(zero_zero_int,type,
zero_zero_int: int ).
tff(f_89,axiom,
! [K_1: int] : ( number_number_of_int(K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
tff(f_389,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
tff(f_242,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nat__1__add__1) ).
tff(f_388,axiom,
! [Z: int,W: int] : ( plus_plus_int(Z,W) = plus_plus_int(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
tff(f_392,negated_conjecture,
~ ord_less_int(plus_plus_int(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_91,axiom,
! [Z: int,W: int] : ( times_times_int(Z,W) = times_times_int(W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
tff(f_35,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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
tff(f_244,axiom,
! [W: int] : ( times_times_int(pls,W) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
tff(f_34,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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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) ).
tff(c_62,plain,
! [K_1_13: int] : ( number_number_of_int(K_1_13) = K_1_13 ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_323,plain,
number_number_of_int(pls) = zero_zero_int,
inference(cnfTransformation,[status(thm)],[f_389]) ).
tff(c_338,plain,
zero_zero_int = pls,
inference(demodulation,[status(thm),theory(equality)],[c_62,c_323]) ).
tff(c_192,plain,
number_number_of_nat(bit0(bit1(pls))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_321,plain,
! [Z_158: int,W_159: int] : ( plus_plus_int(Z_158,W_159) = plus_plus_int(W_159,Z_158) ),
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_325,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(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_326,plain,
~ ord_less_int(plus_plus_int(one_one_int,power_power_int(s,number_number_of_nat(bit0(bit1(pls))))),zero_zero_int),
inference(demodulation,[status(thm),theory(equality)],[c_321,c_325]) ).
tff(c_331,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),
inference(demodulation,[status(thm),theory(equality)],[c_192,c_326]) ).
tff(c_369,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(demodulation,[status(thm),theory(equality)],[c_338,c_331]) ).
tff(c_64,plain,
! [Z_14: int,W_15: int] : ( times_times_int(Z_14,W_15) = times_times_int(W_15,Z_14) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_8,plain,
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(power_power_int(s,number_number_of_nat(bit0(bit1(pls)))),one_one_int),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_402,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(demodulation,[status(thm),theory(equality)],[c_64,c_64,c_192,c_321,c_321,c_62,c_8]) ).
tff(c_194,plain,
! [W_85: int] : ( times_times_int(pls,W_85) = pls ),
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_6,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(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_404,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(demodulation,[status(thm),theory(equality)],[c_402,c_194,c_64,c_64,c_64,c_64,c_321,c_321,c_62,c_62,c_338,c_6]) ).
tff(c_405,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_369,c_404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM924_1 : TPTP v9.0.0. Released v5.3.0.
% 0.07/0.13 % 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
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 15:45:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.15/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.15/2.15
% 5.15/2.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------