TSTP Solution File: NUM925+5 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM925+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n028.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 : Tue Aug 22 10:53:10 EDT 2023
% Result : Theorem 19.85s 7.30s
% Output : CNFRefutation 19.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 49
% Syntax : Number of formulae : 93 ( 43 unt; 29 typ; 0 def)
% Number of atoms : 92 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 27 ~; 21 |; 0 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 24 >; 9 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 52 (; 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ord_less > zero_neq_one > semiring_1 > semiring_0 > ring_char_0 > ring_11004092258visors > power > number_semiring > number_ring > number > no_zero_divisors > mult_zero > linordered_idom > linord219039673up_add > power_power > plus_plus > ti > semiring_1_of_nat > number_number_of > #nlpp > zero_zero > undefined > one_one > bit1 > bit0 > t > pls > nat > n > int
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(semiring_1,type,
semiring_1: $i > $o ).
tff(power,type,
power: $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(ring_11004092258visors,type,
ring_11004092258visors: $i > $o ).
tff(bit0,type,
bit0: $i > $i ).
tff(no_zero_divisors,type,
no_zero_divisors: $i > $o ).
tff(plus_plus,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(zero_neq_one,type,
zero_neq_one: $i > $o ).
tff(number_ring,type,
number_ring: $i > $o ).
tff(power_power,type,
power_power: ( $i * $i * $i ) > $i ).
tff(linord219039673up_add,type,
linord219039673up_add: $i > $o ).
tff(nat,type,
nat: $i ).
tff(semiring_1_of_nat,type,
semiring_1_of_nat: ( $i * $i ) > $i ).
tff(undefined,type,
undefined: $i > $i ).
tff(int,type,
int: $i ).
tff(ti,type,
ti: ( $i * $i ) > $i ).
tff(semiring_0,type,
semiring_0: $i > $o ).
tff(n,type,
n: $i ).
tff(linordered_idom,type,
linordered_idom: $i > $o ).
tff(bit1,type,
bit1: $i > $i ).
tff(mult_zero,type,
mult_zero: $i > $o ).
tff(number_number_of,type,
number_number_of: ( $i * $i ) > $i ).
tff(ring_char_0,type,
ring_char_0: $i > $o ).
tff(zero_zero,type,
zero_zero: $i > $i ).
tff(number_semiring,type,
number_semiring: $i > $o ).
tff(f_548,axiom,
! [K] : ( bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
tff(f_479,axiom,
! [K] : ( plus_plus(int,K,pls) = K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
tff(f_475,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
tff(f_177,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(f_410,axiom,
~ ord_less(int,pls,zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bin__less__0__simps_I1_J) ).
tff(f_82,hypothesis,
! [B_1] : ( bit0(ti(int,B_1)) = bit0(B_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
tff(f_349,axiom,
! [K_1,L_1] :
( ( bit0(K_1) = bit0(L_1) )
<=> ( K_1 = L_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).
tff(f_485,axiom,
! [K] : ( bit0(K) = plus_plus(int,K,K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
tff(f_583,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f_453,axiom,
! [X_a] :
( linord219039673up_add(X_a)
=> ! [A_2] :
( ( plus_plus(X_a,A_2,A_2) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_double__eq__0__iff) ).
tff(f_404,axiom,
! [K_1] :
( ord_less(int,pls,bit0(K_1))
<=> ord_less(int,pls,K_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I4_J) ).
tff(f_584,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(f_593,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f_267,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
tff(f_506,axiom,
! [X_a] :
( number_ring(X_a)
=> ! [A_1] : ( plus_plus(X_a,number_number_of(X_a,pls),A_1) = ti(X_a,A_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
tff(f_481,axiom,
! [K] : ( plus_plus(int,pls,K) = K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__Pls) ).
tff(f_544,axiom,
! [K,L] : ( plus_plus(int,bit1(K),bit0(L)) = bit1(plus_plus(int,K,L)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__Bit1__Bit0) ).
tff(f_362,axiom,
! [Z,W] : ( plus_plus(int,Z,W) = plus_plus(int,W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
tff(f_610,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f_202,axiom,
! [X_a] :
( ring_11004092258visors(X_a)
=> ! [A_2] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
tff(c_2171,plain,
! [K_333] : ( plus_plus(int,plus_plus(int,one_one(int),K_333),K_333) = bit1(K_333) ),
inference(cnfTransformation,[status(thm)],[f_548]) ).
tff(c_300,plain,
! [K_185] : ( plus_plus(int,K_185,pls) = K_185 ),
inference(cnfTransformation,[status(thm)],[f_479]) ).
tff(c_2188,plain,
plus_plus(int,one_one(int),pls) = bit1(pls),
inference(superposition,[status(thm),theory(equality)],[c_2171,c_300]) ).
tff(c_2290,plain,
one_one(int) = bit1(pls),
inference(superposition,[status(thm),theory(equality)],[c_2188,c_300]) ).
tff(c_296,plain,
zero_zero(int) = pls,
inference(cnfTransformation,[status(thm)],[f_475]) ).
tff(c_74,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnfTransformation,[status(thm)],[f_177]) ).
tff(c_427,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(demodulation,[status(thm),theory(equality)],[c_296,c_74]) ).
tff(c_2307,plain,
ord_less(int,pls,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n))),
inference(demodulation,[status(thm),theory(equality)],[c_2290,c_427]) ).
tff(c_246,plain,
~ ord_less(int,pls,zero_zero(int)),
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_417,plain,
~ ord_less(int,pls,pls),
inference(demodulation,[status(thm),theory(equality)],[c_296,c_246]) ).
tff(c_24,plain,
! [B_1_24] : ( bit0(ti(int,B_1_24)) = bit0(B_1_24) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_654,plain,
! [L_1_258,K_1_259] :
( ( L_1_258 = K_1_259 )
| ( bit0(L_1_258) != bit0(K_1_259) ) ),
inference(cnfTransformation,[status(thm)],[f_349]) ).
tff(c_660,plain,
! [B_1_24,L_1_258] :
( ( ti(int,B_1_24) = L_1_258 )
| ( bit0(L_1_258) != bit0(B_1_24) ) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_654]) ).
tff(c_1129,plain,
! [B_1_24] : ( ti(int,B_1_24) = B_1_24 ),
inference(reflexivity,[status(thm),theory(equality)],[c_660]) ).
tff(c_306,plain,
! [K_189] : ( plus_plus(int,K_189,K_189) = bit0(K_189) ),
inference(cnfTransformation,[status(thm)],[f_485]) ).
tff(c_356,plain,
linord219039673up_add(int),
inference(cnfTransformation,[status(thm)],[f_583]) ).
tff(c_11711,plain,
! [X_a_518,A_2_519] :
( ( plus_plus(X_a_518,A_2_519,A_2_519) = zero_zero(X_a_518) )
| ( ti(X_a_518,A_2_519) != zero_zero(X_a_518) )
| ~ linord219039673up_add(X_a_518) ),
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_11713,plain,
! [A_2_519] :
( ( plus_plus(int,A_2_519,A_2_519) = zero_zero(int) )
| ( ti(int,A_2_519) != zero_zero(int) ) ),
inference(resolution,[status(thm)],[c_356,c_11711]) ).
tff(c_11718,plain,
! [A_2_520] :
( ( bit0(A_2_520) = pls )
| ( pls != A_2_520 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_296,c_1129,c_296,c_306,c_11713]) ).
tff(c_240,plain,
! [K_1_161] :
( ord_less(int,pls,bit0(K_1_161))
| ~ ord_less(int,pls,K_1_161) ),
inference(cnfTransformation,[status(thm)],[f_404]) ).
tff(c_11945,plain,
! [A_2_520] :
( ord_less(int,pls,pls)
| ~ ord_less(int,pls,A_2_520)
| ( pls != A_2_520 ) ),
inference(superposition,[status(thm),theory(equality)],[c_11718,c_240]) ).
tff(c_12445,plain,
! [A_2_527] :
( ~ ord_less(int,pls,A_2_527)
| ( pls != A_2_527 ) ),
inference(negUnitSimplification,[status(thm)],[c_417,c_11945]) ).
tff(c_12608,plain,
plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)) != pls,
inference(resolution,[status(thm)],[c_2307,c_12445]) ).
tff(c_358,plain,
ring_11004092258visors(int),
inference(cnfTransformation,[status(thm)],[f_584]) ).
tff(c_376,plain,
number_ring(int),
inference(cnfTransformation,[status(thm)],[f_593]) ).
tff(c_124,plain,
number_number_of(int,pls) = zero_zero(int),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_426,plain,
number_number_of(int,pls) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_296,c_124]) ).
tff(c_318,plain,
! [X_a_195,A_1_197] :
( ( plus_plus(X_a_195,number_number_of(X_a_195,pls),A_1_197) = ti(X_a_195,A_1_197) )
| ~ number_ring(X_a_195) ),
inference(cnfTransformation,[status(thm)],[f_506]) ).
tff(c_302,plain,
! [K_186] : ( plus_plus(int,pls,K_186) = K_186 ),
inference(cnfTransformation,[status(thm)],[f_481]) ).
tff(c_3669,plain,
! [K_366,L_367] : ( plus_plus(int,bit1(K_366),bit0(L_367)) = bit1(plus_plus(int,K_366,L_367)) ),
inference(cnfTransformation,[status(thm)],[f_544]) ).
tff(c_207,plain,
! [Z_145,W_146] : ( plus_plus(int,Z_145,W_146) = plus_plus(int,W_146,Z_145) ),
inference(cnfTransformation,[status(thm)],[f_362]) ).
tff(c_3693,plain,
! [L_367,K_366] : ( plus_plus(int,bit0(L_367),bit1(K_366)) = bit1(plus_plus(int,K_366,L_367)) ),
inference(superposition,[status(thm),theory(equality)],[c_3669,c_207]) ).
tff(c_11838,plain,
! [K_366,A_2_520] :
( ( plus_plus(int,pls,bit1(K_366)) = bit1(plus_plus(int,K_366,A_2_520)) )
| ( pls != A_2_520 ) ),
inference(superposition,[status(thm),theory(equality)],[c_11718,c_3693]) ).
tff(c_14765,plain,
! [K_560,A_2_561] :
( ( bit1(plus_plus(int,K_560,A_2_561)) = bit1(K_560) )
| ( pls != A_2_561 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_302,c_11838]) ).
tff(c_15113,plain,
! [A_1_197] :
( ( bit1(ti(int,A_1_197)) = bit1(number_number_of(int,pls)) )
| ( pls != A_1_197 )
| ~ number_ring(int) ),
inference(superposition,[status(thm),theory(equality)],[c_318,c_14765]) ).
tff(c_15260,plain,
! [A_1_564] :
( ( bit1(pls) = bit1(A_1_564) )
| ( pls != A_1_564 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_376,c_426,c_1129,c_15113]) ).
tff(c_400,plain,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(cnfTransformation,[status(thm)],[f_610]) ).
tff(c_404,plain,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_296,c_400]) ).
tff(c_2319,plain,
power_power(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_2290,c_404]) ).
tff(c_15738,plain,
! [A_1_564] :
( ( power_power(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(A_1_564)))) = pls )
| ( pls != A_1_564 ) ),
inference(superposition,[status(thm),theory(equality)],[c_15260,c_2319]) ).
tff(c_38926,plain,
! [X_a_749,A_2_750] :
( ( ti(X_a_749,A_2_750) = zero_zero(X_a_749) )
| ( power_power(X_a_749,A_2_750,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(X_a_749) )
| ~ ring_11004092258visors(X_a_749) ),
inference(cnfTransformation,[status(thm)],[f_202]) ).
tff(c_38973,plain,
( ( ti(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n))) = zero_zero(int) )
| ( zero_zero(int) != pls )
| ~ ring_11004092258visors(int) ),
inference(superposition,[status(thm),theory(equality)],[c_15738,c_38926]) ).
tff(c_39045,plain,
plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)) = pls,
inference(demodulation,[status(thm),theory(equality)],[c_358,c_296,c_296,c_1129,c_38973]) ).
tff(c_39047,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12608,c_39045]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM925+5 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.15 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 15:11:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 19.85/7.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.85/7.30
% 19.85/7.30 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.93/7.33
% 19.93/7.33 Inference rules
% 19.93/7.33 ----------------------
% 19.93/7.33 #Ref : 27
% 19.93/7.33 #Sup : 10264
% 19.93/7.33 #Fact : 4
% 19.93/7.33 #Define : 0
% 19.93/7.33 #Split : 5
% 19.93/7.33 #Chain : 0
% 19.93/7.33 #Close : 0
% 19.93/7.33
% 19.93/7.33 Ordering : KBO
% 19.93/7.33
% 19.93/7.33 Simplification rules
% 19.93/7.33 ----------------------
% 19.93/7.33 #Subsume : 5161
% 19.93/7.33 #Demod : 5724
% 19.93/7.33 #Tautology : 1724
% 19.93/7.33 #SimpNegUnit : 428
% 19.93/7.33 #BackRed : 43
% 19.93/7.33
% 19.93/7.33 #Partial instantiations: 0
% 19.93/7.33 #Strategies tried : 1
% 19.93/7.33
% 19.93/7.33 Timing (in seconds)
% 19.93/7.34 ----------------------
% 19.93/7.34 Preprocessing : 0.83
% 19.93/7.34 Parsing : 0.43
% 19.93/7.34 CNF conversion : 0.07
% 19.93/7.34 Main loop : 5.38
% 19.93/7.34 Inferencing : 0.94
% 19.93/7.34 Reduction : 2.53
% 19.93/7.34 Demodulation : 2.04
% 19.93/7.34 BG Simplification : 0.12
% 19.93/7.34 Subsumption : 1.54
% 19.93/7.34 Abstraction : 0.11
% 19.93/7.34 MUC search : 0.00
% 19.93/7.34 Cooper : 0.00
% 19.93/7.34 Total : 6.26
% 19.93/7.34 Index Insertion : 0.00
% 19.93/7.34 Index Deletion : 0.00
% 19.93/7.34 Index Matching : 0.00
% 19.93/7.34 BG Taut test : 0.00
%------------------------------------------------------------------------------