%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:18:24 AM UTC 2026
% Result : Theorem 2.35s 0.76s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 70 ( 51 unt; 0 def)
% Number of atoms : 98 ( 58 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 30 ~; 24 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_45_zadd__assoc,axiom,
! [Z1,Z2,Z3] : plus_plus(int,plus_plus(int,Z1,Z2),Z3) = plus_plus(int,Z1,plus_plus(int,Z2,Z3)),
file('theBenchmark.p',fact_45_zadd__assoc) ).
fof(fact_47_zadd__commute,axiom,
! [Z,W] : plus_plus(int,Z,W) = plus_plus(int,W,Z),
file('theBenchmark.p',fact_47_zadd__commute) ).
fof(fact_55_rel__simps_I4_J,axiom,
! [K_1] :
( ord_less(int,pls,bit0(K_1))
<=> ord_less(int,pls,K_1) ),
file('theBenchmark.p',fact_55_rel__simps_I4_J) ).
fof(fact_75_add__Pls__right,axiom,
! [K] : plus_plus(int,K,pls) = K,
file('theBenchmark.p',fact_75_add__Pls__right) ).
fof(fact_76_add__Pls,axiom,
! [K] : plus_plus(int,pls,K) = K,
file('theBenchmark.p',fact_76_add__Pls) ).
fof(fact_78_Bit0__def,axiom,
! [K] : bit0(K) = plus_plus(int,K,K),
file('theBenchmark.p',fact_78_Bit0__def) ).
fof(fact_85_add__numeral__0__right,axiom,
! [X_a] :
( number_ring(X_a)
=> ! [A_1] : plus_plus(X_a,A_1,number_number_of(X_a,pls)) = ti(X_a,A_1) ),
file('theBenchmark.p',fact_85_add__numeral__0__right) ).
fof(fact_92_Bit1__def,axiom,
! [K] : bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K),
file('theBenchmark.p',fact_92_Bit1__def) ).
fof(fact_5_zero__eq__power2,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('theBenchmark.p',fact_5_zero__eq__power2) ).
fof(conj_0,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('theBenchmark.p',conj_0) ).
fof(conj_0_neg,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) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_140,plain,
( zero_zero(A) = ti(A,B)
| power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(clausify,[status(thm)],[fact_5_zero__eq__power2]) ).
cnf(c_141,plain,
( ti(A,B) = zero_zero(A)
| power_power(A,B,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(copy,[status(thm)],[c_140]) ).
fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors,axiom,
ring_11004092258visors(int),
file('theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
cnf(c_158,plain,
ring_11004092258visors(int),
inference(clausify,[status(thm)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
fof(fact_0_n1pos,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('theBenchmark.p',fact_0_n1pos) ).
cnf(c_197,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(clausify,[status(thm)],[fact_0_n1pos]) ).
fof(fact_19_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls),
file('theBenchmark.p',fact_19_zero__is__num__zero) ).
cnf(c_220,plain,
zero_zero(int) = number_number_of(int,pls),
inference(clausify,[status(thm)],[fact_19_zero__is__num__zero]) ).
cnf(c_221,plain,
number_number_of(int,pls) = zero_zero(int),
inference(copy,[status(thm)],[c_220]) ).
cnf(c_256,plain,
plus_plus(int,plus_plus(int,A,B),C) = plus_plus(int,A,plus_plus(int,B,C)),
inference(clausify,[status(thm)],[fact_45_zadd__assoc]) ).
cnf(c_258,plain,
plus_plus(int,A,B) = plus_plus(int,B,A),
inference(clausify,[status(thm)],[fact_47_zadd__commute]) ).
cnf(c_272,plain,
( ~ ord_less(int,pls,A)
| ord_less(int,pls,bit0(A)) ),
inference(clausify,[status(thm)],[fact_55_rel__simps_I4_J]) ).
fof(fact_57_bin__less__0__simps_I1_J,axiom,
~ ord_less(int,pls,zero_zero(int)),
file('theBenchmark.p',fact_57_bin__less__0__simps_I1_J) ).
cnf(c_275,plain,
~ ord_less(int,pls,zero_zero(int)),
inference(clausify,[status(thm)],[fact_57_bin__less__0__simps_I1_J]) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int),
file('theBenchmark.p',fact_73_Pls__def) ).
cnf(c_300,plain,
pls = zero_zero(int),
inference(clausify,[status(thm)],[fact_73_Pls__def]) ).
cnf(c_302,plain,
plus_plus(int,A,pls) = A,
inference(clausify,[status(thm)],[fact_75_add__Pls__right]) ).
cnf(c_303,plain,
plus_plus(int,A,zero_zero(int)) = A,
inference(paramod,[status(thm)],[c_300,c_302]) ).
cnf(c_304,plain,
plus_plus(int,pls,A) = A,
inference(clausify,[status(thm)],[fact_76_add__Pls]) ).
cnf(c_305,plain,
plus_plus(int,zero_zero(int),A) = A,
inference(paramod,[status(thm)],[c_300,c_304]) ).
cnf(c_308,plain,
bit0(A) = plus_plus(int,A,A),
inference(clausify,[status(thm)],[fact_78_Bit0__def]) ).
cnf(c_318,plain,
( plus_plus(A,B,number_number_of(A,pls)) = ti(A,B)
| ~ number_ring(A) ),
inference(clausify,[status(thm)],[fact_85_add__numeral__0__right]) ).
cnf(c_319,plain,
( plus_plus(A,B,number_number_of(A,zero_zero(int))) = ti(A,B)
| ~ number_ring(A) ),
inference(paramod,[status(thm)],[c_300,c_318]) ).
cnf(c_326,plain,
bit1(A) = plus_plus(int,plus_plus(int,one_one(int),A),A),
inference(clausify,[status(thm)],[fact_92_Bit1__def]) ).
cnf(c_327,plain,
bit1(A) = plus_plus(int,A,plus_plus(int,one_one(int),A)),
inference(paramod,[status(thm)],[c_258,c_326]) ).
fof(arity_Int_Oint___Int_Onumber__ring,axiom,
number_ring(int),
file('theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
cnf(c_345,plain,
number_ring(int),
inference(clausify,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]) ).
cnf(c_348,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),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_1705,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(zero_zero(int))))) = zero_zero(int),
inference(paramod,[status(thm)],[c_300,c_348]) ).
cnf(c_1706,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(plus_plus(int,zero_zero(int),plus_plus(int,one_one(int),zero_zero(int)))))) = zero_zero(int),
inference(paramod,[status(thm)],[c_327,c_1705]) ).
cnf(c_1707,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(plus_plus(int,zero_zero(int),one_one(int))))) = zero_zero(int),
inference(paramod,[status(thm)],[c_303,c_1706]) ).
cnf(c_1708,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(plus_plus(int,one_one(int),zero_zero(int))))) = zero_zero(int),
inference(paramod,[status(thm)],[c_258,c_1707]) ).
cnf(c_1709,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(one_one(int)))) = zero_zero(int),
inference(paramod,[status(thm)],[c_303,c_1708]) ).
cnf(c_349,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) = zero_zero(int),
inference(paramod,[status(thm)],[c_308,c_1709]) ).
cnf(c_358,plain,
~ ord_less(int,zero_zero(int),zero_zero(int)),
inference(paramod,[status(thm)],[c_300,c_275]) ).
cnf(c_1710,plain,
( ~ ord_less(int,pls,A)
| ord_less(int,zero_zero(int),bit0(A)) ),
inference(paramod,[status(thm)],[c_300,c_272]) ).
cnf(c_1711,plain,
( ~ ord_less(int,pls,A)
| ord_less(int,zero_zero(int),plus_plus(int,A,A)) ),
inference(paramod,[status(thm)],[c_308,c_1710]) ).
cnf(c_359,plain,
( ~ ord_less(int,zero_zero(int),A)
| ord_less(int,zero_zero(int),plus_plus(int,A,A)) ),
inference(paramod,[status(thm)],[c_300,c_1711]) ).
cnf(c_374,plain,
number_number_of(int,zero_zero(int)) = zero_zero(int),
inference(paramod,[status(thm)],[c_300,c_221]) ).
cnf(c_1712,plain,
( ti(A,B) = zero_zero(A)
| power_power(A,B,number_number_of(nat,bit0(bit1(zero_zero(int))))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(paramod,[status(thm)],[c_300,c_141]) ).
cnf(c_1713,plain,
( ti(A,B) = zero_zero(A)
| power_power(A,B,number_number_of(nat,bit0(plus_plus(int,zero_zero(int),plus_plus(int,one_one(int),zero_zero(int)))))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(paramod,[status(thm)],[c_327,c_1712]) ).
cnf(c_1714,plain,
( ti(A,B) = zero_zero(A)
| power_power(A,B,number_number_of(nat,bit0(plus_plus(int,zero_zero(int),one_one(int))))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(paramod,[status(thm)],[c_303,c_1713]) ).
cnf(c_1715,plain,
( ti(A,B) = zero_zero(A)
| power_power(A,B,number_number_of(nat,bit0(plus_plus(int,one_one(int),zero_zero(int))))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(paramod,[status(thm)],[c_258,c_1714]) ).
cnf(c_1716,plain,
( ti(A,B) = zero_zero(A)
| power_power(A,B,number_number_of(nat,bit0(one_one(int)))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(paramod,[status(thm)],[c_303,c_1715]) ).
cnf(c_386,plain,
( ti(A,B) = zero_zero(A)
| power_power(A,B,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) != zero_zero(A)
| ~ ring_11004092258visors(A) ),
inference(paramod,[status(thm)],[c_308,c_1716]) ).
cnf(c_1717,plain,
ord_less(int,zero_zero(int),plus_plus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))),
inference(resolve,[status(thm)],[c_359,c_197]) ).
cnf(c_553,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),plus_plus(int,semiring_1_of_nat(int,n),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))))),
inference(paramod,[status(thm)],[c_256,c_1717]) ).
cnf(c_1718,plain,
plus_plus(int,A,number_number_of(int,zero_zero(int))) = ti(int,A),
inference(resolve,[status(thm)],[c_345,c_319]) ).
cnf(c_1719,plain,
plus_plus(int,A,zero_zero(int)) = ti(int,A),
inference(paramod,[status(thm)],[c_374,c_1718]) ).
cnf(c_1720,plain,
A = ti(int,A),
inference(paramod,[status(thm)],[c_303,c_1719]) ).
cnf(c_871,plain,
ti(int,A) = A,
inference(copy,[status(thm)],[c_1720]) ).
cnf(c_1721,negated_conjecture,
( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int)
| ~ ring_11004092258visors(int) ),
inference(resolve,[status(thm)],[c_386,c_349]) ).
cnf(c_1722,negated_conjecture,
( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = zero_zero(int)
| ~ ring_11004092258visors(int) ),
inference(paramod,[status(thm)],[c_871,c_1721]) ).
cnf(c_1700,negated_conjecture,
plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = zero_zero(int),
inference(resolve,[status(thm)],[c_158,c_1722]) ).
cnf(c_1723,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),plus_plus(int,semiring_1_of_nat(int,n),zero_zero(int)))),
inference(paramod,[status(thm)],[c_1700,c_553]) ).
cnf(c_1724,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),plus_plus(int,zero_zero(int),semiring_1_of_nat(int,n)))),
inference(paramod,[status(thm)],[c_258,c_1723]) ).
cnf(c_1725,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(paramod,[status(thm)],[c_305,c_1724]) ).
cnf(c_1726,plain,
ord_less(int,zero_zero(int),zero_zero(int)),
inference(paramod,[status(thm)],[c_1700,c_1725]) ).
cnf(c_1704,plain,
$false,
inference(resolve,[status(thm)],[c_358,c_1726]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 04:25:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 893964 was started by sandbox2 on n001,
% 0.09/0.37 % Sat Sep 26 04:25:13 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SInE: 109 to sos, 43 to usable, of 152 axioms (tolerance 2.00, depth 0 fixpoint).
% 2.35/0.76
% 2.35/0.76 % SZS status Theorem for theBenchmark
% 2.35/0.76
% 2.35/0.76 % Proof 1 at 0.25 (+ 0.07) seconds.
% 2.35/0.76 % Length of proof is 41.
% 2.35/0.76 % Level of proof is 5.
% 2.35/0.76 % Maximum clause weight is 133.000.
% 2.35/0.76 % Given clauses 275.
% 2.35/0.76
% 2.35/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------