%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:18:22 AM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 12 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_22_number__of__is__id,axiom,
! [K_1] : number_number_of(int,K_1) = K_1,
file('theBenchmark.p',fact_22_number__of__is__id) ).
fof(fact_23_zmult__commute,axiom,
! [Z,W] : times_times(int,Z,W) = times_times(int,W,Z),
file('theBenchmark.p',fact_23_zmult__commute) ).
fof(fact_62_mult__Pls,axiom,
! [W] : times_times(int,pls,W) = pls,
file('theBenchmark.p',fact_62_mult__Pls) ).
fof(fact_96_zadd__commute,axiom,
! [Z,W] : plus_plus(int,Z,W) = plus_plus(int,W,Z),
file('theBenchmark.p',fact_96_zadd__commute) ).
fof(conj_0,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('theBenchmark.p',conj_0) ).
fof(conj_0_neg,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)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(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,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('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) ).
cnf(c_217,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(clausify,[status(thm)],[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]) ).
fof(fact_3_t,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('theBenchmark.p',fact_3_t) ).
cnf(c_218,plain,
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),
inference(clausify,[status(thm)],[fact_3_t]) ).
cnf(c_219,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(copy,[status(thm)],[c_218]) ).
cnf(c_249,plain,
number_number_of(int,A) = A,
inference(clausify,[status(thm)],[fact_22_number__of__is__id]) ).
cnf(c_250,plain,
times_times(int,A,B) = times_times(int,B,A),
inference(clausify,[status(thm)],[fact_23_zmult__commute]) ).
cnf(c_299,plain,
times_times(int,pls,A) = pls,
inference(clausify,[status(thm)],[fact_62_mult__Pls]) ).
cnf(c_348,plain,
plus_plus(int,A,B) = plus_plus(int,B,A),
inference(clausify,[status(thm)],[fact_96_zadd__commute]) ).
fof(fact_97_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls),
file('theBenchmark.p',fact_97_zero__is__num__zero) ).
cnf(c_349,plain,
zero_zero(int) = number_number_of(int,pls),
inference(clausify,[status(thm)],[fact_97_zero__is__num__zero]) ).
cnf(c_350,plain,
zero_zero(int) = pls,
inference(paramod,[status(thm)],[c_249,c_349]) ).
cnf(c_360,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)),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_379,negated_conjecture,
~ ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),zero_zero(int)),
inference(paramod,[status(thm)],[c_348,c_360]) ).
cnf(c_361,negated_conjecture,
~ ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls),
inference(paramod,[status(thm)],[c_350,c_379]) ).
cnf(c_380,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(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(paramod,[status(thm)],[c_249,c_217]) ).
cnf(c_381,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),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(paramod,[status(thm)],[c_250,c_380]) ).
cnf(c_382,plain,
ord_less(int,times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),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(paramod,[status(thm)],[c_348,c_381]) ).
cnf(c_383,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),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(paramod,[status(thm)],[c_250,c_382]) ).
cnf(c_384,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),times_times(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),zero_zero(int))),
inference(paramod,[status(thm)],[c_249,c_383]) ).
cnf(c_385,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),times_times(int,plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),one_one(int)),zero_zero(int))),
inference(paramod,[status(thm)],[c_250,c_384]) ).
cnf(c_386,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),zero_zero(int))),
inference(paramod,[status(thm)],[c_348,c_385]) ).
cnf(c_387,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),pls)),
inference(paramod,[status(thm)],[c_350,c_386]) ).
cnf(c_388,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),times_times(int,pls,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))))),
inference(paramod,[status(thm)],[c_250,c_387]) ).
cnf(c_362,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),pls),
inference(paramod,[status(thm)],[c_299,c_388]) ).
cnf(c_389,plain,
times_times(int,plus_plus(int,times_times(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(paramod,[status(thm)],[c_249,c_219]) ).
cnf(c_390,plain,
times_times(int,plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),one_one(int)),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(paramod,[status(thm)],[c_250,c_389]) ).
cnf(c_391,plain,
times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(paramod,[status(thm)],[c_348,c_390]) ).
cnf(c_392,plain,
times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(paramod,[status(thm)],[c_250,c_391]) ).
cnf(c_369,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,number_number_of(nat,bit0(bit1(pls))))),
inference(paramod,[status(thm)],[c_348,c_392]) ).
cnf(c_393,plain,
ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls),
inference(paramod,[status(thm)],[c_369,c_362]) ).
cnf(c_378,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_361,c_393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 04:23:31 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 4166494 was started by sandbox on n016,
% 0.09/0.37 % Sat Sep 26 04:23:31 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.40
% 0.09/0.40 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SInE: 120 to sos, 34 to usable, of 154 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.09/0.44
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.44 % Length of proof is 19.
% 0.09/0.44 % Level of proof is 4.
% 0.09/0.44 % Maximum clause weight is 185.000.
% 0.09/0.44 % Given clauses 0.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------