%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM924+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 01:41:58 PM UTC 2026
% Result : Theorem 0.33s 0.51s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 22 unt; 3 def)
% Number of atoms : 74 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 21 |; 0 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 4 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,hypothesis,
is_int(zero_zero_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
! [B_1_1] :
( is_int(B_1_1)
=> is_int(bit1(B_1_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_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') ).
fof(f29,axiom,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [K_1] :
( is_int(K_1)
=> number_number_of_int(K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f393,axiom,
! [A_90] : hAPP_int_int(times_times_int(A_90),zero_zero_int) = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1230,conjecture,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_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') ).
fof(f1231,negated_conjecture,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(negated_conjecture,[status(cth)],[f1230]) ).
fof(f1233,plain,
is_int(zero_zero_int),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f1241,plain,
! [B_1_1] :
( is_int(bit1(B_1_1))
| ~ is_int(B_1_1) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f1242,plain,
! [X0] :
( is_int(bit1(X0))
| ~ is_int(X0) ),
inference(cnf_transformation,[status(thm)],[f1241]) ).
fof(f1275,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f1276,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f1339,plain,
! [K_1] :
( number_number_of_int(K_1) = K_1
| ~ is_int(K_1) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f1340,plain,
! [X0] :
( number_number_of_int(X0) = X0
| ~ is_int(X0) ),
inference(cnf_transformation,[status(thm)],[f1339]) ).
fof(f1682,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f1710,plain,
pls = zero_zero_int,
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f2052,plain,
! [X0] : hAPP_int_int(times_times_int(X0),zero_zero_int) = zero_zero_int,
inference(cnf_transformation,[status(thm)],[f393]) ).
fof(f4406,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),
inference(cnf_transformation,[status(thm)],[f1231]) ).
fof(f4622,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),pls)),
inference(backward_demodulation,[status(thm)],[f1710,f4406]) ).
fof(f4633,plain,
is_int(pls),
inference(forward_demodulation,[status(thm)],[f1710,f1233]) ).
fof(f4664,definition,
( sQ10_spl
<=> is_int(pls) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f4666,plain,
( sQ10_spl
| ~ is_int(pls) ),
inference(component_clause,[status(thm)],[f4664]) ).
fof(f4671,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4666,f4633]) ).
fof(f4672,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f4671]) ).
fof(f4721,definition,
( sQ17_spl
<=> is_int(bit1(pls)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f4723,plain,
( sQ17_spl
| ~ is_int(bit1(pls)) ),
inference(component_clause,[status(thm)],[f4721]) ).
fof(f4791,plain,
( one_one_int = bit1(pls)
| ~ is_int(bit1(pls)) ),
inference(paramodulation,[status(thm)],[f1682,f1340]) ).
fof(f4793,definition,
( sQ22_spl
<=> one_one_int = bit1(pls) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f4794,plain,
( ~ sQ22_spl
| one_one_int = bit1(pls) ),
inference(component_clause,[status(thm)],[f4793]) ).
fof(f4796,plain,
( sQ22_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f4791,f4721,f4793]) ).
fof(f4797,plain,
( sQ17_spl
| ~ is_int(pls) ),
inference(resolution,[status(thm)],[f4723,f1242]) ).
fof(f4798,plain,
( sQ17_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4797,f4664,f4721]) ).
fof(f4807,plain,
( ~ sQ22_spl
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(one_one_int)))),one_one_int)),pls)) ),
inference(backward_demodulation,[status(thm)],[f4794,f4622]) ).
fof(f4996,plain,
! [X0] : hAPP_int_int(times_times_int(X0),pls) = zero_zero_int,
inference(forward_demodulation,[status(thm)],[f1710,f2052]) ).
fof(f4997,plain,
! [X0] : hAPP_int_int(times_times_int(X0),pls) = pls,
inference(forward_demodulation,[status(thm)],[f1710,f4996]) ).
fof(f5005,plain,
( ~ sQ22_spl
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int)))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(forward_demodulation,[status(thm)],[f4794,f1275]) ).
fof(f5006,plain,
( ~ sQ22_spl
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int)))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int)))),m)),one_one_int)),zero_zero_int))) ),
inference(forward_demodulation,[status(thm)],[f4794,f5005]) ).
fof(f5007,plain,
( ~ sQ22_spl
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int)))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int)))),m)),one_one_int)),pls))) ),
inference(forward_demodulation,[status(thm)],[f1710,f5006]) ).
fof(f5008,plain,
( ~ sQ22_spl
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int)))),m)),one_one_int)),t)),pls)) ),
inference(forward_demodulation,[status(thm)],[f4997,f5007]) ).
fof(f5133,plain,
( ~ sQ22_spl
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(one_one_int)))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t) ),
inference(forward_demodulation,[status(thm)],[f4794,f1276]) ).
fof(f5134,plain,
( ~ sQ22_spl
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(one_one_int)))),one_one_int)),pls)) ),
inference(backward_demodulation,[status(thm)],[f5135,f5008]) ).
fof(f5135,plain,
( ~ sQ22_spl
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(one_one_int)))),one_one_int) = hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(one_one_int)))),m)),one_one_int)),t) ),
inference(forward_demodulation,[status(thm)],[f4794,f5133]) ).
fof(f5139,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5134,f4807]) ).
fof(f5140,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f5139]) ).
fof(f5141,plain,
$false,
inference(sat_refutation,[status(thm)],[f4672,f4796,f4798,f5140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM924+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.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 : Mon Sep 21 03:16:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.42 % Drodi V4.1.1
% 0.33/0.51 % Refutation found
% 0.33/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.33/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.33/0.54 % Elapsed time: 0.164362 seconds
% 0.33/0.54 % CPU time: 0.742566 seconds
% 0.33/0.54 % Total memory used: 215.646 MB
% 0.33/0.54 % Net memory used: 214.497 MB
%------------------------------------------------------------------------------