%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM924+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 01:41:57 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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') ).
fof(f4,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') ).
fof(f25,axiom,
! [K_1] : number_number_of_int(K_1) = K_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Z,W] : times_times_int(Z,W) = times_times_int(W,Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [W] : times_times_int(pls,W) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [K_1,L_1] : times_times_int(bit0(K_1),L_1) = bit0(times_times_int(K_1,L_1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f106,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f107,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') ).
fof(f108,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(negated_conjecture,[status(cth)],[f107]) ).
fof(f111,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(cnf_transformation,[status(thm)],[f3]) ).
fof(f112,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(cnf_transformation,[status(thm)],[f4]) ).
fof(f150,plain,
! [X0] : number_number_of_int(X0) = X0,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f151,plain,
! [X0,X1] : times_times_int(X0,X1) = times_times_int(X1,X0),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f270,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f271,plain,
! [X0] : times_times_int(pls,X0) = pls,
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f272,plain,
! [X0,X1] : times_times_int(bit0(X0),X1) = bit0(times_times_int(X0,X1)),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f375,plain,
zero_zero_int = number_number_of_int(pls),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f376,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(cnf_transformation,[status(thm)],[f108]) ).
fof(f377,plain,
ord_less_int(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),zero_zero_int)),
inference(backward_demodulation,[status(thm)],[f112,f111]) ).
fof(f469,plain,
zero_zero_int = pls,
inference(forward_demodulation,[status(thm)],[f150,f375]) ).
fof(f470,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),zero_zero_int),
inference(forward_demodulation,[status(thm)],[f270,f376]) ).
fof(f471,plain,
~ ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),pls),
inference(forward_demodulation,[status(thm)],[f469,f470]) ).
fof(f472,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),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(forward_demodulation,[status(thm)],[f270,f377]) ).
fof(f473,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(times_times_int(bit0(bit0(bit1(pls))),m),one_one_int),zero_zero_int)),
inference(forward_demodulation,[status(thm)],[f150,f472]) ).
fof(f474,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(bit0(times_times_int(bit0(bit1(pls)),m)),one_one_int),zero_zero_int)),
inference(forward_demodulation,[status(thm)],[f272,f473]) ).
fof(f475,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(bit0(bit0(times_times_int(bit1(pls),m))),one_one_int),zero_zero_int)),
inference(forward_demodulation,[status(thm)],[f272,f474]) ).
fof(f476,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),times_times_int(plus_plus_int(bit0(bit0(times_times_int(bit1(pls),m))),one_one_int),pls)),
inference(forward_demodulation,[status(thm)],[f469,f475]) ).
fof(f578,plain,
! [X0] : pls = times_times_int(X0,pls),
inference(paramodulation,[status(thm)],[f271,f151]) ).
fof(f594,plain,
ord_less_int(plus_plus_int(power_power_int(s,plus_plus_nat(one_one_nat,one_one_nat)),one_one_int),pls),
inference(backward_demodulation,[status(thm)],[f578,f476]) ).
fof(f595,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f594,f471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 03:16:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.069326 seconds
% 0.12/0.43 % CPU time: 0.290207 seconds
% 0.12/0.43 % Total memory used: 98.534 MB
% 0.12/0.43 % Net memory used: 98.092 MB
%------------------------------------------------------------------------------