%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM925+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 : 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 01:42:00 PM UTC 2026
% Result : Theorem 0.23s 0.49s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 25 unt; 0 def)
% Number of atoms : 90 ( 44 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 93 ( 45 ~; 38 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,hypothesis,
! [B_1_1,B_2_1] :
( ( is_int(B_2_1)
& is_int(B_1_1) )
=> is_int(plus_plus_int(B_1_1,B_2_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [B_1_1,B_2_1] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [Xa,Ya] :
( ( is_int(Ya)
& is_int(Xa) )
=> ( plus_plus_int(hAPP_nat_int(power_power_int(Xa),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(Ya),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
<=> ( Ya = zero_zero_int
& Xa = zero_zero_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f126,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f127,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,axiom,
! [K_1] : bit0(K_1) = plus_plus_int(K_1,K_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1233,conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1234,negated_conjecture,
~ ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f1233]) ).
fof(f1239,plain,
is_int(one_one_int),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1240,plain,
! [B_1_1,B_2_1] :
( is_int(plus_plus_int(B_1_1,B_2_1))
| ~ is_int(B_2_1)
| ~ is_int(B_1_1) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f1241,plain,
! [X0,X1] :
( is_int(plus_plus_int(X0,X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[status(thm)],[f1240]) ).
fof(f1266,plain,
! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f1275,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f1277,plain,
! [Xa,Ya] :
( ( plus_plus_int(hAPP_nat_int(power_power_int(Xa),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(Ya),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int
<=> ( Ya = zero_zero_int
& Xa = zero_zero_int ) )
| ~ is_int(Ya)
| ~ is_int(Xa) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f1278,plain,
! [Xa,Ya] :
( ( ( Ya != zero_zero_int
| Xa != zero_zero_int
| plus_plus_int(hAPP_nat_int(power_power_int(Xa),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(Ya),number_number_of_nat(bit0(bit1(pls))))) = zero_zero_int )
& ( ( Ya = zero_zero_int
& Xa = zero_zero_int )
| plus_plus_int(hAPP_nat_int(power_power_int(Xa),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(Ya),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int ) )
| ~ is_int(Ya)
| ~ is_int(Xa) ),
inference(NNF_transformation,[status(thm)],[f1277]) ).
fof(f1279,plain,
! [X0,X1] :
( X0 = zero_zero_int
| plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[status(thm)],[f1278]) ).
fof(f1365,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f1521,plain,
bit0(pls) = pls,
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f1522,plain,
pls = zero_zero_int,
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f1529,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f4524,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(cnf_transformation,[status(thm)],[f1234]) ).
fof(f4724,plain,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(zero_zero_int)))) = zero_zero_int,
inference(backward_demodulation,[status(thm)],[f1522,f4524]) ).
fof(f4730,plain,
bit0(zero_zero_int) = pls,
inference(forward_demodulation,[status(thm)],[f1522,f1521]) ).
fof(f4731,plain,
bit0(zero_zero_int) = zero_zero_int,
inference(forward_demodulation,[status(thm)],[f1522,f4730]) ).
fof(f4739,plain,
! [X0,X1] :
( X0 = zero_zero_int
| plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(zero_zero_int)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))) != zero_zero_int
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(forward_demodulation,[status(thm)],[f1522,f1279]) ).
fof(f4740,plain,
! [X0,X1] :
( X0 = zero_zero_int
| plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(zero_zero_int)))),hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(zero_zero_int))))) != zero_zero_int
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(forward_demodulation,[status(thm)],[f1522,f4739]) ).
fof(f4743,plain,
! [X0] :
( X0 = zero_zero_int
| plus_plus_int(hAPP_nat_int(power_power_int(X0),number_number_of_nat(bit0(bit1(zero_zero_int)))),zero_zero_int) != zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(X0) ),
inference(paramodulation,[status(thm)],[f4724,f4740]) ).
fof(f4752,plain,
( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
| plus_plus_int(zero_zero_int,zero_zero_int) != zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(paramodulation,[status(thm)],[f4724,f4743]) ).
fof(f4753,plain,
( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
| bit0(zero_zero_int) != zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(forward_demodulation,[status(thm)],[f1529,f4752]) ).
fof(f4754,plain,
( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
| zero_zero_int != zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(forward_demodulation,[status(thm)],[f4731,f4753]) ).
fof(f4755,plain,
( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
| zero_zero_int != zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(duplicate_literals_removal,[status(thm)],[f4754]) ).
fof(f4756,plain,
( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(trivial_equality_resolution,[status(thm)],[f4755]) ).
fof(f4757,plain,
( ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(one_one_int)
| plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ),
inference(resolution,[status(thm)],[f4756,f1241]) ).
fof(f4758,plain,
( ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ),
inference(forward_subsumption_resolution,[status(thm)],[f4757,f1239]) ).
fof(f4819,plain,
plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(backward_subsumption_resolution,[status(thm)],[f4758,f1266]) ).
fof(f4886,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
inference(backward_demodulation,[status(thm)],[f4819,f1275]) ).
fof(f5193,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),pls)),
inference(forward_demodulation,[status(thm)],[f1522,f1365]) ).
fof(f5194,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
inference(forward_demodulation,[status(thm)],[f1522,f5193]) ).
fof(f5195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5194,f4886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+3 : 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 03:17:13 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.45 % Drodi V4.1.1
% 0.23/0.49 % Refutation found
% 0.23/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.54 % Elapsed time: 0.176596 seconds
% 0.23/0.54 % CPU time: 0.466002 seconds
% 0.23/0.54 % Total memory used: 204.309 MB
% 0.23/0.54 % Net memory used: 202.828 MB
%------------------------------------------------------------------------------