%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 01:42:02 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 12 unt; 4 def)
% Number of atoms : 74 ( 33 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 64 ( 28 ~; 24 |; 5 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 30 ( 18 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( t = one_one(int)
=> ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
( ord_less(int,one_one(int),t)
=> ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [Z_1,W_1] :
( ord_less(int,Z_1,W_1)
<=> ( Z_1 != W_1
& ord_less_eq(int,Z_1,W_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,axiom,
! [K_1] : number_number_of(int,K_1) = K_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f142,conjecture,
? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f143,negated_conjecture,
~ ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(negated_conjecture,[status(cth)],[f142]) ).
fof(f216,plain,
ord_less_eq(int,one_one(int),t),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f217,plain,
( ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| t != one_one(int) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f218,plain,
( plus_plus(int,power_power(int,sK0_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| t != one_one(int) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f217]) ).
fof(f219,plain,
( plus_plus(int,power_power(int,sK0_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| t != one_one(int) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
( ? [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f221,plain,
( plus_plus(int,power_power(int,sK2_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f220]) ).
fof(f222,plain,
( plus_plus(int,power_power(int,sK2_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f253,plain,
! [Z_1,W_1] :
( ( Z_1 = W_1
| ~ ord_less_eq(int,Z_1,W_1)
| ord_less(int,Z_1,W_1) )
& ( ( Z_1 != W_1
& ord_less_eq(int,Z_1,W_1) )
| ~ ord_less(int,Z_1,W_1) ) ),
inference(NNF_transformation,[status(thm)],[f50]) ).
fof(f254,plain,
( ! [Z_1,W_1] :
( Z_1 = W_1
| ~ ord_less_eq(int,Z_1,W_1)
| ord_less(int,Z_1,W_1) )
& ! [Z_1,W_1] :
( ( Z_1 != W_1
& ord_less_eq(int,Z_1,W_1) )
| ~ ord_less(int,Z_1,W_1) ) ),
inference(miniscoping,[status(thm)],[f253]) ).
fof(f257,plain,
! [X0,X1] :
( X0 = X1
| ~ ord_less_eq(int,X0,X1)
| ord_less(int,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f434,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f486,plain,
! [X,Y] : plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(pre_NNF_transformation,[status(thm)],[f143]) ).
fof(f487,plain,
! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),
inference(cnf_transformation,[status(thm)],[f486]) ).
fof(f488,definition,
( sQ0_spl
<=> t = one_one(int) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f491,definition,
( sQ1_spl
<=> plus_plus(int,power_power(int,sK0_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ1_spl
| plus_plus(int,power_power(int,sK0_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f219,f488,f491]) ).
fof(f495,definition,
( sQ2_spl
<=> ord_less(int,one_one(int),t) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f498,definition,
( sQ3_spl
<=> plus_plus(int,power_power(int,sK2_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( ~ sQ3_spl
| plus_plus(int,power_power(int,sK2_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f222,f495,f498]) ).
fof(f503,plain,
! [X0,X1] : plus_plus(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,X1,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),
inference(backward_demodulation,[status(thm)],[f434,f487]) ).
fof(f755,plain,
( one_one(int) = t
| ord_less(int,one_one(int),t) ),
inference(resolution,[status(thm)],[f257,f216]) ).
fof(f760,plain,
( sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f755,f495,f488]) ).
fof(f761,plain,
( ~ sQ3_spl
| plus_plus(int,power_power(int,sK2_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)) ),
inference(forward_demodulation,[status(thm)],[f434,f499]) ).
fof(f762,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f761,f503]) ).
fof(f763,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f762]) ).
fof(f764,plain,
( ~ sQ1_spl
| plus_plus(int,power_power(int,sK0_skl,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1_skl,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)) ),
inference(forward_demodulation,[status(thm)],[f434,f492]) ).
fof(f765,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f764,f503]) ).
fof(f766,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f765]) ).
fof(f767,plain,
$false,
inference(sat_refutation,[status(thm)],[f494,f501,f760,f763,f766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 03:19:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.069209 seconds
% 0.11/0.45 % CPU time: 0.220421 seconds
% 0.11/0.45 % Total memory used: 105.571 MB
% 0.11/0.45 % Net memory used: 105.416 MB
%------------------------------------------------------------------------------