%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 01:42:01 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : CNFRefutation 0.09s
% 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 ( 3 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 30 ( 18 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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(f3,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(f29,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(f112,axiom,
! [K_1] : number_number_of_int(K_1) = K_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f124,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(f125,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)],[f124]) ).
fof(f126,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f127,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)],[f2]) ).
fof(f128,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)],[f127]) ).
fof(f129,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)],[f128]) ).
fof(f130,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)],[f3]) ).
fof(f131,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)],[f130]) ).
fof(f132,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)],[f131]) ).
fof(f160,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)],[f29]) ).
fof(f161,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)],[f160]) ).
fof(f164,plain,
! [X0,X1] :
( X0 = X1
| ~ ord_less_eq_int(X0,X1)
| ord_less_int(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f344,plain,
! [X0] : number_number_of_int(X0) = X0,
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f380,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)],[f125]) ).
fof(f381,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)],[f380]) ).
fof(f382,definition,
( sQ0_spl
<=> t = one_one_int ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f385,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(f386,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)],[f385]) ).
fof(f388,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f382,f385]) ).
fof(f389,definition,
( sQ2_spl
<=> ord_less_int(one_one_int,t) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f392,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(f393,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)],[f392]) ).
fof(f395,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f132,f389,f392]) ).
fof(f397,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)],[f344,f381]) ).
fof(f555,plain,
( one_one_int = t
| ord_less_int(one_one_int,t) ),
inference(resolution,[status(thm)],[f164,f126]) ).
fof(f560,plain,
( sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f555,f389,f382]) ).
fof(f561,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)],[f344,f393]) ).
fof(f562,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f397]) ).
fof(f563,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f562]) ).
fof(f564,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)],[f344,f386]) ).
fof(f565,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f397]) ).
fof(f566,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f567,plain,
$false,
inference(sat_refutation,[status(thm)],[f388,f395,f560,f563,f566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n020.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 21 03:19:02 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.40 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.39/0.46 % Elapsed time: 0.070045 seconds
% 0.39/0.46 % CPU time: 0.177111 seconds
% 0.39/0.46 % Total memory used: 108.916 MB
% 0.39/0.46 % Net memory used: 108.774 MB
%------------------------------------------------------------------------------