%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM926+3 : 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 0.24s 0.59s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 15 unt; 6 def)
% Number of atoms : 106 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 96 ( 35 ~; 33 |; 17 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-2 aty)
% Number of variables : 24 ( 12 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
is_int(t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( t = one_one_int
=> ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
& is_int(Y)
& is_int(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
=> ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
& is_int(Y)
& is_int(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [Z_1,W_1] :
( ( is_int(W_1)
& is_int(Z_1) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1))
<=> ( Z_1 != W_1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1230,conjecture,
? [X,Y] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1231,negated_conjecture,
~ ? [X,Y] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
inference(negated_conjecture,[status(cth)],[f1230]) ).
fof(f1232,plain,
is_int(one_one_int),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f1272,plain,
is_int(t),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f1273,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f1274,plain,
( ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
& is_int(Y)
& is_int(X) )
| t != one_one_int ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f1275,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK0_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK1_skl),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
& is_int(sK1_skl)
& is_int(sK0_skl) )
| t != one_one_int ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f1274]) ).
fof(f1278,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK0_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK1_skl),number_number_of_nat(bit0(bit1(pls))))) = 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 != one_one_int ),
inference(cnf_transformation,[status(thm)],[f1275]) ).
fof(f1279,plain,
( ? [X,Y] :
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
& is_int(Y)
& is_int(X) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f1280,plain,
( ( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK2_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK3_skl),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
& is_int(sK3_skl)
& is_int(sK2_skl) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(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)],[f1279]) ).
fof(f1283,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK2_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK3_skl),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
fof(f1321,plain,
! [Z_1,W_1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1))
<=> ( Z_1 != W_1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) ) )
| ~ is_int(W_1)
| ~ is_int(Z_1) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f1322,plain,
! [Z_1,W_1] :
( ( ( Z_1 = W_1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1)) )
& ( ( Z_1 != W_1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_1),W_1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),W_1)) ) )
| ~ is_int(W_1)
| ~ is_int(Z_1) ),
inference(NNF_transformation,[status(thm)],[f1321]) ).
fof(f1325,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[status(thm)],[f1322]) ).
fof(f4442,plain,
! [X,Y] : hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(Y),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
inference(pre_NNF_transformation,[status(thm)],[f1231]) ).
fof(f4443,plain,
! [X0,X1] : hAPP_int_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))))) != hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int),
inference(cnf_transformation,[status(thm)],[f4442]) ).
fof(f4494,definition,
( sQ0_spl
<=> t = one_one_int ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f4505,definition,
( sQ3_spl
<=> hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK0_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK1_skl),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_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(f4506,plain,
( ~ sQ3_spl
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK0_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK1_skl),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
inference(component_clause,[status(thm)],[f4505]) ).
fof(f4508,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1278,f4494,f4505]) ).
fof(f4509,definition,
( sQ4_spl
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f4520,definition,
( sQ7_spl
<=> hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK2_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK3_skl),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f4521,plain,
( ~ sQ7_spl
| hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(sK2_skl),number_number_of_nat(bit0(bit1(pls))))),hAPP_nat_int(power_power_int(sK3_skl),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int) ),
inference(component_clause,[status(thm)],[f4520]) ).
fof(f4523,plain,
( sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1283,f4509,f4520]) ).
fof(f5399,definition,
( sQ12_spl
<=> is_int(t) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f5401,plain,
( sQ12_spl
| ~ is_int(t) ),
inference(component_clause,[status(thm)],[f5399]) ).
fof(f5456,plain,
( one_one_int = t
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,one_one_int),t))
| ~ is_int(t)
| ~ is_int(one_one_int) ),
inference(resolution,[status(thm)],[f1325,f1273]) ).
fof(f5462,definition,
( sQ15_spl
<=> is_int(one_one_int) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f5464,plain,
( sQ15_spl
| ~ is_int(one_one_int) ),
inference(component_clause,[status(thm)],[f5462]) ).
fof(f5465,plain,
( sQ0_spl
| sQ4_spl
| ~ sQ12_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5456,f5462,f5399,f4509,f4494]) ).
fof(f5466,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5401,f1272]) ).
fof(f5467,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f5466]) ).
fof(f5468,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4506,f4443]) ).
fof(f5469,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f5468]) ).
fof(f5470,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4521,f4443]) ).
fof(f5471,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f5470]) ).
fof(f5472,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5464,f1232]) ).
fof(f5473,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f5472]) ).
fof(f5474,plain,
$false,
inference(sat_refutation,[status(thm)],[f4508,f4523,f5465,f5467,f5469,f5471,f5473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 03:19:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.15/0.47 % Drodi V4.1.1
% 0.24/0.59 % Refutation found
% 0.24/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.64 % Elapsed time: 0.264984 seconds
% 0.24/0.64 % CPU time: 1.117355 seconds
% 0.24/0.64 % Total memory used: 220.488 MB
% 0.24/0.64 % Net memory used: 218.895 MB
%------------------------------------------------------------------------------