%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 08:18:25 AM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 18 unt; 0 def)
% Number of atoms : 56 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 21 ~; 16 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 34 ( 8 sgn 7 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,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('theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,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('theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
fof(fact_22_zless__le,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('theBenchmark.p',fact_22_zless__le) ).
fof(fact_85_zmult__commute,axiom,
! [Z,W] : times_times(int,Z,W) = times_times(int,W,Z),
file('theBenchmark.p',fact_85_zmult__commute) ).
fof(fact_86_number__of__is__id,axiom,
! [K_1] : number_number_of(int,K_1) = K_1,
file('theBenchmark.p',fact_86_number__of__is__id) ).
fof(fact_89_zadd__commute,axiom,
! [Z,W] : plus_plus(int,Z,W) = plus_plus(int,W,Z),
file('theBenchmark.p',fact_89_zadd__commute) ).
fof(conj_0,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('theBenchmark.p',conj_0) ).
fof(conj_0_neg,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(assume_negation,[status(cth)],[conj_0]) ).
fof(fact_0_tpos,axiom,
ord_less_eq(int,one_one(int),t),
file('theBenchmark.p',fact_0_tpos) ).
cnf(c_189,plain,
ord_less_eq(int,one_one(int),t),
inference(clausify,[status(thm)],[fact_0_tpos]) ).
fof(nnf_8,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))
| one_one(int) != t ),
inference(fof_nnf,[status(thm)],[fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
fof(sk_fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,plain,
( plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,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))
| one_one(int) != t ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_8]) ).
cnf(c_190,plain,
( plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,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))
| one_one(int) != t ),
inference(split_conjunct,[status(thm)],[sk_fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
fof(nnf_9,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(fof_nnf,[status(thm)],[fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
fof(sk_fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,plain,
( plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,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,sK3]),skolemize(X,sK2),skolemize(Y,sK3)],[nnf_9]) ).
cnf(c_191,plain,
( plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,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(split_conjunct,[status(thm)],[sk_fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06]) ).
cnf(c_203,plain,
( B = A
| ~ ord_less_eq(int,A,B)
| ord_less(int,A,B) ),
inference(clausify,[status(thm)],[fact_22_zless__le]) ).
cnf(c_269,plain,
times_times(int,A,B) = times_times(int,B,A),
inference(clausify,[status(thm)],[fact_85_zmult__commute]) ).
cnf(c_270,plain,
number_number_of(int,A) = A,
inference(clausify,[status(thm)],[fact_86_number__of__is__id]) ).
cnf(c_273,plain,
plus_plus(int,A,B) = plus_plus(int,B,A),
inference(clausify,[status(thm)],[fact_89_zadd__commute]) ).
cnf(c_289,negated_conjecture,
plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,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(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_336,negated_conjecture,
plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),
inference(paramod,[status(thm)],[c_270,c_289]) ).
cnf(c_337,negated_conjecture,
plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),one_one(int)),
inference(paramod,[status(thm)],[c_269,c_336]) ).
cnf(c_290,negated_conjecture,
plus_plus(int,power_power(int,A,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))) != plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),
inference(paramod,[status(thm)],[c_273,c_337]) ).
cnf(c_338,plain,
( plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(paramod,[status(thm)],[c_270,c_191]) ).
cnf(c_339,plain,
( plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),one_one(int))
| ~ ord_less(int,one_one(int),t) ),
inference(paramod,[status(thm)],[c_269,c_338]) ).
cnf(c_340,plain,
( plus_plus(int,power_power(int,sK2,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK3,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))
| ~ ord_less(int,one_one(int),t) ),
inference(paramod,[status(thm)],[c_273,c_339]) ).
cnf(c_297,negated_conjecture,
~ ord_less(int,one_one(int),t),
inference(resolve,[status(thm)],[c_290,c_340]) ).
cnf(c_341,plain,
( plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int))
| one_one(int) != t ),
inference(paramod,[status(thm)],[c_270,c_190]) ).
cnf(c_342,plain,
( plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,times_times(int,m,bit0(bit0(bit1(pls)))),one_one(int))
| one_one(int) != t ),
inference(paramod,[status(thm)],[c_269,c_341]) ).
cnf(c_343,plain,
( plus_plus(int,power_power(int,sK0,number_number_of(nat,bit0(bit1(pls)))),power_power(int,sK1,number_number_of(nat,bit0(bit1(pls))))) = plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))
| one_one(int) != t ),
inference(paramod,[status(thm)],[c_273,c_342]) ).
cnf(c_298,negated_conjecture,
one_one(int) != t,
inference(resolve,[status(thm)],[c_290,c_343]) ).
cnf(c_344,plain,
( t = one_one(int)
| ord_less(int,one_one(int),t) ),
inference(resolve,[status(thm)],[c_203,c_189]) ).
cnf(c_345,plain,
( one_one(int) = t
| ord_less(int,one_one(int),t) ),
inference(copy,[status(thm)],[c_344]) ).
cnf(c_346,plain,
one_one(int) = t,
inference(resolve,[status(thm)],[c_297,c_345]) ).
cnf(c_335,plain,
$false,
inference(resolve,[status(thm)],[c_298,c_346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n017.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 04:16:24 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 3984994 was started by sandbox on n017,
% 0.10/5.39 % Sat Sep 26 04:16:24 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.42
% 0.14/5.42 % From the command line: assign(max_seconds, 300).
% 0.14/5.42
% 0.14/5.42 % SInE: 93 to sos, 48 to usable, of 141 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.14/5.45
% 0.14/5.45 % SZS status Theorem for theBenchmark
% 0.14/5.45
% 0.14/5.45 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/5.45 % Length of proof is 19.
% 0.14/5.45 % Level of proof is 4.
% 0.14/5.45 % Maximum clause weight is 116.000.
% 0.14/5.45 % Given clauses 46.
% 0.14/5.45
% 0.14/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------