%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 08:18:24 AM UTC 2026
% Result : Theorem 0.67s 0.64s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 76 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 25 ~; 24 |; 18 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn 2 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_37_zless__le,axiom,
! [Z_1,W_1] :
( ( is_int(W_1)
& is_int(Z_1) )
=> ( ord_less_int(Z_1,W_1)
<=> ( Z_1 != W_1
& ord_less_eq_int(Z_1,W_1) ) ) ),
file('theBenchmark.p',fact_37_zless__le) ).
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)
& is_int(Y)
& is_int(X) ) ),
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)
& is_int(Y)
& is_int(X) ) ),
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(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(gsy_v_t____,axiom,
is_int(t),
file('theBenchmark.p',gsy_v_t____) ).
cnf(c_642,plain,
is_int(t),
inference(clausify,[status(thm)],[gsy_v_t____]) ).
fof(fact_0_tpos,axiom,
ord_less_eq_int(one_one_int,t),
file('theBenchmark.p',fact_0_tpos) ).
cnf(c_643,plain,
ord_less_eq_int(one_one_int,t),
inference(clausify,[status(thm)],[fact_0_tpos]) ).
fof(nnf_598,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)
& is_int(Y)
& is_int(X) )
| t != one_one_int ),
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_sk,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)
& is_int(sK1)
& is_int(sK0) )
| t != one_one_int ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_598]) ).
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)
| t != one_one_int )
& ( is_int(sK1)
| t != one_one_int )
& ( is_int(sK0)
| t != one_one_int ) ),
inference(cnf_transformation,[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_sk]) ).
cnf(c_646,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)
| t != one_one_int ),
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]) ).
cnf(c_647,plain,
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = 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)))))
| t != one_one_int ),
inference(copy,[status(thm)],[c_646]) ).
fof(nnf_599,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)
& is_int(Y)
& is_int(X) )
| ~ 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_sk,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)
& is_int(sK3)
& is_int(sK2) )
| ~ ord_less_int(one_one_int,t) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X,sK2),skolemize(Y,sK3)],[nnf_599]) ).
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) )
& ( is_int(sK3)
| ~ ord_less_int(one_one_int,t) )
& ( is_int(sK2)
| ~ ord_less_int(one_one_int,t) ) ),
inference(cnf_transformation,[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_sk]) ).
cnf(c_650,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_651,plain,
( plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = 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)))))
| ~ ord_less_int(one_one_int,t) ),
inference(copy,[status(thm)],[c_650]) ).
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,axiom,
is_int(one_one_int),
file('theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
cnf(c_739,plain,
is_int(one_one_int),
inference(clausify,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(c_791,plain,
( B = A
| ~ ord_less_eq_int(A,B)
| ord_less_int(A,B)
| ~ is_int(B)
| ~ is_int(A) ),
inference(clausify,[status(thm)],[fact_37_zless__le]) ).
cnf(c_1573,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_1677,negated_conjecture,
~ ord_less_int(one_one_int,t),
inference(resolve,[status(thm)],[c_1573,c_651]) ).
cnf(c_1678,negated_conjecture,
t != one_one_int,
inference(resolve,[status(thm)],[c_1573,c_647]) ).
cnf(c_2610,plain,
( t = one_one_int
| ord_less_int(one_one_int,t)
| ~ is_int(t)
| ~ is_int(one_one_int) ),
inference(resolve,[status(thm)],[c_791,c_643]) ).
cnf(c_2611,plain,
( t = one_one_int
| ord_less_int(one_one_int,t)
| ~ is_int(t) ),
inference(resolve,[status(thm)],[c_739,c_2610]) ).
cnf(c_2612,plain,
( t = one_one_int
| ord_less_int(one_one_int,t) ),
inference(resolve,[status(thm)],[c_642,c_2611]) ).
cnf(c_2613,plain,
t = one_one_int,
inference(resolve,[status(thm)],[c_1677,c_2612]) ).
cnf(c_2609,plain,
$false,
inference(resolve,[status(thm)],[c_1678,c_2613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 04:25:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 894799 was started by sandbox2 on n001,
% 0.10/0.37 % Sat Sep 26 04:25:43 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.51
% 0.21/0.51 % From the command line: assign(max_seconds, 300).
% 0.21/0.51
% 0.21/0.51 % SInE: 659 to sos, 57 to usable, of 716 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.67/0.64
% 0.67/0.64 % SZS status Theorem for theBenchmark
% 0.67/0.64
% 0.67/0.64 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.67/0.64 % Length of proof is 16.
% 0.67/0.64 % Level of proof is 4.
% 0.67/0.64 % Maximum clause weight is 118.000.
% 0.67/0.64 % Given clauses 145.
% 0.67/0.64
% 0.67/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------