%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM926+1 : 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 : n016.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 0.08s 0.45s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 37 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 11 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of predicates : 4 ( 2 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_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_28_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_28_zless__le) ).
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]) ).
cnf(c_111,negated_conjecture,
plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) != 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))))),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_199,plain,
( B = A
| ~ ord_less_eq_int(A,B)
| ord_less_int(A,B) ),
inference(clausify,[status(thm)],[fact_28_zless__le]) ).
fof(nnf_2,plain,
( ? [X,Y] : plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = 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)))))
| ~ 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(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)))))
| ~ ord_less_int(one_one_int,t) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_2]) ).
cnf(c_233,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)))))
| ~ 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_761,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)
| ~ ord_less_int(one_one_int,t) ),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_234,negated_conjecture,
~ ord_less_int(one_one_int,t),
inference(resolve,[status(thm)],[c_111,c_761]) ).
fof(nnf_1,plain,
( ? [X,Y] : plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int) = 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)))))
| 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,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)))))
| t != one_one_int ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X,sK2),skolemize(Y,sK3)],[nnf_1]) ).
cnf(c_235,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)))))
| 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_762,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)
| t != one_one_int ),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_236,negated_conjecture,
t != one_one_int,
inference(resolve,[status(thm)],[c_111,c_762]) ).
fof(fact_0_tpos,axiom,
ord_less_eq_int(one_one_int,t),
file('theBenchmark.p',fact_0_tpos) ).
cnf(c_237,plain,
ord_less_eq_int(one_one_int,t),
inference(clausify,[status(thm)],[fact_0_tpos]) ).
cnf(c_763,plain,
( t = one_one_int
| ord_less_int(one_one_int,t) ),
inference(resolve,[status(thm)],[c_237,c_199]) ).
cnf(c_764,plain,
t = one_one_int,
inference(resolve,[status(thm)],[c_234,c_763]) ).
cnf(c_760,plain,
$false,
inference(resolve,[status(thm)],[c_236,c_764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n016.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 04:24:45 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 4168314 was started by sandbox on n016,
% 0.08/0.37 % Sat Sep 26 04:24:45 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.40
% 0.08/0.40 % From the command line: assign(max_seconds, 300).
% 0.08/0.45
% 0.08/0.45 % SZS status Theorem for theBenchmark
% 0.08/0.45
% 0.08/0.45 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.08/0.45 % Length of proof is 12.
% 0.08/0.45 % Level of proof is 3.
% 0.08/0.45 % Maximum clause weight is 60.000.
% 0.08/0.45 % Given clauses 107.
% 0.08/0.45
% 0.08/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------