%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 24 unt; 0 def)
% Number of atoms : 104 ( 51 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 99 ( 44 ~; 33 |; 17 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 37 ( 25 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
is_int(t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
ord_less_eq_int(one_one_int,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X_21] : times_times_int(X_21,X_21) = power_power_int(X_21,number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f375,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f717,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/sandbox/benchmark/theBenchmark.p') ).
fof(f718,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)],[f717]) ).
fof(f721,plain,
is_int(one_one_int),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f745,plain,
is_int(t),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f746,plain,
ord_less_eq_int(one_one_int,t),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f747,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(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f748,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)
& 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)],[f747]) ).
fof(f751,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)],[f748]) ).
fof(f752,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(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f753,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)
& is_int(sK3_skl)
& is_int(sK2_skl) )
| ~ 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)],[f752]) ).
fof(f756,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)],[f753]) ).
fof(f775,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f794,plain,
! [Z_1,W_1] :
( ( ord_less_int(Z_1,W_1)
<=> ( Z_1 != W_1
& ord_less_eq_int(Z_1,W_1) ) )
| ~ is_int(W_1)
| ~ is_int(Z_1) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f795,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) ) )
| ~ is_int(W_1)
| ~ is_int(Z_1) ),
inference(NNF_transformation,[status(thm)],[f794]) ).
fof(f798,plain,
! [X0,X1] :
( X0 = X1
| ~ ord_less_eq_int(X0,X1)
| ord_less_int(X0,X1)
| ~ is_int(X1)
| ~ is_int(X0) ),
inference(cnf_transformation,[status(thm)],[f795]) ).
fof(f1470,plain,
pls = zero_zero_int,
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f2405,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)],[f718]) ).
fof(f2406,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)],[f2405]) ).
fof(f2528,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(zero_zero_int)))),m),one_one_int),
inference(backward_demodulation,[status(thm)],[f1470,f2406]) ).
fof(f2542,plain,
! [X0,X1] : plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(zero_zero_int)))),power_power_int(X1,number_number_of_nat(bit0(bit1(pls))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int),
inference(forward_demodulation,[status(thm)],[f1470,f2528]) ).
fof(f2543,plain,
! [X0,X1] : plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(zero_zero_int)))),power_power_int(X1,number_number_of_nat(bit0(bit1(zero_zero_int))))) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int),
inference(forward_demodulation,[status(thm)],[f1470,f2542]) ).
fof(f2602,plain,
! [X0] : times_times_int(X0,X0) = power_power_int(X0,number_number_of_nat(bit0(bit1(zero_zero_int)))),
inference(forward_demodulation,[status(thm)],[f1470,f775]) ).
fof(f2612,plain,
! [X0,X1] : plus_plus_int(power_power_int(X0,number_number_of_nat(bit0(bit1(zero_zero_int)))),times_times_int(X1,X1)) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int),
inference(paramodulation,[status(thm)],[f2602,f2543]) ).
fof(f2622,plain,
( plus_plus_int(power_power_int(sK0_skl,number_number_of_nat(bit0(bit1(zero_zero_int)))),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(forward_demodulation,[status(thm)],[f1470,f751]) ).
fof(f2623,plain,
( plus_plus_int(times_times_int(sK0_skl,sK0_skl),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(forward_demodulation,[status(thm)],[f2602,f2622]) ).
fof(f2624,plain,
( plus_plus_int(times_times_int(sK0_skl,sK0_skl),power_power_int(sK1_skl,number_number_of_nat(bit0(bit1(zero_zero_int))))) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| t != one_one_int ),
inference(forward_demodulation,[status(thm)],[f1470,f2623]) ).
fof(f2625,plain,
( plus_plus_int(times_times_int(sK0_skl,sK0_skl),times_times_int(sK1_skl,sK1_skl)) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)
| t != one_one_int ),
inference(forward_demodulation,[status(thm)],[f2602,f2624]) ).
fof(f2626,plain,
( plus_plus_int(times_times_int(sK0_skl,sK0_skl),times_times_int(sK1_skl,sK1_skl)) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int)
| t != one_one_int ),
inference(forward_demodulation,[status(thm)],[f1470,f2625]) ).
fof(f2751,plain,
( plus_plus_int(power_power_int(sK2_skl,number_number_of_nat(bit0(bit1(zero_zero_int)))),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(forward_demodulation,[status(thm)],[f1470,f756]) ).
fof(f2752,plain,
( plus_plus_int(times_times_int(sK2_skl,sK2_skl),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(forward_demodulation,[status(thm)],[f2602,f2751]) ).
fof(f2753,plain,
( plus_plus_int(times_times_int(sK2_skl,sK2_skl),power_power_int(sK3_skl,number_number_of_nat(bit0(bit1(zero_zero_int))))) = 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(forward_demodulation,[status(thm)],[f1470,f2752]) ).
fof(f2754,plain,
( plus_plus_int(times_times_int(sK2_skl,sK2_skl),times_times_int(sK3_skl,sK3_skl)) = 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(forward_demodulation,[status(thm)],[f2602,f2753]) ).
fof(f2755,plain,
( plus_plus_int(times_times_int(sK2_skl,sK2_skl),times_times_int(sK3_skl,sK3_skl)) = plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int)
| ~ ord_less_int(one_one_int,t) ),
inference(forward_demodulation,[status(thm)],[f1470,f2754]) ).
fof(f2758,plain,
! [X0,X1] : plus_plus_int(times_times_int(X0,X0),times_times_int(X1,X1)) != plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int),
inference(paramodulation,[status(thm)],[f2602,f2612]) ).
fof(f2867,plain,
~ ord_less_int(one_one_int,t),
inference(backward_subsumption_resolution,[status(thm)],[f2755,f2758]) ).
fof(f2868,plain,
t != one_one_int,
inference(backward_subsumption_resolution,[status(thm)],[f2626,f2758]) ).
fof(f3486,plain,
( one_one_int = t
| ~ ord_less_eq_int(one_one_int,t)
| ~ is_int(t)
| ~ is_int(one_one_int) ),
inference(resolution,[status(thm)],[f798,f2867]) ).
fof(f3494,plain,
( one_one_int = t
| ~ ord_less_eq_int(one_one_int,t)
| ~ is_int(t) ),
inference(forward_subsumption_resolution,[status(thm)],[f3486,f721]) ).
fof(f3495,plain,
( one_one_int = t
| ~ ord_less_eq_int(one_one_int,t) ),
inference(forward_subsumption_resolution,[status(thm)],[f3494,f745]) ).
fof(f3496,plain,
one_one_int = t,
inference(resolution,[status(thm)],[f3495,f746]) ).
fof(f3500,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3496,f2868]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 03:17:49 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.46 % Elapsed time: 0.111346 seconds
% 0.12/0.46 % CPU time: 0.412300 seconds
% 0.12/0.46 % Total memory used: 150.189 MB
% 0.12/0.46 % Net memory used: 149.643 MB
%------------------------------------------------------------------------------