%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 01:44:07 PM UTC 2026
% Result : Theorem 0.12s 0.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 03:21:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.50 % Refutation found
% 0.12/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.50 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.50 fof(f2,hypothesis,(
% 0.12/0.50 is_int(one_one_int) ),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f18,axiom,(
% 0.12/0.50 is_int(t) ),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f19,axiom,(
% 0.12/0.50 ord_less_eq_int(one_one_int,t) ),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f20,axiom,(
% 0.12/0.50 ( t = one_one_int=> (? [X,Y] :( is_int(X)& is_int(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) ) )) ),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f21,axiom,(
% 0.12/0.50 ( ord_less_int(one_one_int,t)=> (? [X,Y] :( is_int(X)& is_int(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) ) )) ),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f56,axiom,(
% 0.12/0.50 (! [Z_1,W_1] :( ( is_int(Z_1)& is_int(W_1) )=> ( ord_less_int(Z_1,W_1)<=> ( ord_less_eq_int(Z_1,W_1)& Z_1 != W_1 ) ) ) )),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f375,axiom,(
% 0.12/0.50 pls = zero_zero_int ),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f717,conjecture,(
% 0.12/0.50 (? [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) )),
% 0.12/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.50 fof(f718,negated_conjecture,(
% 0.12/0.50 ~((? [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) ))),
% 0.12/0.50 inference(negated_conjecture,[status(cth)],[f717])).
% 0.12/0.50 fof(f721,plain,(
% 0.12/0.50 is_int(one_one_int)),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.50 fof(f745,plain,(
% 0.12/0.50 is_int(t)),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f18])).
% 0.12/0.50 fof(f746,plain,(
% 0.12/0.50 ord_less_eq_int(one_one_int,t)),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f19])).
% 0.12/0.50 fof(f747,plain,(
% 0.12/0.50 ~t=one_one_int|(?[X,Y]: ((is_int(X)&is_int(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)))),
% 0.12/0.50 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.12/0.50 fof(f748,plain,(
% 0.12/0.50 ~t=one_one_int|((is_int(sK0_skl)&is_int(sK1_skl))&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))),
% 0.12/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f747])).
% 0.12/0.50 fof(f751,plain,(
% 0.12/0.50 ~t=one_one_int|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)),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f748])).
% 0.12/0.50 fof(f752,plain,(
% 0.12/0.50 ~ord_less_int(one_one_int,t)|(?[X,Y]: ((is_int(X)&is_int(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)))),
% 0.12/0.50 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.12/0.50 fof(f753,plain,(
% 0.12/0.50 ~ord_less_int(one_one_int,t)|((is_int(sK2_skl)&is_int(sK3_skl))&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))),
% 0.12/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f752])).
% 0.12/0.50 fof(f756,plain,(
% 0.12/0.50 ~ord_less_int(one_one_int,t)|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)),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f753])).
% 0.12/0.50 fof(f794,plain,(
% 0.12/0.50 ![Z_1,W_1]: ((~is_int(Z_1)|~is_int(W_1))|(ord_less_int(Z_1,W_1)<=>(ord_less_eq_int(Z_1,W_1)&~Z_1=W_1)))),
% 0.12/0.50 inference(pre_NNF_transformation,[status(thm)],[f56])).
% 0.12/0.50 fof(f795,plain,(
% 0.12/0.50 ![Z_1,W_1]: ((~is_int(Z_1)|~is_int(W_1))|((~ord_less_int(Z_1,W_1)|(ord_less_eq_int(Z_1,W_1)&~Z_1=W_1))&(ord_less_int(Z_1,W_1)|(~ord_less_eq_int(Z_1,W_1)|Z_1=W_1))))),
% 0.12/0.50 inference(NNF_transformation,[status(thm)],[f794])).
% 0.12/0.50 fof(f798,plain,(
% 0.12/0.50 ![X0,X1]: (~is_int(X0)|~is_int(X1)|ord_less_int(X0,X1)|~ord_less_eq_int(X0,X1)|X0=X1)),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f795])).
% 0.12/0.50 fof(f1470,plain,(
% 0.12/0.50 pls=zero_zero_int),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f375])).
% 0.12/0.50 fof(f2405,plain,(
% 0.12/0.50 (![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))),
% 0.12/0.50 inference(pre_NNF_transformation,[status(thm)],[f718])).
% 0.12/0.50 fof(f2406,plain,(
% 0.12/0.50 ![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))),
% 0.12/0.50 inference(cnf_transformation,[status(thm)],[f2405])).
% 0.12/0.50 fof(f2407,definition,(
% 0.12/0.50 sQ0_spl <=> (t=one_one_int)),
% 0.12/0.50 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.50 fof(f2418,definition,(
% 0.12/0.50 sQ3_spl <=> (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))),
% 0.12/0.50 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.50 fof(f2419,plain,(
% 0.12/0.50 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)|~sQ3_spl),
% 0.12/0.50 inference(component_clause,[status(thm)],[f2418])).
% 0.12/0.50 fof(f2421,plain,(
% 0.12/0.50 ~sQ0_spl|sQ3_spl),
% 0.12/0.50 inference(split_clause,[status(thm)],[f751,f2407,f2418])).
% 0.12/0.50 fof(f2422,definition,(
% 0.12/0.50 sQ4_spl <=> (ord_less_int(one_one_int,t))),
% 0.12/0.50 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.50 fof(f2433,definition,(
% 0.12/0.50 sQ7_spl <=> (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))),
% 0.12/0.50 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.50 fof(f2434,plain,(
% 0.12/0.50 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)|~sQ7_spl),
% 0.12/0.50 inference(component_clause,[status(thm)],[f2433])).
% 0.12/0.50 fof(f2436,plain,(
% 0.12/0.50 ~sQ4_spl|sQ7_spl),
% 0.12/0.50 inference(split_clause,[status(thm)],[f756,f2422,f2433])).
% 0.12/0.50 fof(f2645,plain,(
% 0.12/0.50 ![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))),
% 0.12/0.50 inference(backward_demodulation,[status(thm)],[f1470,f2406])).
% 0.12/0.50 fof(f2662,plain,(
% 0.12/0.50 ![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))),
% 0.12/0.50 inference(forward_demodulation,[status(thm)],[f1470,f2645])).
% 0.12/0.50 fof(f2663,plain,(
% 0.12/0.50 ![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))),
% 0.12/0.50 inference(forward_demodulation,[status(thm)],[f1470,f2662])).
% 0.12/0.50 fof(f3006,definition,(
% 0.12/0.50 sQ11_spl <=> (is_int(one_one_int))),
% 0.12/0.50 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.12/0.50 fof(f3008,plain,(
% 0.12/0.50 ~is_int(one_one_int)|sQ11_spl),
% 0.12/0.50 inference(component_clause,[status(thm)],[f3006])).
% 0.12/0.50 fof(f3013,definition,(
% 0.12/0.50 sQ13_spl <=> (is_int(t))),
% 0.12/0.50 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.12/0.50 fof(f3015,plain,(
% 0.12/0.50 ~is_int(t)|sQ13_spl),
% 0.12/0.50 inference(component_clause,[status(thm)],[f3013])).
% 0.12/0.50 fof(f3023,plain,(
% 0.12/0.50 $false|sQ13_spl),
% 0.12/0.50 inference(forward_subsumption_resolution,[status(thm)],[f3015,f745])).
% 0.12/0.50 fof(f3024,plain,(
% 0.12/0.50 sQ13_spl),
% 0.12/0.50 inference(contradiction_clause,[status(thm)],[f3023])).
% 0.12/0.50 fof(f3060,plain,(
% 0.12/0.50 ~is_int(one_one_int)|~is_int(t)|ord_less_int(one_one_int,t)|one_one_int=t),
% 0.12/0.50 inference(resolution,[status(thm)],[f798,f746])).
% 0.12/0.50 fof(f3103,plain,(
% 0.12/0.50 ~sQ11_spl|~sQ13_spl|sQ4_spl|sQ0_spl),
% 0.12/0.50 inference(split_clause,[status(thm)],[f3060,f3006,f3013,f2422,f2407])).
% 0.12/0.50 fof(f3106,plain,(
% 0.12/0.50 $false|sQ11_spl),
% 0.12/0.50 inference(forward_subsumption_resolution,[status(thm)],[f3008,f721])).
% 0.12/0.50 fof(f3107,plain,(
% 0.12/0.50 sQ11_spl),
% 0.12/0.50 inference(contradiction_clause,[status(thm)],[f3106])).
% 0.12/0.50 fof(f3114,plain,(
% 0.12/0.50 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)|~sQ7_spl),
% 0.12/0.50 inference(forward_demodulation,[status(thm)],[f1470,f2434])).
% 0.12/0.50 fof(f3115,plain,(
% 0.12/0.50 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(zero_zero_int)))))=plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)|~sQ7_spl),
% 0.12/0.50 inference(forward_demodulation,[status(thm)],[f1470,f3114])).
% 0.12/0.50 fof(f3116,plain,(
% 0.12/0.50 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(zero_zero_int)))))=plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int)|~sQ7_spl),
% 0.12/0.50 inference(forward_demodulation,[status(thm)],[f1470,f3115])).
% 0.12/0.50 fof(f3117,plain,(
% 0.12/0.50 $false|~sQ7_spl),
% 0.12/0.50 inference(forward_subsumption_resolution,[status(thm)],[f3116,f2663])).
% 0.12/0.50 fof(f3118,plain,(
% 0.12/0.50 ~sQ7_spl),
% 0.12/0.50 inference(contradiction_clause,[status(thm)],[f3117])).
% 0.12/0.50 fof(f3119,plain,(
% 0.12/0.51 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)|~sQ3_spl),
% 0.12/0.51 inference(forward_demodulation,[status(thm)],[f1470,f2419])).
% 0.12/0.51 fof(f3120,plain,(
% 0.12/0.51 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(zero_zero_int)))))=plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls)))),m),one_one_int)|~sQ3_spl),
% 0.12/0.51 inference(forward_demodulation,[status(thm)],[f1470,f3119])).
% 0.12/0.51 fof(f3121,plain,(
% 0.12/0.51 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(zero_zero_int)))))=plus_plus_int(times_times_int(number_number_of_int(bit0(bit0(bit1(zero_zero_int)))),m),one_one_int)|~sQ3_spl),
% 0.12/0.51 inference(forward_demodulation,[status(thm)],[f1470,f3120])).
% 0.12/0.51 fof(f3122,plain,(
% 0.12/0.51 $false|~sQ3_spl),
% 0.12/0.51 inference(forward_subsumption_resolution,[status(thm)],[f3121,f2663])).
% 0.12/0.51 fof(f3123,plain,(
% 0.12/0.51 ~sQ3_spl),
% 0.12/0.51 inference(contradiction_clause,[status(thm)],[f3122])).
% 0.12/0.51 fof(f3124,plain,(
% 0.12/0.51 $false),
% 0.12/0.51 inference(sat_refutation,[status(thm)],[f2421,f2436,f3024,f3103,f3107,f3118,f3123])).
% 0.12/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.53 % Elapsed time: 0.169753 seconds
% 0.12/0.53 % CPU time: 0.833725 seconds
% 0.12/0.53 % Total memory used: 159.174 MB
% 0.12/0.53 % Net memory used: 158.479 MB
%------------------------------------------------------------------------------