%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.15s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n013.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Mon Sep 21 03:17:36 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.15/0.59 % Drodi V4.1.1
% 0.15/0.62 % Refutation found
% 0.15/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.62 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.62 fof(f1,axiom,(
% 0.15/0.62 ord_less_eq_int(one_one_int,t) ),
% 0.15/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.62 fof(f2,axiom,(
% 0.15/0.62 ( 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) )) ),
% 0.15/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.62 fof(f3,axiom,(
% 0.15/0.62 ( 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) )) ),
% 0.15/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.62 fof(f29,axiom,(
% 0.15/0.62 (! [Z_1,W_1] :( ord_less_int(Z_1,W_1)<=> ( ord_less_eq_int(Z_1,W_1)& Z_1 != W_1 ) ) )),
% 0.15/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.62 fof(f112,axiom,(
% 0.15/0.62 (! [K_1] : number_number_of_int(K_1) = K_1 )),
% 0.15/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.62 fof(f124,conjecture,(
% 0.15/0.62 (? [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) )),
% 0.15/0.62 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.62 fof(f125,negated_conjecture,(
% 0.15/0.62 ~((? [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) ))),
% 0.15/0.62 inference(negated_conjecture,[status(cth)],[f124])).
% 0.15/0.62 fof(f126,plain,(
% 0.15/0.62 ord_less_eq_int(one_one_int,t)),
% 0.15/0.62 inference(cnf_transformation,[status(thm)],[f1])).
% 0.15/0.62 fof(f127,plain,(
% 0.15/0.62 ~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))),
% 0.15/0.62 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.15/0.62 fof(f128,plain,(
% 0.15/0.62 ~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)),
% 0.15/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f127])).
% 0.15/0.62 fof(f129,plain,(
% 0.15/0.62 ~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)),
% 0.15/0.62 inference(cnf_transformation,[status(thm)],[f128])).
% 0.15/0.62 fof(f130,plain,(
% 0.15/0.62 ~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))),
% 0.15/0.62 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.15/0.62 fof(f131,plain,(
% 0.15/0.62 ~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)),
% 0.15/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f130])).
% 0.15/0.62 fof(f132,plain,(
% 0.15/0.62 ~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)),
% 0.15/0.62 inference(cnf_transformation,[status(thm)],[f131])).
% 0.15/0.62 fof(f160,plain,(
% 0.15/0.62 ![Z_1,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)))),
% 0.15/0.62 inference(NNF_transformation,[status(thm)],[f29])).
% 0.15/0.62 fof(f161,plain,(
% 0.15/0.62 (![Z_1,W_1]: (~ord_less_int(Z_1,W_1)|(ord_less_eq_int(Z_1,W_1)&~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)))),
% 0.15/0.62 inference(miniscoping,[status(thm)],[f160])).
% 0.15/0.62 fof(f164,plain,(
% 0.15/0.62 ![X0,X1]: (ord_less_int(X0,X1)|~ord_less_eq_int(X0,X1)|X0=X1)),
% 0.15/0.62 inference(cnf_transformation,[status(thm)],[f161])).
% 0.15/0.62 fof(f344,plain,(
% 0.15/0.62 ![X0]: (number_number_of_int(X0)=X0)),
% 0.15/0.62 inference(cnf_transformation,[status(thm)],[f112])).
% 0.15/0.62 fof(f380,plain,(
% 0.15/0.62 (![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))),
% 0.15/0.62 inference(pre_NNF_transformation,[status(thm)],[f125])).
% 0.15/0.62 fof(f381,plain,(
% 0.15/0.62 ![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))),
% 0.15/0.62 inference(cnf_transformation,[status(thm)],[f380])).
% 0.15/0.62 fof(f382,definition,(
% 0.15/0.62 sQ0_spl <=> (t=one_one_int)),
% 0.15/0.62 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.62 fof(f385,definition,(
% 0.15/0.62 sQ1_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))),
% 0.15/0.62 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.62 fof(f386,plain,(
% 0.15/0.62 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)|~sQ1_spl),
% 0.15/0.63 inference(component_clause,[status(thm)],[f385])).
% 0.15/0.63 fof(f388,plain,(
% 0.15/0.63 ~sQ0_spl|sQ1_spl),
% 0.15/0.63 inference(split_clause,[status(thm)],[f129,f382,f385])).
% 0.15/0.63 fof(f389,definition,(
% 0.15/0.63 sQ2_spl <=> (ord_less_int(one_one_int,t))),
% 0.15/0.63 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/0.63 fof(f392,definition,(
% 0.15/0.63 sQ3_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))),
% 0.15/0.63 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/0.63 fof(f393,plain,(
% 0.15/0.63 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)|~sQ3_spl),
% 0.15/0.63 inference(component_clause,[status(thm)],[f392])).
% 0.15/0.63 fof(f395,plain,(
% 0.15/0.63 ~sQ2_spl|sQ3_spl),
% 0.15/0.63 inference(split_clause,[status(thm)],[f132,f389,f392])).
% 0.15/0.63 fof(f397,plain,(
% 0.15/0.63 ![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(bit0(bit0(bit1(pls))),m),one_one_int))),
% 0.15/0.63 inference(backward_demodulation,[status(thm)],[f344,f381])).
% 0.15/0.63 fof(f539,plain,(
% 0.15/0.63 ord_less_int(one_one_int,t)|one_one_int=t),
% 0.15/0.63 inference(resolution,[status(thm)],[f164,f126])).
% 0.15/0.63 fof(f547,plain,(
% 0.15/0.63 sQ2_spl|sQ0_spl),
% 0.15/0.63 inference(split_clause,[status(thm)],[f539,f389,f382])).
% 0.15/0.63 fof(f548,plain,(
% 0.15/0.63 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(bit0(bit0(bit1(pls))),m),one_one_int)|~sQ3_spl),
% 0.15/0.63 inference(forward_demodulation,[status(thm)],[f344,f393])).
% 0.15/0.63 fof(f549,plain,(
% 0.15/0.63 $false|~sQ3_spl),
% 0.15/0.63 inference(forward_subsumption_resolution,[status(thm)],[f548,f397])).
% 0.15/0.63 fof(f550,plain,(
% 0.15/0.63 ~sQ3_spl),
% 0.15/0.63 inference(contradiction_clause,[status(thm)],[f549])).
% 0.15/0.63 fof(f551,plain,(
% 0.15/0.63 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(bit0(bit0(bit1(pls))),m),one_one_int)|~sQ1_spl),
% 0.15/0.63 inference(forward_demodulation,[status(thm)],[f344,f386])).
% 0.15/0.63 fof(f552,plain,(
% 0.15/0.63 $false|~sQ1_spl),
% 0.15/0.63 inference(forward_subsumption_resolution,[status(thm)],[f551,f397])).
% 0.15/0.63 fof(f553,plain,(
% 0.15/0.63 ~sQ1_spl),
% 0.15/0.63 inference(contradiction_clause,[status(thm)],[f552])).
% 0.15/0.63 fof(f554,plain,(
% 0.15/0.63 $false),
% 0.15/0.63 inference(sat_refutation,[status(thm)],[f388,f395,f547,f550,f553])).
% 0.15/0.63 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.64 % Elapsed time: 0.059829 seconds
% 0.15/0.64 % CPU time: 0.185971 seconds
% 0.15/0.64 % Total memory used: 92.294 MB
% 0.15/0.64 % Net memory used: 92.113 MB
%------------------------------------------------------------------------------