%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM926+5 : 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 : n011.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 01:44:08 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 03:18:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f28,axiom,(
% 0.10/0.40 ord_less_eq(int,one_one(int),t) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f29,axiom,(
% 0.10/0.40 ( 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)) )) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f30,axiom,(
% 0.10/0.40 ( 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)) )) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f50,axiom,(
% 0.10/0.40 (! [Z_1,W_1] :( ord_less(int,Z_1,W_1)<=> ( ord_less_eq(int,Z_1,W_1)& Z_1 != W_1 ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f114,axiom,(
% 0.10/0.40 (! [K_1] : number_number_of(int,K_1) = K_1 )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f142,conjecture,(
% 0.10/0.40 (? [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)) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f143,negated_conjecture,(
% 0.10/0.40 ~((? [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)) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f142])).
% 0.10/0.40 fof(f216,plain,(
% 0.10/0.40 ord_less_eq(int,one_one(int),t)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f28])).
% 0.10/0.40 fof(f217,plain,(
% 0.10/0.40 ~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)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.10/0.40 fof(f218,plain,(
% 0.10/0.40 ~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))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f217])).
% 0.10/0.40 fof(f219,plain,(
% 0.10/0.40 ~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))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f218])).
% 0.10/0.40 fof(f220,plain,(
% 0.10/0.40 ~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)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.10/0.40 fof(f221,plain,(
% 0.10/0.40 ~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))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f220])).
% 0.10/0.40 fof(f222,plain,(
% 0.10/0.40 ~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))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f221])).
% 0.10/0.40 fof(f253,plain,(
% 0.10/0.40 ![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)))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f50])).
% 0.10/0.40 fof(f254,plain,(
% 0.10/0.40 (![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)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f253])).
% 0.10/0.40 fof(f257,plain,(
% 0.10/0.40 ![X0,X1]: (ord_less(int,X0,X1)|~ord_less_eq(int,X0,X1)|X0=X1)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f254])).
% 0.10/0.40 fof(f434,plain,(
% 0.10/0.40 ![X0]: (number_number_of(int,X0)=X0)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f114])).
% 0.10/0.40 fof(f486,plain,(
% 0.10/0.40 (![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)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f143])).
% 0.10/0.40 fof(f487,plain,(
% 0.10/0.40 ![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)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f486])).
% 0.10/0.40 fof(f488,definition,(
% 0.10/0.40 sQ0_spl <=> (t=one_one(int))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f491,definition,(
% 0.10/0.40 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)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f492,plain,(
% 0.10/0.40 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),
% 0.10/0.40 inference(component_clause,[status(thm)],[f491])).
% 0.10/0.40 fof(f494,plain,(
% 0.10/0.40 ~sQ0_spl|sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f219,f488,f491])).
% 0.10/0.40 fof(f495,definition,(
% 0.10/0.40 sQ2_spl <=> (ord_less(int,one_one(int),t))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f498,definition,(
% 0.10/0.40 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)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f499,plain,(
% 0.10/0.40 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),
% 0.10/0.40 inference(component_clause,[status(thm)],[f498])).
% 0.10/0.40 fof(f501,plain,(
% 0.10/0.40 ~sQ2_spl|sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f222,f495,f498])).
% 0.10/0.40 fof(f503,plain,(
% 0.10/0.40 ![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)))),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f434,f487])).
% 0.10/0.40 fof(f820,plain,(
% 0.10/0.40 ord_less(int,one_one(int),t)|one_one(int)=t),
% 0.10/0.40 inference(resolution,[status(thm)],[f257,f216])).
% 0.10/0.40 fof(f835,plain,(
% 0.10/0.40 sQ2_spl|sQ0_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f820,f495,f488])).
% 0.10/0.40 fof(f836,plain,(
% 0.10/0.40 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),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f434,f499])).
% 0.10/0.40 fof(f837,plain,(
% 0.10/0.40 $false|~sQ3_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f836,f503])).
% 0.10/0.40 fof(f838,plain,(
% 0.10/0.41 ~sQ3_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f837])).
% 0.10/0.41 fof(f839,plain,(
% 0.10/0.41 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),
% 0.10/0.41 inference(forward_demodulation,[status(thm)],[f434,f492])).
% 0.10/0.41 fof(f840,plain,(
% 0.10/0.41 $false|~sQ1_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f839,f503])).
% 0.10/0.41 fof(f841,plain,(
% 0.10/0.41 ~sQ1_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f840])).
% 0.10/0.41 fof(f842,plain,(
% 0.10/0.41 $false),
% 0.10/0.41 inference(sat_refutation,[status(thm)],[f494,f501,f835,f838,f841])).
% 0.10/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.067480 seconds
% 0.10/0.43 % CPU time: 0.239907 seconds
% 0.10/0.43 % Total memory used: 62.183 MB
% 0.10/0.43 % Net memory used: 62.012 MB
%------------------------------------------------------------------------------