%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM925+6 : 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 : n005.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 01:44:06 PM UTC 2026
% Result : Theorem 0.21s 0.54s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+6 : 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 : n005.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 03:17:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.43 % Drodi V4.1.1
% 0.21/0.54 % Refutation found
% 0.21/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.54 % SZS output start CNFRefutation for theBenchmark
% 0.21/0.54 fof(f15,axiom,(
% 0.21/0.54 (! [B_1_1,X_a] :( number(X_a)=> number_number_of(X_a,ti(int,B_1_1)) = number_number_of(X_a,B_1_1) ) )),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f46,axiom,(
% 0.21/0.54 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f51,axiom,(
% 0.21/0.54 (! [X_a] :( ring_11004092258visors(X_a)=> (! [A_2] :( hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a)<=> ti(X_a,A_2) = zero_zero(X_a) ) )) )),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f78,axiom,(
% 0.21/0.54 ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) ),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f83,axiom,(
% 0.21/0.54 one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)) ),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f119,axiom,(
% 0.21/0.54 pls = zero_zero(int) ),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f165,axiom,(
% 0.21/0.54 (! [K] : number_number_of(int,K) = K )),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f554,axiom,(
% 0.21/0.54 ring_11004092258visors(int) ),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f581,axiom,(
% 0.21/0.54 number(int) ),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f660,conjecture,(
% 0.21/0.54 hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
% 0.21/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.21/0.54 fof(f661,negated_conjecture,(
% 0.21/0.54 ~(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) )),
% 0.21/0.54 inference(negated_conjecture,[status(cth)],[f660])).
% 0.21/0.54 fof(f691,plain,(
% 0.21/0.54 ![B_1_1,X_a]: (~number(X_a)|number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1))),
% 0.21/0.54 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.21/0.54 fof(f692,plain,(
% 0.21/0.54 ![X_a]: (~number(X_a)|(![B_1_1]: number_number_of(X_a,ti(int,B_1_1))=number_number_of(X_a,B_1_1)))),
% 0.21/0.54 inference(miniscoping,[status(thm)],[f691])).
% 0.21/0.54 fof(f693,plain,(
% 0.21/0.54 ![X0,X1]: (~number(X0)|number_number_of(X0,ti(int,X1))=number_number_of(X0,X1))),
% 0.21/0.54 inference(cnf_transformation,[status(thm)],[f692])).
% 0.21/0.54 fof(f748,plain,(
% 0.21/0.54 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))),
% 0.21/0.54 inference(cnf_transformation,[status(thm)],[f46])).
% 0.21/0.54 fof(f760,plain,(
% 0.21/0.54 ![X_a]: (~ring_11004092258visors(X_a)|(![A_2]: (hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)<=>ti(X_a,A_2)=zero_zero(X_a))))),
% 0.21/0.54 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 0.21/0.54 fof(f761,plain,(
% 0.21/0.54 ![X_a]: (~ring_11004092258visors(X_a)|(![A_2]: ((~hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a))&(hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)|~ti(X_a,A_2)=zero_zero(X_a)))))),
% 0.21/0.54 inference(NNF_transformation,[status(thm)],[f760])).
% 0.21/0.54 fof(f762,plain,(
% 0.21/0.54 ![X_a]: (~ring_11004092258visors(X_a)|((![A_2]: (~hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)|ti(X_a,A_2)=zero_zero(X_a)))&(![A_2]: (hAPP(nat,X_a,power_power(X_a,A_2),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X_a)|~ti(X_a,A_2)=zero_zero(X_a)))))),
% 0.21/0.54 inference(miniscoping,[status(thm)],[f761])).
% 0.21/0.54 fof(f763,plain,(
% 0.21/0.54 ![X0,X1]: (~ring_11004092258visors(X0)|~hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(X0)|ti(X0,X1)=zero_zero(X0))),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f762])).
% 0.21/0.55 fof(f816,plain,(
% 0.21/0.55 ~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls))),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f78])).
% 0.21/0.55 fof(f833,plain,(
% 0.21/0.55 one_one(int)=number_number_of(int,hAPP(int,int,bit1,pls))),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f83])).
% 0.21/0.55 fof(f944,plain,(
% 0.21/0.55 pls=zero_zero(int)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f119])).
% 0.21/0.55 fof(f1040,plain,(
% 0.21/0.55 ![X0]: (number_number_of(int,X0)=X0)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f165])).
% 0.21/0.55 fof(f2255,plain,(
% 0.21/0.55 ring_11004092258visors(int)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f554])).
% 0.21/0.55 fof(f2282,plain,(
% 0.21/0.55 number(int)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f581])).
% 0.21/0.55 fof(f2361,plain,(
% 0.21/0.55 hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=zero_zero(int)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f661])).
% 0.21/0.55 fof(f2427,plain,(
% 0.21/0.55 hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))=pls),
% 0.21/0.55 inference(backward_demodulation,[status(thm)],[f944,f2361])).
% 0.21/0.55 fof(f2430,plain,(
% 0.21/0.55 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f944,f748])).
% 0.21/0.55 fof(f2465,plain,(
% 0.21/0.55 hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))=pls),
% 0.21/0.55 inference(backward_demodulation,[status(thm)],[f2466,f2427])).
% 0.21/0.55 fof(f2466,plain,(
% 0.21/0.55 one_one(int)=hAPP(int,int,bit1,pls)),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f1040,f833])).
% 0.21/0.55 fof(f2548,plain,(
% 0.21/0.55 ![X0]: (number_number_of(int,ti(int,X0))=number_number_of(int,X0))),
% 0.21/0.55 inference(resolution,[status(thm)],[f2282,f693])).
% 0.21/0.55 fof(f2549,plain,(
% 0.21/0.55 ![X0]: (ti(int,X0)=number_number_of(int,X0))),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f1040,f2548])).
% 0.21/0.55 fof(f2550,plain,(
% 0.21/0.55 ![X0]: (ti(int,X0)=X0)),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f1040,f2549])).
% 0.21/0.55 fof(f3584,plain,(
% 0.21/0.55 ![X0,X1]: (~ring_11004092258visors(X0)|~hAPP(nat,X0,power_power(X0,X1),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))=zero_zero(X0)|ti(X0,X1)=zero_zero(X0))),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f2466,f763])).
% 0.21/0.55 fof(f3586,plain,(
% 0.21/0.55 ![X0]: (~hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))=zero_zero(int)|ti(int,X0)=zero_zero(int))),
% 0.21/0.55 inference(resolution,[status(thm)],[f3584,f2255])).
% 0.21/0.55 fof(f3587,plain,(
% 0.21/0.55 ![X0]: (~hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))=pls|ti(int,X0)=zero_zero(int))),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f944,f3586])).
% 0.21/0.55 fof(f3588,plain,(
% 0.21/0.55 ![X0]: (~hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))=pls|X0=zero_zero(int))),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f2550,f3587])).
% 0.21/0.55 fof(f3589,plain,(
% 0.21/0.55 ![X0]: (~hAPP(nat,int,power_power(int,X0),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))=pls|X0=pls)),
% 0.21/0.55 inference(forward_demodulation,[status(thm)],[f944,f3588])).
% 0.21/0.55 fof(f3602,plain,(
% 0.21/0.55 hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))=pls),
% 0.21/0.55 inference(resolution,[status(thm)],[f3589,f2465])).
% 0.21/0.55 fof(f3615,plain,(
% 0.21/0.55 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls))),
% 0.21/0.55 inference(backward_demodulation,[status(thm)],[f3602,f2430])).
% 0.21/0.55 fof(f3620,plain,(
% 0.21/0.55 $false),
% 0.21/0.55 inference(forward_subsumption_resolution,[status(thm)],[f3615,f816])).
% 0.21/0.55 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/0.56 % Elapsed time: 0.199141 seconds
% 0.21/0.56 % CPU time: 0.821284 seconds
% 0.21/0.56 % Total memory used: 174.639 MB
% 0.21/0.56 % Net memory used: 173.640 MB
%------------------------------------------------------------------------------