%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM925+7 : 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 : 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 01:44:06 PM UTC 2026
% Result : Theorem 3.74s 1.10s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.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 03:18:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.23/0.48 % Drodi V4.1.1
% 3.74/1.10 % Refutation found
% 3.74/1.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.74/1.10 % SZS output start CNFRefutation for theBenchmark
% 3.74/1.10 fof(f47,hypothesis,(
% 3.74/1.10 (! [B_1_1] : bit0(ti(int,B_1_1)) = bit0(B_1_1) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f50,hypothesis,(
% 3.74/1.10 (! [B_1_1] : ti(int,bit1(B_1_1)) = bit1(B_1_1) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f53,axiom,(
% 3.74/1.10 (! [B_1_1] : nat_1(ti(int,B_1_1)) = nat_1(B_1_1) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f135,axiom,(
% 3.74/1.10 one_one(int) = number_number_of(int,bit1(pls)) ),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f143,axiom,(
% 3.74/1.10 (! [Z1,Z2,Z3] : plus_plus(int,plus_plus(int,Z1,Z2),Z3) = plus_plus(int,Z1,plus_plus(int,Z2,Z3)) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f145,axiom,(
% 3.74/1.10 (! [Z,W] : plus_plus(int,Z,W) = plus_plus(int,W,Z) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f159,axiom,(
% 3.74/1.10 (! [K_1] : ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_1)),zero_zero(int))) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f170,axiom,(
% 3.74/1.10 bit0(pls) = pls ),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f171,axiom,(
% 3.74/1.10 pls = zero_zero(int) ),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f173,axiom,(
% 3.74/1.10 (! [K_1] : plus_plus(int,K_1,pls) = ti(int,K_1) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f176,axiom,(
% 3.74/1.10 (! [K_1] : bit0(K_1) = plus_plus(int,K_1,K_1) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f190,axiom,(
% 3.74/1.10 (! [K_1] : bit1(K_1) = plus_plus(int,plus_plus(int,one_one(int),K_1),K_1) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f218,axiom,(
% 3.74/1.10 (! [K_1] : number_number_of(int,K_1) = ti(int,K_1) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f524,axiom,(
% 3.74/1.10 (! [W] : nat_1(number_number_of(int,W)) = number_number_of(nat,W) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f615,axiom,(
% 3.74/1.10 (! [Wa,Z_1] :( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),plus_plus(int,Wa,one_one(int))),Z_1))<=> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)) ) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f617,axiom,(
% 3.74/1.10 (! [K_1] : succ(K_1) = plus_plus(int,K_1,one_one(int)) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f642,axiom,(
% 3.74/1.10 (! [X] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,bit0(bit1(pls)))))) )),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f1251,conjecture,(
% 3.74/1.10 hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ),
% 3.74/1.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.74/1.10 fof(f1252,negated_conjecture,(
% 3.74/1.10 ~(hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) )),
% 3.74/1.10 inference(negated_conjecture,[status(cth)],[f1251])).
% 3.74/1.10 fof(f1365,plain,(
% 3.74/1.10 ![X0]: (bit0(ti(int,X0))=bit0(X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f47])).
% 3.74/1.10 fof(f1368,plain,(
% 3.74/1.10 ![X0]: (ti(int,bit1(X0))=bit1(X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f50])).
% 3.74/1.10 fof(f1371,plain,(
% 3.74/1.10 ![X0]: (nat_1(ti(int,X0))=nat_1(X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f53])).
% 3.74/1.10 fof(f1546,plain,(
% 3.74/1.10 one_one(int)=number_number_of(int,bit1(pls))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f135])).
% 3.74/1.10 fof(f1572,plain,(
% 3.74/1.10 ![X0,X1,X2]: (plus_plus(int,plus_plus(int,X0,X1),X2)=plus_plus(int,X0,plus_plus(int,X1,X2)))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f143])).
% 3.74/1.10 fof(f1574,plain,(
% 3.74/1.10 ![X0,X1]: (plus_plus(int,X0,X1)=plus_plus(int,X1,X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f145])).
% 3.74/1.10 fof(f1624,plain,(
% 3.74/1.10 ![X0]: (~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X0)),zero_zero(int))))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f159])).
% 3.74/1.10 fof(f1656,plain,(
% 3.74/1.10 bit0(pls)=pls),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f170])).
% 3.74/1.10 fof(f1657,plain,(
% 3.74/1.10 pls=zero_zero(int)),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f171])).
% 3.74/1.10 fof(f1659,plain,(
% 3.74/1.10 ![X0]: (plus_plus(int,X0,pls)=ti(int,X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f173])).
% 3.74/1.10 fof(f1662,plain,(
% 3.74/1.10 ![X0]: (bit0(X0)=plus_plus(int,X0,X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f176])).
% 3.74/1.10 fof(f1689,plain,(
% 3.74/1.10 ![X0]: (bit1(X0)=plus_plus(int,plus_plus(int,one_one(int),X0),X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f190])).
% 3.74/1.10 fof(f1754,plain,(
% 3.74/1.10 ![X0]: (number_number_of(int,X0)=ti(int,X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f218])).
% 3.74/1.10 fof(f2696,plain,(
% 3.74/1.10 ![X0]: (nat_1(number_number_of(int,X0))=number_number_of(nat,X0))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f524])).
% 3.74/1.10 fof(f2989,plain,(
% 3.74/1.10 ![Wa,Z_1]: ((~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),plus_plus(int,Wa,one_one(int))),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1)))&(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),plus_plus(int,Wa,one_one(int))),Z_1))|~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))))),
% 3.74/1.10 inference(NNF_transformation,[status(thm)],[f615])).
% 3.74/1.10 fof(f2990,plain,(
% 3.74/1.10 (![Wa,Z_1]: (~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),plus_plus(int,Wa,one_one(int))),Z_1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))))&(![Wa,Z_1]: (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),plus_plus(int,Wa,one_one(int))),Z_1))|~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Z_1))))),
% 3.74/1.10 inference(miniscoping,[status(thm)],[f2989])).
% 3.74/1.10 fof(f2991,plain,(
% 3.74/1.10 ![X0,X1]: (~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),plus_plus(int,X0,one_one(int))),X1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f2990])).
% 3.74/1.10 fof(f2995,plain,(
% 3.74/1.10 ![X0]: (succ(X0)=plus_plus(int,X0,one_one(int)))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f617])).
% 3.74/1.10 fof(f3052,plain,(
% 3.74/1.10 ![X0]: (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),number_number_of(nat,bit0(bit1(pls)))))))),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f642])).
% 3.74/1.10 fof(f4535,plain,(
% 3.74/1.10 hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls))))=zero_zero(int)),
% 3.74/1.10 inference(cnf_transformation,[status(thm)],[f1252])).
% 3.74/1.10 fof(f4634,plain,(
% 3.74/1.10 hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(bit1(pls))))=pls),
% 3.74/1.10 inference(backward_demodulation,[status(thm)],[f1657,f4535])).
% 3.74/1.10 fof(f5447,plain,(
% 3.74/1.10 ![X0]: (~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X0)),pls)))),
% 3.74/1.10 inference(forward_demodulation,[status(thm)],[f1657,f1624])).
% 3.74/1.10 fof(f5608,plain,(
% 3.74/1.10 ![X0]: (bit1(X0)=plus_plus(int,one_one(int),plus_plus(int,X0,X0)))),
% 3.74/1.10 inference(forward_demodulation,[status(thm)],[f1572,f1689])).
% 3.74/1.10 fof(f5611,plain,(
% 3.74/1.10 ![X0]: (bit1(X0)=plus_plus(int,one_one(int),bit0(X0)))),
% 3.74/1.10 inference(forward_demodulation,[status(thm)],[f1662,f5608])).
% 3.74/1.10 fof(f5612,plain,(
% 3.74/1.10 bit1(pls)=plus_plus(int,one_one(int),pls)),
% 3.74/1.10 inference(paramodulation,[status(thm)],[f1656,f5611])).
% 3.74/1.10 fof(f5617,plain,(
% 3.74/1.10 bit1(pls)=ti(int,one_one(int))),
% 3.74/1.10 inference(forward_demodulation,[status(thm)],[f1659,f5612])).
% 3.74/1.10 fof(f5643,plain,(
% 3.74/1.10 bit0(bit1(pls))=bit0(one_one(int))),
% 3.74/1.10 inference(paramodulation,[status(thm)],[f5617,f1365])).
% 3.74/1.10 fof(f5976,plain,(
% 3.74/1.10 hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,bit0(one_one(int))))=pls),
% 3.74/1.10 inference(backward_demodulation,[status(thm)],[f5643,f4634])).
% 3.74/1.10 fof(f9211,plain,(
% 3.74/1.10 one_one(int)=ti(int,bit1(pls))),
% 3.74/1.10 inference(backward_demodulation,[status(thm)],[f1754,f1546])).
% 3.74/1.10 fof(f9226,plain,(
% 3.74/1.10 one_one(int)=bit1(pls)),
% 3.74/1.13 inference(forward_demodulation,[status(thm)],[f1368,f9211])).
% 3.74/1.13 fof(f11646,plain,(
% 3.74/1.13 ![X0]: (nat_1(ti(int,X0))=number_number_of(nat,X0))),
% 3.74/1.13 inference(forward_demodulation,[status(thm)],[f1754,f2696])).
% 3.74/1.13 fof(f11671,plain,(
% 3.74/1.13 hAPP(nat,int,power_power(int,plus_plus(int,one_one(int),hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(bit0(one_one(int))))=pls),
% 3.74/1.13 inference(backward_demodulation,[status(thm)],[f11686,f5976])).
% 3.74/1.13 fof(f11686,plain,(
% 3.74/1.13 ![X0]: (nat_1(X0)=number_number_of(nat,X0))),
% 3.74/1.13 inference(forward_demodulation,[status(thm)],[f1371,f11646])).
% 3.74/1.13 fof(f11774,plain,(
% 3.74/1.13 ![X0]: (succ(X0)=plus_plus(int,one_one(int),X0))),
% 3.74/1.13 inference(paramodulation,[status(thm)],[f1574,f2995])).
% 3.74/1.13 fof(f11833,plain,(
% 3.74/1.13 hAPP(nat,int,power_power(int,succ(hAPP(nat,int,semiring_1_of_nat(int),n))),nat_1(bit0(one_one(int))))=pls),
% 3.74/1.13 inference(backward_demodulation,[status(thm)],[f11774,f11671])).
% 3.74/1.13 fof(f12577,plain,(
% 3.74/1.13 ![X0,X1]: (~hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),succ(X0)),X1))|hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X0),X1)))),
% 3.74/1.13 inference(forward_demodulation,[status(thm)],[f2995,f2991])).
% 3.74/1.13 fof(f13093,plain,(
% 3.74/1.13 ![X0]: (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),nat_1(bit0(bit1(pls)))))))),
% 3.74/1.13 inference(forward_demodulation,[status(thm)],[f11686,f3052])).
% 3.74/1.13 fof(f13094,plain,(
% 3.74/1.13 ![X0]: (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X0),hAPP(nat,int,power_power(int,X0),nat_1(bit0(one_one(int)))))))),
% 3.74/1.13 inference(forward_demodulation,[status(thm)],[f9226,f13093])).
% 3.74/1.13 fof(f13110,plain,(
% 3.74/1.13 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),succ(hAPP(nat,int,semiring_1_of_nat(int),n))),pls))),
% 3.74/1.13 inference(paramodulation,[status(thm)],[f11833,f13094])).
% 3.74/1.13 fof(f13316,plain,(
% 3.74/1.13 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),n)),pls))),
% 3.74/1.13 inference(resolution,[status(thm)],[f13110,f12577])).
% 3.74/1.13 fof(f13326,plain,(
% 3.74/1.13 $false),
% 3.74/1.13 inference(forward_subsumption_resolution,[status(thm)],[f13316,f5447])).
% 3.74/1.13 % SZS output end CNFRefutation for theBenchmark.p
% 3.74/1.14 % Elapsed time: 0.777449 seconds
% 3.74/1.14 % CPU time: 5.094280 seconds
% 3.74/1.14 % Total memory used: 298.005 MB
% 3.74/1.14 % Net memory used: 293.222 MB
%------------------------------------------------------------------------------