%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWV632-1 : TPTP v9.3.1. Released v4.1.0.
% 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 02:52:56 PM UTC 2026
% Result : Unsatisfiable 199.58s 25.91s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV632-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 09:15:26 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.26/0.59 % Drodi V4.1.1
% 199.58/25.91 % Refutation found
% 199.58/25.91 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 199.58/25.91 % SZS output start CNFRefutation for theBenchmark
% 199.58/25.91 fof(f67,axiom,(
% 199.58/25.91 (![V_n,V_m]: (( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| V_m = V_n ) ))),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f290,axiom,(
% 199.58/25.91 (![V_nat_H]: (c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ))),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f623,axiom,(
% 199.58/25.91 (![V_m]: (~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ))),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f822,axiom,(
% 199.58/25.91 c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f1127,axiom,(
% 199.58/25.91 (![V_d,V_n,V_k]: (( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex)| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) ) ))),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f1150,axiom,(
% 199.58/25.91 c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f1306,axiom,(
% 199.58/25.91 (![V_z]: (c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ))),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f1307,axiom,(
% 199.58/25.91 (![V_z]: (c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ))),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f1326,axiom,(
% 199.58/25.91 (![V_m,V_n,V_k]: (c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat) ))),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f1352,negated_conjecture,(
% 199.58/25.91 c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ),
% 199.58/25.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 199.58/25.91 fof(f1590,plain,(
% 199.58/25.91 ![X0,X1]: (c_HOL_Oord__class_Oless(X0,X1,tc_nat)|c_HOL_Oord__class_Oless(X1,X0,tc_nat)|X1=X0)),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f67])).
% 199.58/25.91 fof(f1941,plain,(
% 199.58/25.91 ![X0]: (~c_HOL_Ozero__class_Ozero(tc_nat)=c_Suc(X0))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f290])).
% 199.58/25.91 fof(f2462,plain,(
% 199.58/25.91 ![X0]: (~c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f623])).
% 199.58/25.91 fof(f2769,plain,(
% 199.58/25.91 c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f822])).
% 199.58/25.91 fof(f3260,plain,(
% 199.58/25.91 ![V_d]: ((![V_n,V_k]: c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex))|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat))),
% 199.58/25.91 inference(miniscoping,[status(thm)],[f1127])).
% 199.58/25.91 fof(f3261,plain,(
% 199.58/25.91 ![X0,X1,X2]: (c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X2,tc_Complex_Ocomplex)|~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f3260])).
% 199.58/25.91 fof(f3300,plain,(
% 199.58/25.91 c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f1150])).
% 199.58/25.91 fof(f3535,plain,(
% 199.58/25.91 ![X0]: (c_HOL_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(X0,X0,tc_nat))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f1306])).
% 199.58/25.91 fof(f3536,plain,(
% 199.58/25.91 ![X0]: (c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X0,tc_nat)=c_HOL_Oplus__class_Oplus(X0,X0,tc_nat))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f1307])).
% 199.58/25.91 fof(f3565,plain,(
% 199.58/25.91 ![X0,X1,X2]: (c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat)=c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat))),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f1326])).
% 199.58/25.91 fof(f3612,plain,(
% 199.58/25.91 ~c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex)),
% 199.58/25.91 inference(cnf_transformation,[status(thm)],[f1352])).
% 199.58/25.91 fof(f3837,plain,(
% 199.58/25.91 c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=c_Suc(c_HOL_Oone__class_Oone(tc_nat))),
% 199.58/25.91 inference(forward_demodulation,[status(thm)],[f2769,f3300])).
% 199.58/25.91 fof(f3894,plain,(
% 199.58/25.91 ![X0]: (c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=c_HOL_Oplus__class_Oplus(X0,X0,tc_nat))),
% 199.58/25.91 inference(forward_demodulation,[status(thm)],[f3837,f3535])).
% 199.58/25.91 fof(f3895,plain,(
% 199.58/25.91 ![X0]: (c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),X0,tc_nat)=c_HOL_Oplus__class_Oplus(X0,X0,tc_nat))),
% 199.58/25.91 inference(forward_demodulation,[status(thm)],[f3837,f3536])).
% 199.58/25.91 fof(f3911,plain,(
% 199.58/25.91 ~c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex)),
% 199.58/25.91 inference(forward_demodulation,[status(thm)],[f3837,f3612])).
% 199.58/25.91 fof(f3912,plain,(
% 199.58/25.91 ~c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex)),
% 199.58/25.91 inference(forward_demodulation,[status(thm)],[f3837,f3911])).
% 199.58/25.91 fof(f4419,plain,(
% 199.58/25.91 ![X0,X1]: (c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),X1,tc_nat)=c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat))),
% 199.58/25.91 inference(paramodulation,[status(thm)],[f3895,f3565])).
% 199.58/25.91 fof(f4421,plain,(
% 199.58/25.91 ![X0,X1]: (c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),X1,tc_nat)=c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),X1,tc_nat),tc_nat))),
% 199.58/25.91 inference(paramodulation,[status(thm)],[f3894,f3565])).
% 199.58/25.91 fof(f4811,plain,(
% 199.58/25.91 ![X0,X1,X2]: (c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)|X0=c_HOL_Ozero__class_Ozero(tc_nat)|c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X2,tc_Complex_Ocomplex))),
% 199.58/26.01 inference(resolution,[status(thm)],[f1590,f3261])).
% 199.58/26.01 fof(f4837,plain,(
% 199.58/26.01 ![X0,X1,X2]: (X0=c_HOL_Ozero__class_Ozero(tc_nat)|c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X2,tc_Complex_Ocomplex))),
% 199.58/26.01 inference(forward_subsumption_resolution,[status(thm)],[f4811,f2462])).
% 199.58/26.01 fof(f11370,plain,(
% 199.58/26.01 ~c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(v_i,v_i,tc_nat),v_j,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex)),
% 199.58/26.01 inference(paramodulation,[status(thm)],[f4421,f3912])).
% 199.58/26.01 fof(f21983,plain,(
% 199.58/26.01 ![X0,X1,X2]: (c_Suc(c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat)|c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),X0,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),X2,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_Complex_Ocomplex))),
% 199.58/26.01 inference(paramodulation,[status(thm)],[f4419,f4837])).
% 199.58/26.01 fof(f22027,plain,(
% 199.58/26.01 ~c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex)),
% 199.58/26.01 inference(backward_demodulation,[status(thm)],[f22029,f11370])).
% 199.58/26.01 fof(f22029,plain,(
% 199.58/26.01 ![X0,X1,X2]: (c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),X0,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X1,tc_nat),X2,tc_nat),tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_Complex_Ocomplex))),
% 199.58/26.01 inference(forward_subsumption_resolution,[status(thm)],[f21983,f1941])).
% 199.58/26.01 fof(f22035,plain,(
% 199.58/26.01 $false),
% 199.58/26.01 inference(trivial_equality_resolution,[status(thm)],[f22027])).
% 199.58/26.01 % SZS output end CNFRefutation for theBenchmark.p
% 69.11/26.07 % Elapsed time: 25.627425 seconds
% 69.11/26.07 % CPU time: 201.282167 seconds
% 69.11/26.07 % Total memory used: 1.006 GB
% 69.11/26.07 % Net memory used: 968.560 MB
%------------------------------------------------------------------------------