%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV633-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:49:16 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.67s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1114,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1150,axiom,
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))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1288,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1326,axiom,
! [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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1346,axiom,
! [V_m,V_n] : c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat) = c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1352,negated_conjecture,
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(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(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3241,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(cnf_transformation,[status(thm)],[f1114]) ).
fof(f3300,plain,
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))),
inference(cnf_transformation,[status(thm)],[f1150]) ).
fof(f3506,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(cnf_transformation,[status(thm)],[f1288]) ).
fof(f3565,plain,
! [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),
inference(cnf_transformation,[status(thm)],[f1326]) ).
fof(f3602,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f1346]) ).
fof(f3612,plain,
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(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(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1352]) ).
fof(f3783,plain,
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(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(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f3602,f3612]) ).
fof(f3887,plain,
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(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f3602,f3783]) ).
fof(f3893,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(forward_demodulation,[status(thm)],[f3506,f3241]) ).
fof(f3937,plain,
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(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f3941,f3887]) ).
fof(f3941,plain,
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)),
inference(forward_demodulation,[status(thm)],[f3893,f3300]) ).
fof(f3951,plain,
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(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f3941,f3937]) ).
fof(f3952,plain,
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(c_HOL_Otimes__class_Otimes(v_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f3941,f3951]) ).
fof(f3953,plain,
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(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f3941,f3952]) ).
fof(f4066,plain,
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(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f3602,f3953]) ).
fof(f4263,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f3602,f4066]) ).
fof(f4572,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f3565,f4263]) ).
fof(f4624,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV633-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.55 % Computer : n007.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Mon Sep 21 09:13:21 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.13/0.60 % Drodi V4.1.1
% 0.13/0.67 % Refutation found
% 0.13/0.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.71 % Elapsed time: 0.142481 seconds
% 0.13/0.71 % CPU time: 0.584556 seconds
% 0.13/0.71 % Total memory used: 185.007 MB
% 0.13/0.71 % Net memory used: 183.860 MB
%------------------------------------------------------------------------------