%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV634-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.22s 0.93s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 19 unt; 0 def)
% Number of atoms : 25 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1058,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1071,axiom,
! [V_d,V_n,V_k] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| 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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1094,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1201,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1203,axiom,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1230,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f1295,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(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) != 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),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3095,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)],[f1058]) ).
fof(f3114,plain,
! [V_d] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ! [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) ),
inference(miniscoping,[status(thm)],[f1071]) ).
fof(f3115,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,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) ),
inference(cnf_transformation,[status(thm)],[f3114]) ).
fof(f3154,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)],[f1094]) ).
fof(f3319,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f1201]) ).
fof(f3321,plain,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
inference(cnf_transformation,[status(thm)],[f1203]) ).
fof(f3359,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)],[f1230]) ).
fof(f3466,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(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) != 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),
inference(cnf_transformation,[status(thm)],[f1295]) ).
fof(f4224,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(resolution,[status(thm)],[f3115,f3466]) ).
fof(f4259,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),
inference(forward_demodulation,[status(thm)],[f3154,f4224]) ).
fof(f4273,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(backward_demodulation,[status(thm)],[f3359,f3095]) ).
fof(f4275,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(backward_demodulation,[status(thm)],[f4273,f4259]) ).
fof(f4526,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(backward_demodulation,[status(thm)],[f4530,f3319]) ).
fof(f4530,plain,
c_Suc(c_HOL_Oone__class_Oone(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
inference(forward_demodulation,[status(thm)],[f4273,f3321]) ).
fof(f4532,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4526,f4275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV634-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.69 % Computer : n018.cluster.edu
% 0.18/0.69 % Model : x86_64 x86_64
% 0.18/0.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.69 % Memory : 8046.5625MB
% 0.18/0.69 % OS : Linux 6.8.0-71-generic
% 0.18/0.69 % CPULimit : 300
% 0.18/0.69 % WCLimit : 300
% 0.18/0.69 % DateTime : Mon Sep 21 09:17:44 UTC 2026
% 0.18/0.70 % CPUTime :
% 0.22/0.86 % Drodi V4.1.1
% 0.22/0.93 % Refutation found
% 0.22/0.93 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.22/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.99 % Elapsed time: 0.281060 seconds
% 0.22/0.99 % CPU time: 0.698364 seconds
% 0.22/0.99 % Total memory used: 113.260 MB
% 0.22/0.99 % Net memory used: 112.655 MB
%------------------------------------------------------------------------------