%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV632-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Sun Sep 27 09:08:51 AM UTC 2026
% Result : Unsatisfiable 19.54s 2.88s
% Output : CNFRefutation 19.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 18 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_1,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Ring__and__Field_Ocomm__semiring__1]) ).
fof(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_HOL_Otimes__class_Otimes(VAR_1,c_HOL_Otimes__class_Otimes(VAR_2,VAR_3,VAR_0),VAR_0) = c_HOL_Otimes__class_Otimes(VAR_2,c_HOL_Otimes__class_Otimes(VAR_1,VAR_3,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(c_13,plain,
( c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A) = c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I19_J_0]) ).
cnf(c_1174,plain,
c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat),
inference(resolve,[status(thm)],[c_1,c_13]) ).
fof(cls_conjecture_0,axiom,
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),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1254,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(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_pos2_0,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('theBenchmark.p',cls_pos2_0) ).
cnf(c_1311,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(clausify,[status(thm)],[cls_pos2_0]) ).
fof(cls_root__cancel_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),VAR_0,tc_nat)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(VAR_0,VAR_1,tc_nat)),c_HOL_Otimes__class_Otimes(VAR_0,VAR_2,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(VAR_1),VAR_2,tc_Complex_Ocomplex) ),
file('theBenchmark.p',cls_root__cancel_0) ).
cnf(c_1356,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)
| c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(B),C,tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[cls_root__cancel_0]) ).
cnf(c_6212,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(paramod,[status(thm)],[c_1174,c_1254]) ).
cnf(c_6611,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),A,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),B,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),B,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_1356,c_1311]) ).
cnf(c_6612,plain,
$false,
inference(resolve,[status(thm)],[c_6611,c_6212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV632-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sat Sep 26 14:38:49 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 840758 was started by sandbox2 on n012,
% 0.03/0.31 % Sat Sep 26 14:38:49 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.34
% 0.08/0.34 % From the command line: assign(max_seconds, 300).
% 19.54/2.88
% 19.54/2.88 % SZS status Unsatisfiable for theBenchmark
% 19.54/2.88
% 19.54/2.88 % Proof 1 at 2.44 (+ 0.08) seconds.
% 19.54/2.88 % Length of proof is 9.
% 19.54/2.88 % Level of proof is 3.
% 19.54/2.88 % Maximum clause weight is 66.000.
% 19.54/2.88 % Given clauses 444.
% 19.54/2.88
% 19.54/2.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------