%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG432-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 06:50:11 AM UTC 2026
% Result : Unsatisfiable 14.34s 7.25s
% Output : CNFRefutation 14.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 30 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 12 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_mult_Ozero__right_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Otimes__class_Otimes(VAR_1,c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_RealVector_Oreal__normed__algebra(VAR_0) ),
file('theBenchmark.p',cls_mult_Ozero__right_0) ).
cnf(c_239,plain,
( c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_RealVector_Oreal__normed__algebra(A) ),
inference(clausify,[status(thm)],[cls_mult_Ozero__right_0]) ).
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
cnf(c_258,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(cls_monoid__add__class_Oadd__0__right_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oplus__class_Oplus(VAR_1,c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = VAR_1
| ~ class_OrderedGroup_Omonoid__add(VAR_0) ),
file('theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(c_668,plain,
( c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A) = B
| ~ class_OrderedGroup_Omonoid__add(A) ),
inference(clausify,[status(thm)],[cls_monoid__add__class_Oadd__0__right_0]) ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
cnf(c_670,plain,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add]) ).
cnf(c_674,plain,
c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A,
inference(resolve,[status(thm)],[c_670,c_668]) ).
cnf(c_1053,plain,
c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_258,c_239]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(c_1206,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0]) ).
fof(cls_conjecture_1,axiom,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1240,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1241,plain,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_poly__pCons_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Polynomial_Opoly(c_Polynomial_OpCons(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_HOL_Oplus__class_Oplus(VAR_1,c_HOL_Otimes__class_Otimes(VAR_3,c_Polynomial_Opoly(VAR_2,VAR_3,VAR_0),VAR_0),VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_poly__pCons_0) ).
cnf(c_1272,plain,
( c_Polynomial_Opoly(c_Polynomial_OpCons(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(D,c_Polynomial_Opoly(C,D,A),A),A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_poly__pCons_0]) ).
cnf(c_3230,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(C,c_Polynomial_Opoly(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_1272,c_1206]) ).
cnf(c_3232,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_x,c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_3230,c_1240]) ).
cnf(c_3233,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_x,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1241,c_3232]) ).
cnf(c_3234,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1053,c_3233]) ).
cnf(c_3235,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_674,c_3234]) ).
cnf(c_3231,plain,
$false,
inference(copy,[status(thm)],[c_3235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG432-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n001.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 26 22:06:06 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.37 % Process 2770039 was started by sandbox on n001,
% 0.11/5.37 % Sat Sep 26 22:06:06 2026
% 0.11/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.40
% 0.14/5.40 % From the command line: assign(max_seconds, 300).
% 14.34/7.25
% 14.34/7.25 % SZS status Unsatisfiable for theBenchmark
% 14.34/7.25
% 14.34/7.25 % Proof 1 at 1.79 (+ 0.04) seconds.
% 14.34/7.25 % Length of proof is 12.
% 14.34/7.25 % Level of proof is 2.
% 14.34/7.25 % Maximum clause weight is 40.000.
% 14.34/7.25 % Given clauses 292.
% 14.34/7.25
% 14.34/7.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------