%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG340-1 : 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 : n009.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 06:50:02 AM UTC 2026
% Result : Unsatisfiable 8.20s 1.52s
% Output : CNFRefutation 8.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 41 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 25 ( 6 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(c_247,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(cls_norm__sgn_0,axiom,
! [VAR_0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(VAR_0),VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(VAR_0) ),
file('theBenchmark.p',cls_norm__sgn_0) ).
cnf(c_256,plain,
( c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(A) ),
inference(clausify,[status(thm)],[cls_norm__sgn_0]) ).
fof(cls_sgn__zero_0,axiom,
! [VAR_0] :
( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_RealVector_Oreal__normed__vector(VAR_0) ),
file('theBenchmark.p',cls_sgn__zero_0) ).
cnf(c_257,plain,
( c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_RealVector_Oreal__normed__vector(A) ),
inference(clausify,[status(thm)],[cls_sgn__zero_0]) ).
fof(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(c_417,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(cls_order__less__imp__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_HOL_Oord__class_Oless(VAR_1,VAR_2,VAR_0)
| c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Opreorder(VAR_0) ),
file('theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(c_422,plain,
( ~ c_HOL_Oord__class_Oless(B,C,A)
| c_lessequals(B,C,A)
| ~ class_Orderings_Opreorder(A) ),
inference(clausify,[status(thm)],[cls_order__less__imp__le_0]) ).
cnf(c_429,plain,
( ~ c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal)
| c_lessequals(A,B,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_422,c_417]) ).
cnf(c_564,plain,
c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_257,c_247]) ).
cnf(c_566,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_256,c_247]) ).
cnf(c_567,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_564,c_566]) ).
fof(cls_real__of__preal__zero__less_0,axiom,
! [VAR_0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(VAR_0),tc_RealDef_Oreal),
file('theBenchmark.p',cls_real__of__preal__zero__less_0) ).
cnf(c_791,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(A),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_real__of__preal__zero__less_0]) ).
fof(cls_poly__0_0,axiom,
! [VAR_0,VAR_1] :
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(VAR_0)),VAR_1,VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_poly__0_0) ).
cnf(c_844,plain,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_poly__0_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_0,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(VAR_0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),VAR_0,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_848,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex),A,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
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_867,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0]) ).
cnf(c_1565,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(A),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_791,c_429]) ).
cnf(c_1853,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(c_RealDef_Oreal__of__preal(A)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealDef_Oreal__of__preal(A),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_848,c_791]) ).
cnf(c_2021,plain,
c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_867,c_844]) ).
cnf(c_2027,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealDef_Oreal__of__preal(A),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_2021,c_1853]) ).
cnf(c_2028,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(A),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_567,c_2027]) ).
cnf(c_2026,plain,
$false,
inference(resolve,[status(thm)],[c_1565,c_2028]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG340-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 21:52:44 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1218732 was started by sandbox2 on n009,
% 0.09/0.37 % Sat Sep 26 21:52:44 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 8.20/1.52
% 8.20/1.52 % SZS status Unsatisfiable for theBenchmark
% 8.20/1.52
% 8.20/1.52 % Proof 1 at 1.04 (+ 0.06) seconds.
% 8.20/1.52 % Length of proof is 17.
% 8.20/1.52 % Level of proof is 3.
% 8.20/1.52 % Maximum clause weight is 42.000.
% 8.20/1.52 % Given clauses 284.
% 8.20/1.52
% 8.20/1.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------