%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG372-1 : 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 : n019.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 06:50:05 AM UTC 2026
% Result : Unsatisfiable 22.04s 3.23s
% Output : CNFRefutation 22.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 26 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_norm__zero_0,axiom,
! [VAR_0] :
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(VAR_0) ),
file('theBenchmark.p',cls_norm__zero_0) ).
cnf(c_204,plain,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(A) ),
inference(clausify,[status(thm)],[cls_norm__zero_0]) ).
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_217,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(c_447,plain,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]) ).
fof(cls_minus__minus_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(VAR_1,VAR_0),VAR_0) = VAR_1
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_minus__minus_0) ).
cnf(c_448,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A) = B
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_minus__minus_0]) ).
cnf(c_871,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(resolve,[status(thm)],[c_217,c_204]) ).
cnf(c_1036,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal),tc_RealDef_Oreal) = A,
inference(resolve,[status(thm)],[c_447,c_448]) ).
fof(cls_conjecture_0,axiom,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1369,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_1373,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(paramod,[status(thm)],[c_1036,c_1369]) ).
cnf(c_1374,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(paramod,[status(thm)],[c_871,c_1373]) ).
cnf(c_1370,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(copy,[status(thm)],[c_1374]) ).
fof(cls_CHAINED_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_1371,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_1372,plain,
$false,
inference(resolve,[status(thm)],[c_1370,c_1371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n019.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 21:55:49 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 2265562 was started by sandbox2 on n019,
% 0.07/0.34 % Sat Sep 26 21:55:49 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 22.04/3.23
% 22.04/3.23 % SZS status Unsatisfiable for theBenchmark
% 22.04/3.23
% 22.04/3.23 % Proof 1 at 2.70 (+ 0.02) seconds.
% 22.04/3.23 % Length of proof is 10.
% 22.04/3.23 % Level of proof is 3.
% 22.04/3.23 % Maximum clause weight is 27.000.
% 22.04/3.23 % Given clauses 0.
% 22.04/3.23
% 22.04/3.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------