%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG373-1 : 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 : n003.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 4.20s 0.92s
% Output : CNFRefutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 20 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
! [VAR_0] : ~ c_HOL_Oord__class_Oless(v_x(VAR_0),VAR_0,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_690,plain,
~ c_HOL_Oord__class_Oless(v_x(A),A,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(VAR_0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(VAR_0),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_691,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(A),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(VAR_0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_692,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(A),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oord__class_Oless(VAR_1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(VAR_0,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,VAR_0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(VAR_1,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_693,plain,
( c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(B,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_694,plain,
( c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(B,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(A,tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_693]) ).
cnf(c_2242,plain,
c_HOL_Ouminus__class_Ouminus(v_x(A),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_691]) ).
cnf(c_2243,plain,
( c_HOL_Oord__class_Oless(v_x(A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(A),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_694,c_2242]) ).
cnf(c_2240,plain,
c_HOL_Oord__class_Oless(v_x(A),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_692,c_2243]) ).
cnf(c_2241,plain,
$false,
inference(resolve,[status(thm)],[c_2240,c_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 21:57:09 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3846472 was started by sandbox on n003,
% 0.09/0.35 % Sat Sep 26 21:57:09 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 4.20/0.92
% 4.20/0.92 % SZS status Unsatisfiable for theBenchmark
% 4.20/0.92
% 4.20/0.92 % Proof 1 at 0.50 (+ 0.05) seconds.
% 4.20/0.92 % Length of proof is 7.
% 4.20/0.92 % Level of proof is 3.
% 4.20/0.92 % Maximum clause weight is 36.000.
% 4.20/0.92 % Given clauses 249.
% 4.20/0.92
% 4.20/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------