%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG395-1 : 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 : n014.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 06:50:07 AM UTC 2026
% Result : Unsatisfiable 14.60s 2.35s
% Output : CNFRefutation 14.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 7 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_CHAINED_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(VAR_0,v_sko__CHAINED__1(VAR_0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(VAR_0,VAR_1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_1278,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(A,v_sko__CHAINED__1(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1279,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,VAR_0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,VAR_0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_1280,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,A),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_1281,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_pa____,hAPP(v_x,A),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_1279,c_1280]) ).
cnf(c_1282,plain,
$false,
inference(resolve,[status(thm)],[c_1281,c_1278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG395-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n014.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 21:56:46 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 4180229 was started by sandbox on n014,
% 0.19/0.45 % Sat Sep 26 21:56:46 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 14.60/2.35
% 14.60/2.35 % SZS status Unsatisfiable for theBenchmark
% 14.60/2.35
% 14.60/2.35 % Proof 1 at 1.83 (+ 0.01) seconds.
% 14.60/2.35 % Length of proof is 5.
% 14.60/2.35 % Level of proof is 2.
% 14.60/2.35 % Maximum clause weight is 36.000.
% 14.60/2.35 % Given clauses 0.
% 14.60/2.35
% 14.60/2.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------