%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG386-1 : 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 : n011.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 5.05s 1.15s
% Output : CNFRefutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 8 ( 2 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_721,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
! [VAR_0] :
( ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(VAR_0,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),VAR_0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_722,plain,
( ~ c_lessequals(v_sko__CHAINED__1(v_c____,v_cs____),c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_that_1,axiom,
! [VAR_0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_sko__local__Xthat__1(v_c____,v_cs____,VAR_0),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('theBenchmark.p',cls_that_1) ).
cnf(c_727,plain,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_sko__local__Xthat__1(v_c____,v_cs____,A),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_that_1]) ).
cnf(c_728,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_sko__local__Xthat__1(v_c____,v_cs____,A),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_721,c_727]) ).
fof(cls_that_0,axiom,
! [VAR_0] :
( c_lessequals(VAR_0,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,VAR_0),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
file('theBenchmark.p',cls_that_0) ).
cnf(c_729,plain,
( c_lessequals(A,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,A),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| v_thesis____ ),
inference(clausify,[status(thm)],[cls_that_0]) ).
cnf(c_730,plain,
c_lessequals(A,c_RealVector_Onorm__class_Onorm(v_sko__local__Xthat__1(v_c____,v_cs____,A),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_721,c_729]) ).
cnf(c_1725,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_sko__local__Xthat__1(v_c____,v_cs____,v_sko__CHAINED__1(v_c____,v_cs____)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_730,c_722]) ).
cnf(c_1724,plain,
$false,
inference(resolve,[status(thm)],[c_728,c_1725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG386-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 21:56:44 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1628658 was started by sandbox on n011,
% 0.12/0.36 % Sat Sep 26 21:56:44 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 5.05/1.15
% 5.05/1.15 % SZS status Unsatisfiable for theBenchmark
% 5.05/1.15
% 5.05/1.15 % Proof 1 at 0.55 (+ 0.02) seconds.
% 5.05/1.15 % Length of proof is 7.
% 5.05/1.15 % Level of proof is 2.
% 5.05/1.15 % Maximum clause weight is 29.000.
% 5.05/1.15 % Given clauses 205.
% 5.05/1.15
% 5.05/1.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------