%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG384-1 : 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 : n010.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 06:50:06 AM UTC 2026
% Result : Unsatisfiable 7.47s 6.48s
% Output : CNFRefutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 19 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 2 !; 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_58,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(cls_zero__less__norm__iff_1,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = c_HOL_Ozero__class_Ozero(VAR_0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(VAR_1,VAR_0),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(VAR_0) ),
file('theBenchmark.p',cls_zero__less__norm__iff_1) ).
cnf(c_61,plain,
( B = c_HOL_Ozero__class_Ozero(A)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(B,A),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(A) ),
inference(clausify,[status(thm)],[cls_zero__less__norm__iff_1]) ).
fof(cls_conjecture_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_811,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_812,plain,
v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_813,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_c____,
inference(copy,[status(thm)],[c_812]) ).
cnf(c_950,plain,
( A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_61,c_58]) ).
cnf(c_951,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(copy,[status(thm)],[c_950]) ).
cnf(c_4926,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_c____,
inference(resolve,[status(thm)],[c_951,c_811]) ).
cnf(c_4925,plain,
$false,
inference(resolve,[status(thm)],[c_813,c_4926]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG384-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n010.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Sat Sep 26 21:57:06 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 104309 was started by sandbox2 on n010,
% 0.17/5.45 % Sat Sep 26 21:57:06 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.48
% 0.17/5.48 % From the command line: assign(max_seconds, 300).
% 7.47/6.48
% 7.47/6.48 % SZS status Unsatisfiable for theBenchmark
% 7.47/6.48
% 7.47/6.48 % Proof 1 at 0.89 (+ 0.09) seconds.
% 7.47/6.48 % Length of proof is 8.
% 7.47/6.48 % Level of proof is 3.
% 7.47/6.48 % Maximum clause weight is 21.000.
% 7.47/6.48 % Given clauses 309.
% 7.47/6.48
% 7.47/6.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------