%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG371-1 : 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 : n013.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 6.64s 1.33s
% Output : CNFRefutation 6.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_norm__not__less__zero_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(VAR_1,VAR_0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(VAR_0) ),
file('theBenchmark.p',cls_norm__not__less__zero_0) ).
cnf(c_280,plain,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(B,A),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(A) ),
inference(clausify,[status(thm)],[cls_norm__not__less__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_282,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(c_399,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Oorder]) ).
fof(cls_xt1_I7_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_HOL_Oord__class_Oless(VAR_3,VAR_2,VAR_0)
| ~ c_lessequals(VAR_1,VAR_3,VAR_0)
| c_HOL_Oord__class_Oless(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(c_414,plain,
( ~ c_HOL_Oord__class_Oless(D,C,A)
| ~ c_lessequals(B,D,A)
| c_HOL_Oord__class_Oless(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_xt1_I7_J_0]) ).
cnf(c_450,plain,
( ~ c_HOL_Oord__class_Oless(C,B,tc_RealDef_Oreal)
| ~ c_lessequals(A,C,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(A,B,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_399,c_414]) ).
fof(cls_conjecture_1,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_667,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_668,plain,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_812,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_280,c_282]) ).
cnf(c_1423,plain,
( ~ c_HOL_Oord__class_Oless(v_r,A,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),A,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_450,c_667]) ).
cnf(c_1424,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_1423,c_668]) ).
cnf(c_1422,plain,
$false,
inference(resolve,[status(thm)],[c_812,c_1424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG371-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 21:55:07 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3628943 was started by sandbox on n013,
% 0.08/0.37 % Sat Sep 26 21:55:07 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 6.64/1.33
% 6.64/1.33 % SZS status Unsatisfiable for theBenchmark
% 6.64/1.33
% 6.64/1.33 % Proof 1 at 0.61 (+ 0.04) seconds.
% 6.64/1.33 % Length of proof is 9.
% 6.64/1.33 % Level of proof is 2.
% 6.64/1.33 % Maximum clause weight is 17.000.
% 6.64/1.33 % Given clauses 131.
% 6.64/1.33
% 6.64/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------