%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG341-1 : 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 : n005.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 06:50:02 AM UTC 2026
% Result : Unsatisfiable 8.09s 1.80s
% Output : CNFRefutation 8.09s
% 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 : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 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(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_53,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(cls_norm__ge__zero_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(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_norm__ge__zero_0) ).
cnf(c_58,plain,
( c_lessequals(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_norm__ge__zero_0]) ).
fof(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(c_508,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(cls_order__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_lessequals(VAR_1,VAR_3,VAR_0)
| ~ c_lessequals(VAR_3,VAR_2,VAR_0)
| c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Opreorder(VAR_0) ),
file('theBenchmark.p',cls_order__trans_0) ).
cnf(c_509,plain,
( ~ c_lessequals(B,D,A)
| ~ c_lessequals(D,C,A)
| c_lessequals(B,C,A)
| ~ class_Orderings_Opreorder(A) ),
inference(clausify,[status(thm)],[cls_order__trans_0]) ).
cnf(c_510,plain,
( ~ c_lessequals(A,C,tc_RealDef_Oreal)
| ~ c_lessequals(C,B,tc_RealDef_Oreal)
| c_lessequals(A,B,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_509,c_508]) ).
cnf(c_942,plain,
c_lessequals(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_58,c_53]) ).
fof(cls_CHAINED_0_01,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_1055,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_conjecture_0,axiom,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1056,plain,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_6061,plain,
( ~ c_lessequals(A,c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(A,v_r,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_510,c_1055]) ).
cnf(c_6062,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_6061,c_942]) ).
cnf(c_6060,plain,
$false,
inference(resolve,[status(thm)],[c_1056,c_6062]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG341-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n005.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Sat Sep 26 21:52:31 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 3178034 was started by sandbox on n005,
% 0.17/0.42 % Sat Sep 26 21:52:31 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 8.09/1.80
% 8.09/1.80 % SZS status Unsatisfiable for theBenchmark
% 8.09/1.80
% 8.09/1.80 % Proof 1 at 1.16 (+ 0.17) seconds.
% 8.09/1.80 % Length of proof is 9.
% 8.09/1.80 % Level of proof is 2.
% 8.09/1.80 % Maximum clause weight is 17.000.
% 8.09/1.80 % Given clauses 247.
% 8.09/1.80
% 8.09/1.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------