%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG383-1 : 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 : n026.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 21.70s 7.05s
% Output : CNFRefutation 21.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_th2_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('theBenchmark.p',cls_th2_0) ).
cnf(c_1332,plain,
c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_th2_0]) ).
fof(cls_th1_0,axiom,
c_lessequals(v_da____,c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_th1_0) ).
cnf(c_1334,plain,
c_lessequals(v_da____,c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_th1_0]) ).
fof(cls_real__le__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_lessequals(VAR_0,VAR_2,tc_RealDef_Oreal)
| ~ c_lessequals(VAR_2,VAR_1,tc_RealDef_Oreal)
| c_lessequals(VAR_0,VAR_1,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_real__le__trans_0) ).
cnf(c_1339,plain,
( ~ c_lessequals(A,C,tc_RealDef_Oreal)
| ~ c_lessequals(C,B,tc_RealDef_Oreal)
| c_lessequals(A,B,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_real__le__trans_0]) ).
fof(cls_conjecture_0,axiom,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1346,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_6535,plain,
( ~ c_lessequals(A,c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v_aa____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(A,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_1339,c_1332]) ).
cnf(c_6536,plain,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_6535,c_1334]) ).
cnf(c_6534,plain,
$false,
inference(resolve,[status(thm)],[c_1346,c_6536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG383-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.39 % Computer : n026.cluster.edu
% 0.08/0.39 % Model : x86_64 x86_64
% 0.08/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.39 % Memory : 8046.5625MB
% 0.08/0.39 % OS : Linux 6.8.0-71-generic
% 0.08/0.39 % CPULimit : 300
% 0.08/0.39 % WCLimit : 300
% 0.08/0.39 % DateTime : Sat Sep 26 21:59:11 UTC 2026
% 0.08/0.39 % CPUTime :
% 0.08/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.39 % Process 2020881 was started by sandbox on n026,
% 0.08/0.39 % Sat Sep 26 21:59:11 2026
% 0.08/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.42
% 0.08/0.42 % From the command line: assign(max_seconds, 300).
% 21.70/7.05
% 21.70/7.05 % given #500 (I,wt=20): 1121 -class_SEQ_Obanach(A) | -class_RealVector_Oreal__normed__field(A) | c_Transcendental_Oexp(B,A) != c_HOL_Ozero__class_Ozero(A) # tptp_name(cls_exp__not__eq__zero_0) # clausal_fof(1). [assumption].
% 21.70/7.05
% 21.70/7.05 % SZS status Unsatisfiable for theBenchmark
% 21.70/7.05
% 21.70/7.05 % Proof 1 at 2.80 (+ 0.36) seconds.
% 21.70/7.05 % Length of proof is 5.
% 21.70/7.05 % Level of proof is 1.
% 21.70/7.05 % Maximum clause weight is 61.000.
% 21.70/7.05 % Given clauses 681.
% 21.70/7.05
% 21.70/7.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------