%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG410-1 : 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 : n020.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 06:50:09 AM UTC 2026
% Result : Unsatisfiable 12.03s 7.12s
% Output : CNFRefutation 12.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 2 ( 1 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),VAR_0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1037,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_1038,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_1039,plain,
$false,
inference(resolve,[status(thm)],[c_1037,c_1038]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG410-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n020.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Sat Sep 26 21:59:25 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.47 % Process 2600234 was started by sandbox on n020,
% 0.18/5.47 % Sat Sep 26 21:59:25 2026
% 0.18/5.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.23/5.51
% 0.23/5.51 % From the command line: assign(max_seconds, 300).
% 12.03/7.12
% 12.03/7.12 % SZS status Unsatisfiable for theBenchmark
% 12.03/7.12
% 12.03/7.12 % Proof 1 at 1.59 (+ 0.01) seconds.
% 12.03/7.12 % Length of proof is 3.
% 12.03/7.12 % Level of proof is 1.
% 12.03/7.12 % Maximum clause weight is 54.000.
% 12.03/7.12 % Given clauses 0.
% 12.03/7.12
% 12.03/7.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------