%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG425-1 : 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 : 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 06:50:10 AM UTC 2026
% Result : Unsatisfiable 6.17s 6.27s
% Output : CNFRefutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 6 unt; 0 def)
% Number of atoms : 6 ( 5 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 2 ( 1 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Otimes__class_Otimes(v_pa____,VAR_0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_798,plain,
c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Otimes__class_Otimes(v_pa____,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_pa____,c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_799,plain,
c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_pa____,c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_801,plain,
c_HOL_Otimes__class_Otimes(v_pa____,c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(copy,[status(thm)],[c_799]) ).
cnf(c_800,plain,
$false,
inference(resolve,[status(thm)],[c_798,c_801]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG425-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.39 % Computer : n026.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 26 22:02:32 UTC 2026
% 0.17/5.40 % CPUTime :
% 0.17/5.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.40 % Process 2027124 was started by sandbox2 on n026,
% 0.17/5.40 % Sat Sep 26 22:02:32 2026
% 0.17/5.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.45
% 0.17/5.45 % From the command line: assign(max_seconds, 300).
% 6.17/6.27
% 6.17/6.27 % SZS status Unsatisfiable for theBenchmark
% 6.17/6.27
% 6.17/6.27 % Proof 1 at 0.81 (+ 0.01) seconds.
% 6.17/6.27 % Length of proof is 3.
% 6.17/6.27 % Level of proof is 1.
% 6.17/6.27 % Maximum clause weight is 26.000.
% 6.17/6.27 % Given clauses 0.
% 6.17/6.27
% 6.17/6.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------