%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG359-1 : 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 06:50:04 AM UTC 2026
% Result : Unsatisfiable 18.69s 3.60s
% Output : CNFRefutation 18.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 29 unt; 0 def)
% Number of atoms : 37 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 14 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(c_270,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ofield]) ).
fof(cls_power__divide_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(VAR_1,VAR_3,VAR_0),c_Power_Opower__class_Opower(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Odivision__by__zero(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',cls_power__divide_0) ).
cnf(c_278,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A)
| ~ class_Ring__and__Field_Odivision__by__zero(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[cls_power__divide_0]) ).
fof(cls_complex__eq__cancel__iff2_2,axiom,
! [VAR_0] : c_Complex_Ocomplex_OComplex(VAR_0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(VAR_0,tc_Complex_Ocomplex),
file('theBenchmark.p',cls_complex__eq__cancel__iff2_2) ).
cnf(c_824,plain,
c_Complex_Ocomplex_OComplex(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(A,tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_complex__eq__cancel__iff2_2]) ).
cnf(c_825,plain,
c_RealVector_Oof__real(A,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(copy,[status(thm)],[c_824]) ).
fof(cls_Re_Ozero_0,axiom,
c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',cls_Re_Ozero_0) ).
cnf(c_857,plain,
c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_Re_Ozero_0]) ).
cnf(c_858,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(copy,[status(thm)],[c_857]) ).
fof(cls_complex__of__real__power_0,axiom,
! [VAR_0,VAR_1] : c_Power_Opower__class_Opower(c_RealVector_Oof__real(VAR_0,tc_Complex_Ocomplex),VAR_1,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(VAR_0,VAR_1,tc_RealDef_Oreal),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_complex__of__real__power_0) ).
cnf(c_954,plain,
c_Power_Opower__class_Opower(c_RealVector_Oof__real(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_complex__of__real__power_0]) ).
cnf(c_2568,plain,
c_Power_Opower__class_Opower(c_Complex_Ocomplex_OComplex(A,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),B,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_825,c_954]) ).
cnf(c_2569,plain,
c_Power_Opower__class_Opower(c_Complex_Ocomplex_OComplex(A,c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),B,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_858,c_2568]) ).
cnf(c_2570,plain,
c_Power_Opower__class_Opower(c_Complex_Ocomplex_OComplex(A,c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),B,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(paramod,[status(thm)],[c_825,c_2569]) ).
cnf(c_955,plain,
c_Power_Opower__class_Opower(c_Complex_Ocomplex_OComplex(A,c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),B,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Power_Opower__class_Opower(A,B,tc_RealDef_Oreal),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),
inference(paramod,[status(thm)],[c_858,c_2570]) ).
fof(cls_CHAINED_0,axiom,
c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_994,plain,
c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_conjecture_0,axiom,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_995,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_RealVector_Oof__real(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_2571,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_Complex_Ocomplex_OComplex(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_825,c_995]) ).
cnf(c_2572,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_Complex_Ocomplex_OComplex(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_858,c_2571]) ).
cnf(c_2573,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_Complex_Ocomplex_OComplex(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_825,c_2572]) ).
cnf(c_996,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_v____,c_Complex_Ocomplex_OComplex(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex),v_na____,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_858,c_2573]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(c_1051,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero]) ).
cnf(c_2028,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_278,c_270]) ).
cnf(c_2029,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_1051,c_2028]) ).
cnf(c_2574,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_Complex_Ocomplex_OComplex(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_2029,c_996]) ).
cnf(c_2575,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_Power_Opower__class_Opower(c_NthRoot_Oroot(v_na____,c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex)),v_na____,tc_RealDef_Oreal),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_955,c_2574]) ).
cnf(c_2576,plain,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Complex_ORe(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_994,c_2575]) ).
cnf(c_2567,plain,
$false,
inference(copy,[status(thm)],[c_2576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG359-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n026.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sat Sep 26 21:57:26 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2017178 was started by sandbox on n026,
% 0.19/0.46 % Sat Sep 26 21:57:26 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.24/0.52
% 0.24/0.52 % From the command line: assign(max_seconds, 300).
% 18.69/3.60
% 18.69/3.60 % SZS status Unsatisfiable for theBenchmark
% 18.69/3.60
% 18.69/3.60 % Proof 1 at 3.00 (+ 0.05) seconds.
% 18.69/3.60 % Length of proof is 15.
% 18.69/3.60 % Level of proof is 3.
% 18.69/3.60 % Maximum clause weight is 59.000.
% 18.69/3.60 % Given clauses 0.
% 18.69/3.60
% 18.69/3.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------