%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG385-1 : 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 06:50:07 AM UTC 2026
% Result : Unsatisfiable 26.38s 3.76s
% Output : CNFRefutation 26.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 27 unt; 0 def)
% Number of atoms : 51 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 38 ( 4 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_minus__zero_0,axiom,
! [VAR_0] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_minus__zero_0) ).
cnf(c_326,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_minus__zero_0]) ).
fof(cls_diff__minus_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Ominus__class_Ominus(VAR_1,VAR_2,VAR_0) = c_HOL_Oplus__class_Oplus(VAR_1,c_HOL_Ouminus__class_Ouminus(VAR_2,VAR_0),VAR_0)
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_diff__minus_0) ).
cnf(c_341,plain,
( c_HOL_Ominus__class_Ominus(B,C,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A)
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_diff__minus_0]) ).
fof(cls_diff__0__right_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Ominus__class_Ominus(VAR_1,c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = VAR_1
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_diff__0__right_0) ).
cnf(c_346,plain,
( c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_diff__0__right_0]) ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(c_351,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
cnf(c_545,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(cls_mult__right_Ozero_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Otimes__class_Otimes(VAR_1,c_HOL_Ozero__class_Ozero(VAR_0),VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_RealVector_Oreal__normed__algebra(VAR_0) ),
file('theBenchmark.p',cls_mult__right_Ozero_0) ).
cnf(c_546,plain,
( c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_RealVector_Oreal__normed__algebra(A) ),
inference(clausify,[status(thm)],[cls_mult__right_Ozero_0]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(c_807,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__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_858,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]) ).
fof(cls_CHAINED_0_01,axiom,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_859,plain,
c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_CHAINED_0,axiom,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_860,plain,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_poly__pCons_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Polynomial_Opoly(c_Polynomial_OpCons(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_HOL_Oplus__class_Oplus(VAR_1,c_HOL_Otimes__class_Otimes(VAR_3,c_Polynomial_Opoly(VAR_2,VAR_3,VAR_0),VAR_0),VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_poly__pCons_0) ).
cnf(c_892,plain,
( c_Polynomial_Opoly(c_Polynomial_OpCons(B,C,A),D,A) = c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(D,c_Polynomial_Opoly(C,D,A),A),A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_poly__pCons_0]) ).
fof(cls_poly__0_0,axiom,
! [VAR_0,VAR_1] :
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(VAR_0)),VAR_1,VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_poly__0_0) ).
cnf(c_1114,plain,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_poly__0_0]) ).
cnf(c_1496,plain,
c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_546,c_545]) ).
cnf(c_1829,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_351,c_326]) ).
cnf(c_1842,plain,
c_HOL_Ominus__class_Ominus(A,B,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_351,c_341]) ).
cnf(c_1850,plain,
c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A,
inference(resolve,[status(thm)],[c_351,c_346]) ).
cnf(c_3018,plain,
c_HOL_Oplus__class_Oplus(A,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A,
inference(paramod,[status(thm)],[c_1842,c_1850]) ).
cnf(c_1851,plain,
c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A,
inference(paramod,[status(thm)],[c_1829,c_3018]) ).
cnf(c_2106,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____,c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_860,c_858]) ).
cnf(c_2409,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(C,c_Polynomial_Opoly(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_892,c_807]) ).
cnf(c_3019,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_2409,c_2106]) ).
cnf(c_2410,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_2409,c_3019]) ).
cnf(c_3016,plain,
c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_1114,c_807]) ).
cnf(c_3020,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_3016,c_2410]) ).
cnf(c_3021,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,c_HOL_Oplus__class_Oplus(v_c____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1496,c_3020]) ).
cnf(c_3022,plain,
~ c_lessequals(v_da____,c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_aa____,c_HOL_Otimes__class_Otimes(v_z____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(paramod,[status(thm)],[c_1851,c_3021]) ).
cnf(c_3017,plain,
$false,
inference(resolve,[status(thm)],[c_859,c_3022]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG385-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 21:56:32 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3186575 was started by sandbox on n005,
% 0.14/0.36 % Sat Sep 26 21:56:32 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 26.38/3.76
% 26.38/3.76 % SZS status Unsatisfiable for theBenchmark
% 26.38/3.76
% 26.38/3.76 % Proof 1 at 3.22 (+ 0.11) seconds.
% 26.38/3.76 % Length of proof is 22.
% 26.38/3.76 % Level of proof is 3.
% 26.38/3.76 % Maximum clause weight is 23.000.
% 26.38/3.76 % Given clauses 427.
% 26.38/3.76
% 26.38/3.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------