%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG372-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:40:04 EDT 2022
% Result : Unsatisfiable 1.98s 2.18s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 10 unt; 0 nHn; 17 RR)
% Number of literals : 32 ( 18 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_norm__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
cnf(cls_minus__equation__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ).
cnf(cls_CHAINED_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ).
cnf(cls_conjecture_0,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
cnf(refute_0_0,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(subst,[],[cls_norm__zero_0:[bind(T_a,$fot(tc_Complex_Ocomplex))]]) ).
cnf(refute_0_1,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(resolve,[$cnf( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) )],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,refute_0_0]) ).
cnf(refute_0_2,plain,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),[0],$fot(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))]]) ).
cnf(refute_0_3,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
inference(resolve,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(resolve,[$cnf( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) )],[refute_0_3,cls_conjecture_0]) ).
cnf(refute_0_5,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolve,[$cnf( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) )],[cls_CHAINED_0,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X_609,tc_RealDef_Oreal),tc_RealDef_Oreal) = X_609 ),
inference(subst,[],[cls_minus__equation__iff_1:[bind(T_a,$fot(tc_RealDef_Oreal)),bind(V_b,$fot(X_609))]]) ).
cnf(refute_0_7,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X_609,tc_RealDef_Oreal),tc_RealDef_Oreal) = X_609,
inference(resolve,[$cnf( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) )],[clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,refute_0_6]) ).
cnf(refute_0_8,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(subst,[],[refute_0_7:[bind(X_609,$fot(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_9,plain,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)) ),[1],$fot(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_10,plain,
( c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolve,[$cnf( $equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)) )],[refute_0_10,refute_0_5]) ).
cnf(refute_0_12,plain,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( $equal(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )],[refute_0_12,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG372-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 05:23:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.98/2.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.98/2.18
% 1.98/2.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.98/2.19
%------------------------------------------------------------------------------