%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV573-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : Wed Jul 20 20:39:31 EDT 2022
% Result : Unsatisfiable 0.86s 1.02s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of clauses : 55 ( 28 unt; 0 nHn; 38 RR)
% Number of literals : 96 ( 95 equ; 44 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_complex__Re__i_0,axiom,
c_Complex_ORe(c_Complex_Oii) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).
cnf(cls_complex__surj_0,axiom,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(V_z),c_Complex_OIm(V_z)) = V_z ).
cnf(cls_complex__eq__cancel__iff2_2,axiom,
c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ).
cnf(cls_complex__Im__of__nat_0,axiom,
c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).
cnf(cls_complex__Re__of__nat_0,axiom,
c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( c_Complex_ORe(c_Complex_Oii) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_Complex_Oii) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(c_Complex_ORe(c_Complex_Oii))),bind(Y,$fot(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)))]]) ).
cnf(refute_0_4,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Complex_ORe(c_Complex_Oii),
inference(resolve,[$cnf( $equal(c_Complex_ORe(c_Complex_Oii),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )],[cls_complex__Re__i_0,refute_0_3]) ).
cnf(refute_0_5,plain,
c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
introduced(tautology,[refl,[$fot(c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)))]]) ).
cnf(refute_0_6,plain,
( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Complex_ORe(c_Complex_Oii)
| c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) ),[1,1],$fot(c_Complex_ORe(c_Complex_Oii))]]) ).
cnf(refute_0_7,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Complex_ORe(c_Complex_Oii)
| c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii)) ),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii)),
inference(resolve,[$cnf( $equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii))
| c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex)) ),[0],$fot(c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii)))]]) ).
cnf(refute_0_10,plain,
( c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
c_Complex_Ocomplex_OComplex(V_x,c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex)) )],[cls_complex__eq__cancel__iff2_2,refute_0_10]) ).
cnf(refute_0_12,plain,
c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(subst,[],[refute_0_11:[bind(V_x,$fot(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal)))]]) ).
cnf(refute_0_13,plain,
c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
introduced(tautology,[refl,[$fot(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)))]]) ).
cnf(refute_0_14,plain,
( c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Complex_ORe(c_Complex_Oii)
| c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) ),
introduced(tautology,[equality,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) ),[1,1],$fot(c_Complex_ORe(c_Complex_Oii))]]) ).
cnf(refute_0_15,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Complex_ORe(c_Complex_Oii)
| c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) ),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)),
inference(resolve,[$cnf( $equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) )],[refute_0_4,refute_0_15]) ).
cnf(refute_0_17,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_17]) ).
cnf(refute_0_19,plain,
( c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii))
| c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)))),bind(Y,$fot(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)))),bind(Z,$fot(c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_20,plain,
( c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)),c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
( c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) ),[1],$fot(c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_23,plain,
( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) )],[refute_0_23,cls_conjecture_0]) ).
cnf(refute_0_25,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex))) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex),
inference(subst,[],[cls_complex__surj_0:[bind(V_z,$fot(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_26,plain,
( c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Complex_ORe(c_Complex_Oii)
| c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) = c_Complex_ORe(c_Complex_Oii) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) ),[0],$fot(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))]]) ).
cnf(refute_0_27,plain,
( c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) = c_Complex_ORe(c_Complex_Oii) ),
inference(resolve,[$cnf( $equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_ORe(c_Complex_Oii)) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) = c_Complex_ORe(c_Complex_Oii),
inference(resolve,[$cnf( $equal(c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )],[cls_complex__Im__of__nat_0,refute_0_27]) ).
cnf(refute_0_29,plain,
( c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) != c_Complex_ORe(c_Complex_Oii)
| c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex))) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex))),c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) ),[0,1],$fot(c_Complex_ORe(c_Complex_Oii))]]) ).
cnf(refute_0_30,plain,
( c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex))) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_OIm(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex))),c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_33,plain,
( c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal)
| c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex)) ),[1,0],$fot(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal))]]) ).
cnf(refute_0_34,plain,
( c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal)
| c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal)) )],[cls_complex__Re__of__nat_0,refute_0_34]) ).
cnf(refute_0_36,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
inference(subst,[],[refute_0_11:[bind(V_x,$fot(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex))))]]) ).
cnf(refute_0_37,plain,
( c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) != c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)))),bind(Y,$fot(c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex))),bind(Z,$fot(c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)))]]) ).
cnf(refute_0_38,plain,
( c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)),c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_RealVector_Oof__real(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)
| c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) != c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)
| c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)),c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) ),[0],$fot(c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex))]]) ).
cnf(refute_0_41,plain,
( c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)) != c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)
| c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)),c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)),c_Complex_ORe(c_Complex_Oii)),c_Nat_Osemiring__1__class_Oof__nat(V_n,tc_Complex_Ocomplex)) )],[refute_0_31,refute_0_41]) ).
cnf(refute_0_43,plain,
c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),
inference(subst,[],[refute_0_42:[bind(V_n,$fot(v_n))]]) ).
cnf(refute_0_44,plain,
( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)
| c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)
| c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)) ),[1],$fot(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex))]]) ).
cnf(refute_0_45,plain,
( c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)
| c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ),
inference(resolve,[$cnf( $equal(c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),
inference(resolve,[$cnf( $equal(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_RealDef_Oreal),tc_Complex_Ocomplex)) )],[refute_0_45,refute_0_24]) ).
cnf(refute_0_47,plain,
c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex) = c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),
introduced(tautology,[refl,[$fot(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex))]]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( $equal(c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)) )],[refute_0_47,refute_0_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV573-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 05:39:42 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.86/1.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.86/1.02
% 0.86/1.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.86/1.03
%------------------------------------------------------------------------------