TSTP Solution File: ALG353-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG353-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n023.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 : 300s
% DateTime : Wed Aug 30 16:43:02 EDT 2023
% Result : Unsatisfiable 52.81s 6.99s
% Output : Proof 52.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG353-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 06:19:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 52.81/6.99 Command-line arguments: --no-flatten-goal
% 52.81/6.99
% 52.81/6.99 % SZS status Unsatisfiable
% 52.81/6.99
% 52.81/7.00 % SZS output start Proof
% 52.81/7.00 Take the following subset of the input axioms:
% 52.99/7.01 fof(cls_CHAINED_0, axiom, ~c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) | (~c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) | (~c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) | ~c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)))).
% 52.99/7.01 fof(cls_complex__Im__i_0, axiom, c_Complex_OIm(c_Complex_Oii)=c_HOL_Oone__class_Oone(tc_RealDef_Oreal)).
% 52.99/7.01 fof(cls_conjecture_0, negated_conjecture, c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 52.99/7.01 fof(cls_conjecture_1, negated_conjecture, c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 52.99/7.01 fof(cls_conjecture_2, negated_conjecture, c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 52.99/7.01 fof(cls_conjecture_3, negated_conjecture, c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 52.99/7.01 fof(cls_dist__complex__def_0, axiom, ![V_x, V_y]: c_RealVector_Odist__class_Odist(V_x, V_y, tc_Complex_Ocomplex)=c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_x, V_y, tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 52.99/7.01
% 52.99/7.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 52.99/7.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 52.99/7.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 52.99/7.01 fresh(y, y, x1...xn) = u
% 52.99/7.01 C => fresh(s, t, x1...xn) = v
% 52.99/7.01 where fresh is a fresh function symbol and x1..xn are the free
% 52.99/7.01 variables of u and v.
% 52.99/7.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 52.99/7.01 input problem has no model of domain size 1).
% 52.99/7.01
% 52.99/7.01 The encoding turns the above axioms into the following unit equations and goals:
% 52.99/7.01
% 52.99/7.01 Axiom 1 (cls_complex__Im__i_0): c_Complex_OIm(c_Complex_Oii) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal).
% 52.99/7.01 Axiom 2 (cls_dist__complex__def_0): c_RealVector_Odist__class_Odist(X, Y, tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X, Y, tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 52.99/7.01 Axiom 3 (cls_norm__minus__commute_0): fresh210(X, X, Y, Z, W) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(W, Z, Y), Y).
% 52.99/7.01 Axiom 4 (cls_conjecture_3): c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 52.99/7.01 Axiom 5 (cls_conjecture_2): c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 52.99/7.01 Axiom 6 (cls_conjecture_1): c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 52.99/7.01 Axiom 7 (cls_conjecture_0): c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 52.99/7.01
% 52.99/7.01 Lemma 8: fresh210(X, X, tc_Complex_Ocomplex, Y, Z) = c_RealVector_Odist__class_Odist(Z, Y, tc_Complex_Ocomplex).
% 52.99/7.01 Proof:
% 52.99/7.01 fresh210(X, X, tc_Complex_Ocomplex, Y, Z)
% 52.99/7.01 = { by axiom 3 (cls_norm__minus__commute_0) }
% 52.99/7.01 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(Z, Y, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 52.99/7.01 = { by axiom 2 (cls_dist__complex__def_0) R->L }
% 52.99/7.01 c_RealVector_Odist__class_Odist(Z, Y, tc_Complex_Ocomplex)
% 52.99/7.01
% 52.99/7.01 Goal 1 (cls_CHAINED_0): tuple(c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)) = tuple(true2, true2, true2, true2).
% 52.99/7.01 Proof:
% 52.99/7.01 tuple(c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 3 (cls_norm__minus__commute_0) R->L }
% 52.99/7.01 tuple(c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), fresh210(X, X, tc_Complex_Ocomplex, c_Complex_Oii, v_z), tc_RealDef_Oreal))
% 52.99/7.01 = { by lemma 8 }
% 52.99/7.01 tuple(c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 3 (cls_norm__minus__commute_0) R->L }
% 52.99/7.01 tuple(c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), fresh210(Y, Y, tc_Complex_Ocomplex, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), v_z), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by lemma 8 }
% 52.99/7.01 tuple(c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) R->L }
% 52.99/7.01 tuple(c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) R->L }
% 52.99/7.01 tuple(c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) R->L }
% 52.99/7.01 tuple(c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) R->L }
% 52.99/7.01 tuple(c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) }
% 52.99/7.01 tuple(c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 7 (cls_conjecture_0) }
% 52.99/7.01 tuple(true2, c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) }
% 52.99/7.01 tuple(true2, c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 5 (cls_conjecture_2) }
% 52.99/7.01 tuple(true2, true2, c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 2 (cls_dist__complex__def_0) }
% 52.99/7.01 tuple(true2, true2, c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) }
% 52.99/7.01 tuple(true2, true2, c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 6 (cls_conjecture_1) }
% 52.99/7.01 tuple(true2, true2, true2, c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Odist__class_Odist(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 2 (cls_dist__complex__def_0) }
% 52.99/7.01 tuple(true2, true2, true2, c_lessequals(c_Complex_OIm(c_Complex_Oii), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 1 (cls_complex__Im__i_0) }
% 52.99/7.01 tuple(true2, true2, true2, c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_z, c_Complex_Oii, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 52.99/7.01 = { by axiom 4 (cls_conjecture_3) }
% 52.99/7.01 tuple(true2, true2, true2, true2)
% 52.99/7.01 % SZS output end Proof
% 52.99/7.01
% 52.99/7.01 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------