TSTP Solution File: PUZ064-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ064-2 : TPTP v8.1.2. Released v3.2.0.
% 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 : n001.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 : Thu Aug 31 13:24:09 EDT 2023
% Result : Unsatisfiable 12.17s 1.91s
% Output : Proof 12.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ064-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 22:51:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 12.17/1.91 Command-line arguments: --flatten
% 12.17/1.91
% 12.17/1.91 % SZS status Unsatisfiable
% 12.17/1.91
% 12.17/2.00 % SZS output start Proof
% 12.17/2.00 Take the following subset of the input axioms:
% 12.17/2.01 fof(cls_Mutil_Otiling_OUn_0, axiom, ![V_a, V_A, T_a, V_t]: (~c_in(V_a, V_A, tc_set(T_a)) | (~c_in(V_t, c_Mutil_Otiling(V_A, T_a), tc_set(T_a)) | (c_inter(V_a, V_t, T_a)!=c_emptyset | c_in(c_union(V_a, V_t, T_a), c_Mutil_Otiling(V_A, T_a), tc_set(T_a)))))).
% 12.17/2.01 fof(cls_Set_OCompl__Diff__eq_0, axiom, ![V_B, T_a2, V_A2]: c_uminus(c_minus(V_A2, V_B, tc_set(T_a2)), tc_set(T_a2))=c_union(c_uminus(V_A2, tc_set(T_a2)), V_B, T_a2)).
% 12.17/2.01 fof(cls_Set_OCompl__UNIV__eq_0, axiom, ![T_a2]: c_uminus(c_UNIV, tc_set(T_a2))=c_emptyset).
% 12.17/2.01 fof(cls_Set_ODiff__Compl_0, axiom, ![T_a2, V_A2, V_B2]: c_minus(V_A2, c_uminus(V_B2, tc_set(T_a2)), tc_set(T_a2))=c_inter(V_A2, V_B2, T_a2)).
% 12.17/2.01 fof(cls_Set_OInt__UNIV__left_0, axiom, ![V_y, T_a2]: c_inter(c_UNIV, V_y, T_a2)=V_y).
% 12.17/2.01 fof(cls_Set_OUn__Diff__cancel2_0, axiom, ![T_a2, V_A2, V_B2]: c_union(c_minus(V_B2, V_A2, tc_set(T_a2)), V_A2, T_a2)=c_union(V_B2, V_A2, T_a2)).
% 12.17/2.01 fof(cls_Set_OUn__Diff__cancel_0, axiom, ![T_a2, V_A2, V_B2]: c_union(V_A2, c_minus(V_B2, V_A2, tc_set(T_a2)), T_a2)=c_union(V_A2, V_B2, T_a2)).
% 12.17/2.01 fof(cls_Set_OUn__UNIV__left_0, axiom, ![T_a2, V_B2]: c_union(c_UNIV, V_B2, T_a2)=c_UNIV).
% 12.17/2.01 fof(cls_Set_OUn__absorb_0, axiom, ![T_a2, V_y2]: c_union(V_y2, V_y2, T_a2)=V_y2).
% 12.17/2.01 fof(cls_Set_OUn__assoc_0, axiom, ![V_C, T_a2, V_A2, V_B2]: c_union(c_union(V_A2, V_B2, T_a2), V_C, T_a2)=c_union(V_A2, c_union(V_B2, V_C, T_a2), T_a2)).
% 12.17/2.01 fof(cls_Set_OUn__empty__left_0, axiom, ![T_a2, V_y2]: c_union(c_emptyset, V_y2, T_a2)=V_y2).
% 12.17/2.01 fof(cls_Set_OUn__empty__right_0, axiom, ![T_a2, V_y2]: c_union(V_y2, c_emptyset, T_a2)=V_y2).
% 12.17/2.01 fof(cls_Set_Odouble__complement_0, axiom, ![T_a2, V_y2]: c_uminus(c_uminus(V_y2, tc_set(T_a2)), tc_set(T_a2))=V_y2).
% 12.17/2.01 fof(cls_conjecture_0, negated_conjecture, c_in(v_a, v_A, tc_set(t_a))).
% 12.17/2.01 fof(cls_conjecture_2, negated_conjecture, c_inter(v_a, v_t, t_a)=c_emptyset).
% 12.17/2.01 fof(cls_conjecture_3, negated_conjecture, c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a))).
% 12.17/2.01 fof(cls_conjecture_4, negated_conjecture, c_inter(c_union(v_a, v_t, t_a), v_u, t_a)=c_emptyset).
% 12.17/2.01 fof(cls_conjecture_5, negated_conjecture, ~c_in(c_union(c_union(v_a, v_t, t_a), v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a))).
% 12.17/2.01 fof(cls_conjecture_6, negated_conjecture, c_in(c_union(v_t, v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a)) | (c_inter(v_t, v_u, t_a)!=c_emptyset | ~c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a)))).
% 12.17/2.01
% 12.17/2.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.17/2.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.17/2.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.17/2.01 fresh(y, y, x1...xn) = u
% 12.17/2.01 C => fresh(s, t, x1...xn) = v
% 12.17/2.01 where fresh is a fresh function symbol and x1..xn are the free
% 12.17/2.01 variables of u and v.
% 12.17/2.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.17/2.01 input problem has no model of domain size 1).
% 12.17/2.01
% 12.17/2.01 The encoding turns the above axioms into the following unit equations and goals:
% 12.17/2.01
% 12.17/2.01 Axiom 1 (cls_conjecture_6): fresh12(X, X) = true2.
% 12.17/2.01 Axiom 2 (cls_Set_OCompl__UNIV__eq_0): c_uminus(c_UNIV, tc_set(X)) = c_emptyset.
% 12.17/2.01 Axiom 3 (cls_Set_OInt__UNIV__left_0): c_inter(c_UNIV, X, Y) = X.
% 12.17/2.01 Axiom 4 (cls_conjecture_2): c_inter(v_a, v_t, t_a) = c_emptyset.
% 12.17/2.01 Axiom 5 (cls_Set_OUn__absorb_0): c_union(X, X, Y) = X.
% 12.17/2.01 Axiom 6 (cls_Set_OUn__empty__right_0): c_union(X, c_emptyset, Y) = X.
% 12.17/2.01 Axiom 7 (cls_Set_OUn__UNIV__left_0): c_union(c_UNIV, X, Y) = c_UNIV.
% 12.17/2.01 Axiom 8 (cls_Set_OUn__empty__left_0): c_union(c_emptyset, X, Y) = X.
% 12.17/2.01 Axiom 9 (cls_conjecture_0): c_in(v_a, v_A, tc_set(t_a)) = true2.
% 12.17/2.01 Axiom 10 (cls_conjecture_6): fresh11(X, X) = fresh12(c_inter(v_t, v_u, t_a), c_emptyset).
% 12.17/2.01 Axiom 11 (cls_Mutil_Otiling_OUn_0): fresh10(X, X, Y, Z, W, V) = true2.
% 12.17/2.01 Axiom 12 (cls_Set_Odouble__complement_0): c_uminus(c_uminus(X, tc_set(Y)), tc_set(Y)) = X.
% 12.17/2.01 Axiom 13 (cls_conjecture_4): c_inter(c_union(v_a, v_t, t_a), v_u, t_a) = c_emptyset.
% 12.17/2.01 Axiom 14 (cls_conjecture_3): c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a)) = true2.
% 12.17/2.01 Axiom 15 (cls_Set_OUn__assoc_0): c_union(c_union(X, Y, Z), W, Z) = c_union(X, c_union(Y, W, Z), Z).
% 12.17/2.01 Axiom 16 (cls_Set_ODiff__Compl_0): c_minus(X, c_uminus(Y, tc_set(Z)), tc_set(Z)) = c_inter(X, Y, Z).
% 12.17/2.01 Axiom 17 (cls_Set_OCompl__Diff__eq_0): c_uminus(c_minus(X, Y, tc_set(Z)), tc_set(Z)) = c_union(c_uminus(X, tc_set(Z)), Y, Z).
% 12.17/2.01 Axiom 18 (cls_Set_OUn__Diff__cancel_0): c_union(X, c_minus(Y, X, tc_set(Z)), Z) = c_union(X, Y, Z).
% 12.17/2.01 Axiom 19 (cls_Set_OUn__Diff__cancel2_0): c_union(c_minus(X, Y, tc_set(Z)), Y, Z) = c_union(X, Y, Z).
% 12.17/2.01 Axiom 20 (cls_Mutil_Otiling_OUn_0): fresh9(X, X, Y, Z, W, V) = fresh10(c_inter(Y, V, W), c_emptyset, Y, Z, W, V).
% 12.17/2.01 Axiom 21 (cls_Mutil_Otiling_OUn_0): fresh8(X, X, Y, Z, W, V) = c_in(c_union(Y, V, W), c_Mutil_Otiling(Z, W), tc_set(W)).
% 12.17/2.01 Axiom 22 (cls_conjecture_6): fresh11(c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a)), true2) = c_in(c_union(v_t, v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a)).
% 12.17/2.01 Axiom 23 (cls_Mutil_Otiling_OUn_0): fresh9(c_in(X, c_Mutil_Otiling(Y, Z), tc_set(Z)), true2, W, Y, Z, X) = fresh8(c_in(W, Y, tc_set(Z)), true2, W, Y, Z, X).
% 12.17/2.01
% 12.17/2.01 Lemma 24: c_uminus(c_union(c_uminus(X, tc_set(Y)), Z, Y), tc_set(Y)) = c_minus(X, Z, tc_set(Y)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_uminus(c_union(c_uminus(X, tc_set(Y)), Z, Y), tc_set(Y))
% 12.17/2.01 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) R->L }
% 12.17/2.01 c_uminus(c_uminus(c_minus(X, Z, tc_set(Y)), tc_set(Y)), tc_set(Y))
% 12.17/2.01 = { by axiom 12 (cls_Set_Odouble__complement_0) }
% 12.17/2.01 c_minus(X, Z, tc_set(Y))
% 12.17/2.01
% 12.17/2.01 Lemma 25: c_minus(c_minus(X, Y, tc_set(Z)), W, tc_set(Z)) = c_minus(X, c_union(Y, W, Z), tc_set(Z)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(c_minus(X, Y, tc_set(Z)), W, tc_set(Z))
% 12.17/2.01 = { by lemma 24 R->L }
% 12.17/2.01 c_uminus(c_union(c_uminus(c_minus(X, Y, tc_set(Z)), tc_set(Z)), W, Z), tc_set(Z))
% 12.17/2.01 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.01 c_uminus(c_union(c_union(c_uminus(X, tc_set(Z)), Y, Z), W, Z), tc_set(Z))
% 12.17/2.01 = { by axiom 15 (cls_Set_OUn__assoc_0) }
% 12.17/2.01 c_uminus(c_union(c_uminus(X, tc_set(Z)), c_union(Y, W, Z), Z), tc_set(Z))
% 12.17/2.01 = { by lemma 24 }
% 12.17/2.01 c_minus(X, c_union(Y, W, Z), tc_set(Z))
% 12.17/2.01
% 12.17/2.01 Lemma 26: c_inter(X, c_uminus(Y, tc_set(Z)), Z) = c_minus(X, Y, tc_set(Z)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_inter(X, c_uminus(Y, tc_set(Z)), Z)
% 12.17/2.01 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.01 c_minus(X, c_uminus(c_uminus(Y, tc_set(Z)), tc_set(Z)), tc_set(Z))
% 12.17/2.01 = { by axiom 12 (cls_Set_Odouble__complement_0) }
% 12.17/2.01 c_minus(X, Y, tc_set(Z))
% 12.17/2.01
% 12.17/2.01 Lemma 27: c_minus(c_UNIV, X, tc_set(Y)) = c_uminus(X, tc_set(Y)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(c_UNIV, X, tc_set(Y))
% 12.17/2.01 = { by lemma 26 R->L }
% 12.17/2.01 c_inter(c_UNIV, c_uminus(X, tc_set(Y)), Y)
% 12.17/2.01 = { by axiom 3 (cls_Set_OInt__UNIV__left_0) }
% 12.17/2.01 c_uminus(X, tc_set(Y))
% 12.17/2.01
% 12.17/2.01 Lemma 28: c_union(c_uminus(X, tc_set(Y)), X, Y) = c_UNIV.
% 12.17/2.01 Proof:
% 12.17/2.01 c_union(c_uminus(X, tc_set(Y)), X, Y)
% 12.17/2.01 = { by lemma 27 R->L }
% 12.17/2.01 c_union(c_minus(c_UNIV, X, tc_set(Y)), X, Y)
% 12.17/2.01 = { by axiom 19 (cls_Set_OUn__Diff__cancel2_0) }
% 12.17/2.01 c_union(c_UNIV, X, Y)
% 12.17/2.01 = { by axiom 7 (cls_Set_OUn__UNIV__left_0) }
% 12.17/2.01 c_UNIV
% 12.17/2.01
% 12.17/2.01 Lemma 29: c_minus(X, X, tc_set(Y)) = c_inter(v_a, v_t, t_a).
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(X, X, tc_set(Y))
% 12.17/2.01 = { by lemma 24 R->L }
% 12.17/2.01 c_uminus(c_union(c_uminus(X, tc_set(Y)), X, Y), tc_set(Y))
% 12.17/2.01 = { by lemma 28 }
% 12.17/2.01 c_uminus(c_UNIV, tc_set(Y))
% 12.17/2.01 = { by axiom 2 (cls_Set_OCompl__UNIV__eq_0) }
% 12.17/2.01 c_emptyset
% 12.17/2.01 = { by axiom 4 (cls_conjecture_2) R->L }
% 12.17/2.01 c_inter(v_a, v_t, t_a)
% 12.17/2.01
% 12.17/2.01 Lemma 30: c_minus(X, c_union(Y, X, Z), tc_set(Z)) = c_inter(v_a, v_t, t_a).
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(X, c_union(Y, X, Z), tc_set(Z))
% 12.17/2.01 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) R->L }
% 12.17/2.01 c_minus(X, c_union(Y, c_minus(X, Y, tc_set(Z)), Z), tc_set(Z))
% 12.17/2.01 = { by lemma 25 R->L }
% 12.17/2.01 c_minus(c_minus(X, Y, tc_set(Z)), c_minus(X, Y, tc_set(Z)), tc_set(Z))
% 12.17/2.01 = { by lemma 29 }
% 12.17/2.01 c_inter(v_a, v_t, t_a)
% 12.17/2.01
% 12.17/2.01 Lemma 31: c_union(c_inter(v_a, v_t, t_a), X, Y) = X.
% 12.17/2.01 Proof:
% 12.17/2.01 c_union(c_inter(v_a, v_t, t_a), X, Y)
% 12.17/2.01 = { by axiom 4 (cls_conjecture_2) }
% 12.17/2.01 c_union(c_emptyset, X, Y)
% 12.17/2.01 = { by axiom 8 (cls_Set_OUn__empty__left_0) }
% 12.17/2.01 X
% 12.17/2.01
% 12.17/2.01 Lemma 32: c_union(X, c_union(Y, X, Z), Z) = c_union(Y, X, Z).
% 12.17/2.01 Proof:
% 12.17/2.01 c_union(X, c_union(Y, X, Z), Z)
% 12.17/2.01 = { by axiom 19 (cls_Set_OUn__Diff__cancel2_0) R->L }
% 12.17/2.01 c_union(c_minus(X, c_union(Y, X, Z), tc_set(Z)), c_union(Y, X, Z), Z)
% 12.17/2.01 = { by lemma 30 }
% 12.17/2.01 c_union(c_inter(v_a, v_t, t_a), c_union(Y, X, Z), Z)
% 12.17/2.01 = { by lemma 31 }
% 12.17/2.01 c_union(Y, X, Z)
% 12.17/2.01
% 12.17/2.01 Lemma 33: c_union(X, Y, Z) = c_union(Y, X, Z).
% 12.17/2.01 Proof:
% 12.17/2.01 c_union(X, Y, Z)
% 12.17/2.01 = { by lemma 32 R->L }
% 12.17/2.01 c_union(Y, c_union(X, Y, Z), Z)
% 12.17/2.01 = { by axiom 15 (cls_Set_OUn__assoc_0) R->L }
% 12.17/2.01 c_union(c_union(Y, X, Z), Y, Z)
% 12.17/2.01 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) R->L }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_minus(Y, c_union(Y, X, Z), tc_set(Z)), Z)
% 12.17/2.01 = { by lemma 25 R->L }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_minus(c_minus(Y, Y, tc_set(Z)), X, tc_set(Z)), Z)
% 12.17/2.01 = { by lemma 29 }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_minus(c_inter(v_a, v_t, t_a), X, tc_set(Z)), Z)
% 12.17/2.01 = { by lemma 24 R->L }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_uminus(c_union(c_uminus(c_inter(v_a, v_t, t_a), tc_set(Z)), X, Z), tc_set(Z)), Z)
% 12.17/2.01 = { by axiom 4 (cls_conjecture_2) }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_uminus(c_union(c_uminus(c_emptyset, tc_set(Z)), X, Z), tc_set(Z)), Z)
% 12.17/2.01 = { by axiom 2 (cls_Set_OCompl__UNIV__eq_0) R->L }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_uminus(c_union(c_uminus(c_uminus(c_UNIV, tc_set(Z)), tc_set(Z)), X, Z), tc_set(Z)), Z)
% 12.17/2.01 = { by axiom 12 (cls_Set_Odouble__complement_0) }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_uminus(c_union(c_UNIV, X, Z), tc_set(Z)), Z)
% 12.17/2.01 = { by axiom 7 (cls_Set_OUn__UNIV__left_0) }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_uminus(c_UNIV, tc_set(Z)), Z)
% 12.17/2.01 = { by axiom 2 (cls_Set_OCompl__UNIV__eq_0) }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_emptyset, Z)
% 12.17/2.01 = { by axiom 4 (cls_conjecture_2) R->L }
% 12.17/2.01 c_union(c_union(Y, X, Z), c_inter(v_a, v_t, t_a), Z)
% 12.17/2.01 = { by axiom 15 (cls_Set_OUn__assoc_0) }
% 12.17/2.01 c_union(Y, c_union(X, c_inter(v_a, v_t, t_a), Z), Z)
% 12.17/2.01 = { by axiom 4 (cls_conjecture_2) }
% 12.17/2.01 c_union(Y, c_union(X, c_emptyset, Z), Z)
% 12.17/2.01 = { by axiom 6 (cls_Set_OUn__empty__right_0) }
% 12.17/2.01 c_union(Y, X, Z)
% 12.17/2.01
% 12.17/2.01 Lemma 34: c_minus(X, c_inter(Y, X, Z), tc_set(Z)) = c_minus(X, Y, tc_set(Z)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(X, c_inter(Y, X, Z), tc_set(Z))
% 12.17/2.01 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.01 c_minus(X, c_minus(Y, c_uminus(X, tc_set(Z)), tc_set(Z)), tc_set(Z))
% 12.17/2.01 = { by lemma 24 R->L }
% 12.17/2.01 c_uminus(c_union(c_uminus(X, tc_set(Z)), c_minus(Y, c_uminus(X, tc_set(Z)), tc_set(Z)), Z), tc_set(Z))
% 12.17/2.01 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) }
% 12.17/2.01 c_uminus(c_union(c_uminus(X, tc_set(Z)), Y, Z), tc_set(Z))
% 12.17/2.01 = { by lemma 24 }
% 12.17/2.01 c_minus(X, Y, tc_set(Z))
% 12.17/2.01
% 12.17/2.01 Lemma 35: c_union(c_uminus(X, tc_set(Y)), c_inter(Z, X, Y), Y) = c_union(Z, c_uminus(X, tc_set(Y)), Y).
% 12.17/2.01 Proof:
% 12.17/2.01 c_union(c_uminus(X, tc_set(Y)), c_inter(Z, X, Y), Y)
% 12.17/2.01 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.01 c_union(c_uminus(X, tc_set(Y)), c_minus(Z, c_uminus(X, tc_set(Y)), tc_set(Y)), Y)
% 12.17/2.01 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) }
% 12.17/2.01 c_union(c_uminus(X, tc_set(Y)), Z, Y)
% 12.17/2.01 = { by lemma 33 }
% 12.17/2.01 c_union(Z, c_uminus(X, tc_set(Y)), Y)
% 12.17/2.01
% 12.17/2.01 Lemma 36: c_inter(Y, X, Z) = c_inter(X, Y, Z).
% 12.17/2.01 Proof:
% 12.17/2.01 c_inter(Y, X, Z)
% 12.17/2.01 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.01 c_minus(Y, c_uminus(X, tc_set(Z)), tc_set(Z))
% 12.17/2.01 = { by lemma 34 R->L }
% 12.17/2.01 c_minus(Y, c_inter(c_uminus(X, tc_set(Z)), Y, Z), tc_set(Z))
% 12.17/2.01 = { by lemma 24 R->L }
% 12.17/2.01 c_uminus(c_union(c_uminus(Y, tc_set(Z)), c_inter(c_uminus(X, tc_set(Z)), Y, Z), Z), tc_set(Z))
% 12.17/2.01 = { by lemma 35 }
% 12.17/2.01 c_uminus(c_union(c_uminus(X, tc_set(Z)), c_uminus(Y, tc_set(Z)), Z), tc_set(Z))
% 12.17/2.01 = { by lemma 24 }
% 12.17/2.01 c_minus(X, c_uminus(Y, tc_set(Z)), tc_set(Z))
% 12.17/2.01 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.01 c_inter(X, Y, Z)
% 12.17/2.01
% 12.17/2.01 Lemma 37: c_inter(v_a, v_t, t_a) = c_uminus(c_UNIV, tc_set(X)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_inter(v_a, v_t, t_a)
% 12.17/2.01 = { by axiom 4 (cls_conjecture_2) }
% 12.17/2.01 c_emptyset
% 12.17/2.01 = { by axiom 2 (cls_Set_OCompl__UNIV__eq_0) R->L }
% 12.17/2.01 c_uminus(c_UNIV, tc_set(X))
% 12.17/2.01
% 12.17/2.01 Lemma 38: c_inter(c_uminus(X, tc_set(Y)), Z, Y) = c_minus(Z, X, tc_set(Y)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_inter(c_uminus(X, tc_set(Y)), Z, Y)
% 12.17/2.01 = { by lemma 36 }
% 12.17/2.01 c_inter(Z, c_uminus(X, tc_set(Y)), Y)
% 12.17/2.01 = { by lemma 26 }
% 12.17/2.01 c_minus(Z, X, tc_set(Y))
% 12.17/2.01
% 12.17/2.01 Lemma 39: c_minus(X, c_inter(v_a, v_t, t_a), tc_set(Y)) = X.
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(X, c_inter(v_a, v_t, t_a), tc_set(Y))
% 12.17/2.01 = { by lemma 31 R->L }
% 12.17/2.01 c_union(c_inter(v_a, v_t, t_a), c_minus(X, c_inter(v_a, v_t, t_a), tc_set(Y)), Y)
% 12.17/2.01 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) }
% 12.17/2.01 c_union(c_inter(v_a, v_t, t_a), X, Y)
% 12.17/2.01 = { by lemma 31 }
% 12.17/2.01 X
% 12.17/2.01
% 12.17/2.01 Lemma 40: c_minus(v_u, c_union(v_a, v_t, t_a), tc_set(t_a)) = v_u.
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(v_u, c_union(v_a, v_t, t_a), tc_set(t_a))
% 12.17/2.01 = { by lemma 34 R->L }
% 12.17/2.01 c_minus(v_u, c_inter(c_union(v_a, v_t, t_a), v_u, t_a), tc_set(t_a))
% 12.17/2.01 = { by axiom 13 (cls_conjecture_4) }
% 12.17/2.01 c_minus(v_u, c_emptyset, tc_set(t_a))
% 12.17/2.01 = { by axiom 4 (cls_conjecture_2) R->L }
% 12.17/2.01 c_minus(v_u, c_inter(v_a, v_t, t_a), tc_set(t_a))
% 12.17/2.01 = { by lemma 39 }
% 12.17/2.01 v_u
% 12.17/2.01
% 12.17/2.01 Lemma 41: c_union(c_union(X, Y, Z), c_minus(W, Y, tc_set(Z)), Z) = c_union(c_union(X, Y, Z), W, Z).
% 12.17/2.01 Proof:
% 12.17/2.01 c_union(c_union(X, Y, Z), c_minus(W, Y, tc_set(Z)), Z)
% 12.17/2.01 = { by axiom 15 (cls_Set_OUn__assoc_0) }
% 12.17/2.01 c_union(X, c_union(Y, c_minus(W, Y, tc_set(Z)), Z), Z)
% 12.17/2.01 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) }
% 12.17/2.01 c_union(X, c_union(Y, W, Z), Z)
% 12.17/2.01 = { by axiom 15 (cls_Set_OUn__assoc_0) R->L }
% 12.17/2.01 c_union(c_union(X, Y, Z), W, Z)
% 12.17/2.01
% 12.17/2.01 Lemma 42: c_minus(v_u, c_union(c_union(v_a, v_t, t_a), X, t_a), tc_set(t_a)) = c_minus(v_u, X, tc_set(t_a)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(v_u, c_union(c_union(v_a, v_t, t_a), X, t_a), tc_set(t_a))
% 12.17/2.01 = { by lemma 25 R->L }
% 12.17/2.01 c_minus(c_minus(v_u, c_union(v_a, v_t, t_a), tc_set(t_a)), X, tc_set(t_a))
% 12.17/2.01 = { by lemma 40 }
% 12.17/2.01 c_minus(v_u, X, tc_set(t_a))
% 12.17/2.01
% 12.17/2.01 Lemma 43: c_minus(c_uminus(X, tc_set(Z)), Y, tc_set(Z)) = c_uminus(c_union(X, Y, Z), tc_set(Z)).
% 12.17/2.01 Proof:
% 12.17/2.01 c_minus(c_uminus(X, tc_set(Z)), Y, tc_set(Z))
% 12.17/2.01 = { by axiom 12 (cls_Set_Odouble__complement_0) R->L }
% 12.17/2.01 c_uminus(c_uminus(c_minus(c_uminus(X, tc_set(Z)), Y, tc_set(Z)), tc_set(Z)), tc_set(Z))
% 12.17/2.01 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.01 c_uminus(c_union(c_uminus(c_uminus(X, tc_set(Z)), tc_set(Z)), Y, Z), tc_set(Z))
% 12.17/2.01 = { by axiom 12 (cls_Set_Odouble__complement_0) }
% 12.17/2.02 c_uminus(c_union(X, Y, Z), tc_set(Z))
% 12.17/2.02
% 12.17/2.02 Lemma 44: c_minus(c_union(v_t, v_u, t_a), v_t, tc_set(t_a)) = c_inter(c_union(v_t, v_u, t_a), v_u, t_a).
% 12.17/2.02 Proof:
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), v_t, tc_set(t_a))
% 12.17/2.02 = { by axiom 12 (cls_Set_Odouble__complement_0) R->L }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by lemma 39 R->L }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_inter(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by lemma 37 }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_uminus(c_UNIV, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by lemma 28 R->L }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_uminus(c_union(c_uminus(v_u, tc_set(t_a)), v_u, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by axiom 5 (cls_Set_OUn__absorb_0) R->L }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_uminus(c_union(c_union(c_uminus(v_u, tc_set(t_a)), c_uminus(v_u, tc_set(t_a)), t_a), v_u, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by axiom 15 (cls_Set_OUn__assoc_0) }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_uminus(c_union(c_uminus(v_u, tc_set(t_a)), c_union(c_uminus(v_u, tc_set(t_a)), v_u, t_a), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by lemma 28 }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_uminus(c_union(c_uminus(v_u, tc_set(t_a)), c_UNIV, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) R->L }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_uminus(c_uminus(c_minus(v_u, c_UNIV, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by axiom 12 (cls_Set_Odouble__complement_0) }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_UNIV, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by lemma 28 R->L }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_union(c_uminus(c_minus(c_UNIV, c_union(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), c_minus(c_UNIV, c_union(v_a, v_t, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.02 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.02 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_union(c_union(c_uminus(c_UNIV, tc_set(t_a)), c_union(v_a, v_t, t_a), t_a), c_minus(c_UNIV, c_union(v_a, v_t, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 37 R->L }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_union(c_union(c_inter(v_a, v_t, t_a), c_union(v_a, v_t, t_a), t_a), c_minus(c_UNIV, c_union(v_a, v_t, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 31 }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_union(c_union(v_a, v_t, t_a), c_minus(c_UNIV, c_union(v_a, v_t, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_union(c_union(v_a, v_t, t_a), c_UNIV, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 41 R->L }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_union(c_union(v_a, v_t, t_a), c_minus(c_UNIV, v_t, tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 27 }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_union(c_union(v_a, v_t, t_a), c_uminus(v_t, tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 42 }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_minus(v_u, c_uminus(v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, c_inter(v_u, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 34 }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_uminus(c_minus(v_t, v_u, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_union(c_uminus(v_t, tc_set(t_a)), v_u, t_a), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 33 R->L }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_union(v_u, c_uminus(v_t, tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) R->L }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_union(v_u, c_minus(c_uminus(v_t, tc_set(t_a)), v_u, tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 43 }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(c_union(v_u, c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by lemma 43 R->L }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_minus(c_uminus(v_u, tc_set(t_a)), c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_inter(c_uminus(v_u, tc_set(t_a)), c_union(v_t, v_u, t_a), t_a), tc_set(t_a))
% 12.17/2.03 = { by lemma 34 }
% 12.17/2.03 c_minus(c_union(v_t, v_u, t_a), c_uminus(v_u, tc_set(t_a)), tc_set(t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.03 c_inter(c_union(v_t, v_u, t_a), v_u, t_a)
% 12.17/2.03
% 12.17/2.03 Lemma 45: c_minus(X, c_minus(X, Y, tc_set(Z)), tc_set(Z)) = c_inter(X, Y, Z).
% 12.17/2.03 Proof:
% 12.17/2.03 c_minus(X, c_minus(X, Y, tc_set(Z)), tc_set(Z))
% 12.17/2.03 = { by lemma 38 R->L }
% 12.17/2.03 c_minus(X, c_inter(c_uminus(Y, tc_set(Z)), X, Z), tc_set(Z))
% 12.17/2.03 = { by lemma 34 }
% 12.17/2.03 c_minus(X, c_uminus(Y, tc_set(Z)), tc_set(Z))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.03 c_inter(X, Y, Z)
% 12.17/2.03
% 12.17/2.03 Goal 1 (cls_conjecture_5): c_in(c_union(c_union(v_a, v_t, t_a), v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a)) = true2.
% 12.17/2.03 Proof:
% 12.17/2.03 c_in(c_union(c_union(v_a, v_t, t_a), v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a))
% 12.17/2.03 = { by axiom 15 (cls_Set_OUn__assoc_0) }
% 12.17/2.03 c_in(c_union(v_a, c_union(v_t, v_u, t_a), t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a))
% 12.17/2.03 = { by axiom 21 (cls_Mutil_Otiling_OUn_0) R->L }
% 12.17/2.03 fresh8(c_in(v_a, v_A, tc_set(t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 9 (cls_conjecture_0) }
% 12.17/2.03 fresh8(c_in(v_a, v_A, tc_set(t_a)), true2, v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 23 (cls_Mutil_Otiling_OUn_0) R->L }
% 12.17/2.03 fresh9(c_in(c_union(v_t, v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a)), true2, v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 9 (cls_conjecture_0) R->L }
% 12.17/2.03 fresh9(c_in(c_union(v_t, v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 22 (cls_conjecture_6) R->L }
% 12.17/2.03 fresh9(fresh11(c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a)), true2), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 14 (cls_conjecture_3) }
% 12.17/2.03 fresh9(fresh11(true2, true2), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 9 (cls_conjecture_0) R->L }
% 12.17/2.03 fresh9(fresh11(c_in(v_a, v_A, tc_set(t_a)), true2), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 9 (cls_conjecture_0) R->L }
% 12.17/2.03 fresh9(fresh11(c_in(v_a, v_A, tc_set(t_a)), c_in(v_a, v_A, tc_set(t_a))), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 10 (cls_conjecture_6) }
% 12.17/2.03 fresh9(fresh12(c_inter(v_t, v_u, t_a), c_emptyset), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 4 (cls_conjecture_2) R->L }
% 12.17/2.03 fresh9(fresh12(c_inter(v_t, v_u, t_a), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 40 R->L }
% 12.17/2.03 fresh9(fresh12(c_inter(v_t, c_minus(v_u, c_union(v_a, v_t, t_a), tc_set(t_a)), t_a), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 5 (cls_Set_OUn__absorb_0) R->L }
% 12.17/2.03 fresh9(fresh12(c_inter(v_t, c_minus(v_u, c_union(v_a, c_union(v_t, v_t, t_a), t_a), tc_set(t_a)), t_a), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 15 (cls_Set_OUn__assoc_0) R->L }
% 12.17/2.03 fresh9(fresh12(c_inter(v_t, c_minus(v_u, c_union(c_union(v_a, v_t, t_a), v_t, t_a), tc_set(t_a)), t_a), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 42 }
% 12.17/2.03 fresh9(fresh12(c_inter(v_t, c_minus(v_u, v_t, tc_set(t_a)), t_a), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.03 fresh9(fresh12(c_minus(v_t, c_uminus(c_minus(v_u, v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.03 fresh9(fresh12(c_minus(v_t, c_union(c_uminus(v_u, tc_set(t_a)), v_t, t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 30 }
% 12.17/2.03 fresh9(fresh12(c_inter(v_a, v_t, t_a), c_inter(v_a, v_t, t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 1 (cls_conjecture_6) }
% 12.17/2.03 fresh9(true2, c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 9 (cls_conjecture_0) R->L }
% 12.17/2.03 fresh9(c_in(v_a, v_A, tc_set(t_a)), c_in(v_a, v_A, tc_set(t_a)), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 20 (cls_Mutil_Otiling_OUn_0) }
% 12.17/2.03 fresh10(c_inter(v_a, c_union(v_t, v_u, t_a), t_a), c_emptyset, v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 4 (cls_conjecture_2) R->L }
% 12.17/2.03 fresh10(c_inter(v_a, c_union(v_t, v_u, t_a), t_a), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 36 R->L }
% 12.17/2.03 fresh10(c_inter(c_union(v_t, v_u, t_a), v_a, t_a), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 12 (cls_Set_Odouble__complement_0) R->L }
% 12.17/2.03 fresh10(c_uminus(c_uminus(c_inter(c_union(v_t, v_u, t_a), v_a, t_a), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.03 fresh10(c_uminus(c_uminus(c_minus(c_union(v_t, v_u, t_a), c_uminus(v_a, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_uminus(v_a, tc_set(t_a)), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 35 R->L }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_inter(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), v_a, t_a), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_minus(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_uminus(v_a, tc_set(t_a)), tc_set(t_a)), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 43 }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_uminus(c_union(c_union(v_t, v_u, t_a), c_uminus(v_a, tc_set(t_a)), t_a), tc_set(t_a)), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 18 (cls_Set_OUn__Diff__cancel_0) R->L }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_uminus(c_union(c_union(v_t, v_u, t_a), c_minus(c_uminus(v_a, tc_set(t_a)), c_union(v_t, v_u, t_a), tc_set(t_a)), t_a), tc_set(t_a)), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 43 }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_uminus(c_union(c_union(v_t, v_u, t_a), c_uminus(c_union(v_a, c_union(v_t, v_u, t_a), t_a), tc_set(t_a)), t_a), tc_set(t_a)), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 15 (cls_Set_OUn__assoc_0) R->L }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_uminus(c_union(c_union(v_t, v_u, t_a), c_uminus(c_union(c_union(v_a, v_t, t_a), v_u, t_a), tc_set(t_a)), t_a), tc_set(t_a)), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 43 R->L }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_minus(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_uminus(c_union(c_union(v_a, v_t, t_a), v_u, t_a), tc_set(t_a)), tc_set(t_a)), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.03 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), c_inter(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_union(c_union(v_a, v_t, t_a), v_u, t_a), t_a), t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) R->L }
% 12.17/2.03 fresh10(c_uminus(c_uminus(c_minus(v_a, c_inter(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_union(c_union(v_a, v_t, t_a), v_u, t_a), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.03 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_uminus(c_union(c_union(v_a, v_t, t_a), v_u, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 43 }
% 12.17/2.03 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_union(c_union(v_t, v_u, t_a), c_uminus(c_union(c_union(v_a, v_t, t_a), v_u, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 43 R->L }
% 12.17/2.03 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_union(c_union(v_t, v_u, t_a), c_minus(c_uminus(c_union(v_a, v_t, t_a), tc_set(t_a)), v_u, tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.03 = { by lemma 41 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_union(c_union(v_t, v_u, t_a), c_uminus(c_union(v_a, v_t, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 43 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_uminus(c_union(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_inter(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_union(v_a, v_t, t_a), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 38 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_union(v_t, v_u, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 34 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_inter(c_union(v_t, v_u, t_a), c_union(v_a, v_t, t_a), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 45 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_union(v_t, v_u, t_a), c_union(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 32 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_union(v_t, v_u, t_a), c_union(v_t, c_union(v_a, v_t, t_a), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 25 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_minus(c_union(v_t, v_u, t_a), v_t, tc_set(t_a)), c_union(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 44 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_inter(c_union(v_t, v_u, t_a), v_u, t_a), c_union(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_minus(c_union(v_t, v_u, t_a), c_uminus(v_u, tc_set(t_a)), tc_set(t_a)), c_union(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 25 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_union(v_t, v_u, t_a), c_union(c_uminus(v_u, tc_set(t_a)), c_union(v_a, v_t, t_a), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_union(v_t, v_u, t_a), c_uminus(c_minus(v_u, c_union(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 16 (cls_Set_ODiff__Compl_0) }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_inter(c_union(v_t, v_u, t_a), c_minus(v_u, c_union(v_a, v_t, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 40 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_inter(c_union(v_t, v_u, t_a), v_u, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 44 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(c_union(v_t, v_u, t_a), c_minus(c_union(v_t, v_u, t_a), v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 45 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_inter(c_union(v_t, v_u, t_a), v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 36 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_inter(v_t, c_union(v_t, v_u, t_a), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 34 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_inter(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 16 (cls_Set_ODiff__Compl_0) R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_minus(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), c_uminus(v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 43 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_uminus(c_union(c_union(v_t, v_u, t_a), c_uminus(v_t, tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 41 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_uminus(c_union(c_union(v_t, v_u, t_a), c_minus(c_uminus(v_t, tc_set(t_a)), v_u, tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 43 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_uminus(c_union(c_union(v_t, v_u, t_a), c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 12 (cls_Set_Odouble__complement_0) R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_uminus(c_union(c_uminus(c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), tc_set(t_a)), c_uminus(c_union(v_t, v_u, t_a), tc_set(t_a)), t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 28 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_uminus(c_UNIV, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 37 R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), c_minus(v_t, c_inter(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by lemma 39 }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(c_union(v_a, v_t, t_a), v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 12 (cls_Set_Odouble__complement_0) R->L }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_uminus(c_minus(c_union(v_a, v_t, t_a), v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.04 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.04 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_union(c_uminus(c_union(v_a, v_t, t_a), tc_set(t_a)), v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by lemma 43 R->L }
% 12.17/2.05 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_union(c_minus(c_uminus(v_a, tc_set(t_a)), v_t, tc_set(t_a)), v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by axiom 19 (cls_Set_OUn__Diff__cancel2_0) }
% 12.17/2.05 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) R->L }
% 12.17/2.05 fresh10(c_uminus(c_uminus(c_minus(v_a, c_uminus(c_uminus(c_minus(v_a, v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by axiom 12 (cls_Set_Odouble__complement_0) }
% 12.17/2.05 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(v_a, v_t, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by lemma 34 R->L }
% 12.17/2.05 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(v_a, c_inter(v_t, v_a, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by lemma 36 R->L }
% 12.17/2.05 fresh10(c_uminus(c_uminus(c_minus(v_a, c_minus(v_a, c_inter(v_a, v_t, t_a), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by lemma 39 }
% 12.17/2.05 fresh10(c_uminus(c_uminus(c_minus(v_a, v_a, tc_set(t_a)), tc_set(t_a)), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by axiom 17 (cls_Set_OCompl__Diff__eq_0) }
% 12.17/2.05 fresh10(c_uminus(c_union(c_uminus(v_a, tc_set(t_a)), v_a, t_a), tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by lemma 28 }
% 12.17/2.05 fresh10(c_uminus(c_UNIV, tc_set(t_a)), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by lemma 37 R->L }
% 12.17/2.05 fresh10(c_inter(v_a, v_t, t_a), c_inter(v_a, v_t, t_a), v_a, v_A, t_a, c_union(v_t, v_u, t_a))
% 12.17/2.05 = { by axiom 11 (cls_Mutil_Otiling_OUn_0) }
% 12.17/2.05 true2
% 12.17/2.05 % SZS output end Proof
% 12.17/2.05
% 12.17/2.05 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------