TSTP Solution File: LAT268-10 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n006.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 06:26:05 EDT 2023
% Result : Unsatisfiable 8.27s 8.75s
% Output : CNFRefutation 8.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 07:32:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 8.27/8.75 % SZS status Unsatisfiable
% 8.27/8.75 % SZS output start Proof
% 8.27/8.75 original problem:
% 8.27/8.75 axioms:
% 8.27/8.75 ifeq(A, A, B, C) = B
% 8.27/8.75 c_lessequals(v_S(), v_A(), tc_set(t_a())) = true()
% 8.27/8.75 c_in(v_x(), v_S(), t_a()) = true()
% 8.27/8.75 v_A() = c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit())
% 8.27/8.75 ifeq(c_lessequals(V_S, c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit()), tc_set(T_a)), true(), ifeq(c_in(V_cl, c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit())), true(), ifeq(c_in(V_cl, c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit())), true(), ifeq(c_in(V_x, V_S, T_a), true(), c_in(c_Pair(V_x, c_Tarski_Olub(V_S, V_cl, T_a), T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit()), tc_prod(T_a, T_a)), true()), true()), true()), true()) = true()
% 8.27/8.75 ifeq(c_in(c_Pair(V_x, V_y, T_a, T_a), c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit()), tc_prod(T_a, T_a)), true(), c_in(c_Pair(V_y, V_x, T_a, T_a), c_Tarski_Opotype_Oorder(V_cl, T_a, tc_Product__Type_Ounit()), tc_prod(T_a, T_a)), true()) = true()
% 8.27/8.75 c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = true()
% 8.27/8.75 c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = true()
% 8.27/8.75 c_Tarski_Oglb(V_S, V_cl, T_a) = c_Tarski_Olub(V_S, c_Tarski_Odual(V_cl, T_a), T_a)
% 8.27/8.75 c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl, T_a), T_a, tc_Product__Type_Ounit()) = c_Tarski_Opotype_Opset(V_cl, T_a, tc_Product__Type_Ounit())
% 8.27/8.75 v_r() = c_Tarski_Opotype_Oorder(v_cl(), t_a(), tc_Product__Type_Ounit())
% 8.27/8.75 goal:
% 8.27/8.75 c_in(c_Pair(c_Tarski_Oglb(v_S(), v_cl(), t_a()), v_x(), t_a(), t_a()), v_r(), tc_prod(t_a(), t_a())) != true()
% 8.27/8.75 To show the unsatisfiability of the original goal,
% 8.27/8.75 it suffices to show that c_in(c_Pair(c_Tarski_Oglb(v_S(), v_cl(), t_a()), v_x(), t_a(), t_a()), v_r(), tc_prod(t_a(), t_a())) = true() (skolemized goal) is valid under the axioms.
% 8.27/8.75 Here is an equational proof:
% 8.27/8.75 0: ifeq(X0, X0, X1, X2) = X1.
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 1: c_lessequals(v_S(), v_A(), tc_set(t_a())) = true().
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 2: c_in(v_x(), v_S(), t_a()) = true().
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 3: v_A() = c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()).
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 4: ifeq(c_lessequals(X3, c_Tarski_Opotype_Opset(X4, X5, tc_Product__Type_Ounit()), tc_set(X5)), true(), ifeq(c_in(X4, c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(X5, tc_Product__Type_Ounit())), true(), ifeq(c_in(X4, c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(X5, tc_Product__Type_Ounit())), true(), ifeq(c_in(X6, X3, X5), true(), c_in(c_Pair(X6, c_Tarski_Olub(X3, X4, X5), X5, X5), c_Tarski_Opotype_Oorder(X4, X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), true()), true()), true()), true()) = true().
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 5: ifeq(c_in(c_Pair(X6, X7, X5, X5), c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4, X5), X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), true(), c_in(c_Pair(X7, X6, X5, X5), c_Tarski_Opotype_Oorder(X4, X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), true()) = true().
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 6: c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = true().
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 7: c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = true().
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 8: c_Tarski_Oglb(X3, X4, X5) = c_Tarski_Olub(X3, c_Tarski_Odual(X4, X5), X5).
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 9: c_Tarski_Opotype_Opset(c_Tarski_Odual(X4, X5), X5, tc_Product__Type_Ounit()) = c_Tarski_Opotype_Opset(X4, X5, tc_Product__Type_Ounit()).
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 10: v_r() = c_Tarski_Opotype_Oorder(v_cl(), t_a(), tc_Product__Type_Ounit()).
% 8.27/8.75 Proof: Axiom.
% 8.27/8.75
% 8.27/8.75 11: c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())) = true().
% 8.27/8.75 Proof: Rewrite equation 1,
% 8.27/8.75 lhs with equations [3]
% 8.27/8.75 rhs with equations [].
% 8.27/8.75
% 8.27/8.75 12: c_in(v_x(), v_S(), t_a()) = c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 2,
% 8.27/8.75 lhs with equations []
% 8.27/8.75 rhs with equations [11].
% 8.27/8.75
% 8.27/8.75 13: ifeq(c_lessequals(X3, c_Tarski_Opotype_Opset(X4, X5, tc_Product__Type_Ounit()), tc_set(X5)), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), ifeq(c_in(X4, c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(X5, tc_Product__Type_Ounit())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), ifeq(c_in(X4, c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(X5, tc_Product__Type_Ounit())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), ifeq(c_in(X6, X3, X5), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_in(c_Pair(X6, c_Tarski_Olub(X3, X4, X5), X5, X5), c_Tarski_Opotype_Oorder(X4, X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))) = c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 4,
% 8.27/8.75 lhs with equations [11,11,11,11,11,11,11,11]
% 8.27/8.75 rhs with equations [11].
% 8.27/8.75
% 8.27/8.75 14: ifeq(c_in(c_Pair(X6, X7, X5, X5), c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4, X5), X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_in(c_Pair(X7, X6, X5, X5), c_Tarski_Opotype_Oorder(X4, X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))) = c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 5,
% 8.27/8.75 lhs with equations [11,11]
% 8.27/8.75 rhs with equations [11].
% 8.27/8.75
% 8.27/8.75 15: c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 6,
% 8.27/8.75 lhs with equations []
% 8.27/8.75 rhs with equations [11].
% 8.27/8.75
% 8.27/8.75 16: c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 7,
% 8.27/8.75 lhs with equations []
% 8.27/8.75 rhs with equations [11].
% 8.27/8.75
% 8.27/8.75 20: c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())) = ifeq(c_lessequals(v_S(), c_Tarski_Opotype_Opset(X4, t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), ifeq(c_in(X4, c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), ifeq(c_in(X4, c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), ifeq(c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_in(c_Pair(v_x(), c_Tarski_Olub(v_S(), X4, t_a()), t_a(), t_a()), c_Tarski_Opotype_Oorder(X4, t_a(), tc_Product__Type_Ounit()), tc_prod(t_a(), t_a())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))).
% 8.27/8.75 Proof: A critical pair between equations 13 and 12.
% 8.27/8.75
% 8.27/8.75 30: c_lessequals(v_S(), v_A(), tc_set(t_a())) = ifeq(c_lessequals(v_S(), c_Tarski_Opotype_Opset(X4, t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_lessequals(v_S(), v_A(), tc_set(t_a())), ifeq(c_in(X4, c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())), c_lessequals(v_S(), v_A(), tc_set(t_a())), ifeq(c_in(X4, c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())), c_lessequals(v_S(), v_A(), tc_set(t_a())), c_in(c_Pair(v_x(), c_Tarski_Olub(v_S(), X4, t_a()), t_a(), t_a()), c_Tarski_Opotype_Oorder(X4, t_a(), tc_Product__Type_Ounit()), tc_prod(t_a(), t_a())), c_lessequals(v_S(), v_A(), tc_set(t_a()))), c_lessequals(v_S(), v_A(), tc_set(t_a()))), c_lessequals(v_S(), v_A(), tc_set(t_a()))).
% 8.27/8.75 Proof: Rewrite equation 20,
% 8.27/8.75 lhs with equations [3]
% 8.27/8.75 rhs with equations [3,3,3,3,3,3,0,3,3,3].
% 8.27/8.75
% 8.27/8.75 34: c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = c_lessequals(v_S(), v_A(), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 16,
% 8.27/8.75 lhs with equations []
% 8.27/8.75 rhs with equations [3].
% 8.27/8.75
% 8.27/8.75 35: c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OCompleteLattice(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())) = c_lessequals(v_S(), v_A(), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 15,
% 8.27/8.75 lhs with equations []
% 8.27/8.75 rhs with equations [3].
% 8.27/8.75
% 8.27/8.75 36: ifeq(c_in(c_Pair(X6, X7, X5, X5), c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4, X5), X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), c_lessequals(v_S(), v_A(), tc_set(t_a())), c_in(c_Pair(X7, X6, X5, X5), c_Tarski_Opotype_Oorder(X4, X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), c_lessequals(v_S(), v_A(), tc_set(t_a()))) = c_lessequals(v_S(), v_A(), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 14,
% 8.27/8.75 lhs with equations [3,3]
% 8.27/8.75 rhs with equations [3].
% 8.27/8.75
% 8.27/8.75 39: c_lessequals(v_S(), v_A(), tc_set(t_a())) = true().
% 8.27/8.75 Proof: Rewrite equation 11,
% 8.27/8.75 lhs with equations [3]
% 8.27/8.75 rhs with equations [].
% 8.27/8.75
% 8.27/8.75 45: c_lessequals(v_S(), v_A(), tc_set(t_a())) = ifeq(c_lessequals(v_S(), c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl(), t_a()), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_lessequals(v_S(), v_A(), tc_set(t_a())), ifeq(c_lessequals(v_S(), v_A(), tc_set(t_a())), c_lessequals(v_S(), v_A(), tc_set(t_a())), ifeq(c_in(c_Tarski_Odual(v_cl(), t_a()), c_Tarski_OPartialOrder(), tc_Tarski_Opotype_Opotype__ext__type(t_a(), tc_Product__Type_Ounit())), c_lessequals(v_S(), v_A(), tc_set(t_a())), c_in(c_Pair(v_x(), c_Tarski_Olub(v_S(), c_Tarski_Odual(v_cl(), t_a()), t_a()), t_a(), t_a()), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl(), t_a()), t_a(), tc_Product__Type_Ounit()), tc_prod(t_a(), t_a())), c_lessequals(v_S(), v_A(), tc_set(t_a()))), c_lessequals(v_S(), v_A(), tc_set(t_a()))), c_lessequals(v_S(), v_A(), tc_set(t_a()))).
% 8.27/8.75 Proof: A critical pair between equations 30 and 35.
% 8.27/8.75
% 8.27/8.75 56: c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())) = c_in(c_Pair(v_x(), c_Tarski_Olub(v_S(), c_Tarski_Odual(v_cl(), t_a()), t_a()), t_a(), t_a()), c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl(), t_a()), t_a(), tc_Product__Type_Ounit()), tc_prod(t_a(), t_a())).
% 8.27/8.75 Proof: Rewrite equation 45,
% 8.27/8.75 lhs with equations [3]
% 8.27/8.75 rhs with equations [9,3,3,3,34,3,3,3,0,3,0,3,0].
% 8.27/8.75
% 8.27/8.75 58: c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())) = true().
% 8.27/8.75 Proof: Rewrite equation 39,
% 8.27/8.75 lhs with equations [3]
% 8.27/8.75 rhs with equations [].
% 8.27/8.75
% 8.27/8.75 61: ifeq(c_in(c_Pair(X6, X7, X5, X5), c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4, X5), X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_in(c_Pair(X7, X6, X5, X5), c_Tarski_Opotype_Oorder(X4, X5, tc_Product__Type_Ounit()), tc_prod(X5, X5)), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))) = c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())).
% 8.27/8.75 Proof: Rewrite equation 36,
% 8.27/8.75 lhs with equations [3,3]
% 8.27/8.75 rhs with equations [3].
% 8.27/8.75
% 8.27/8.75 73: c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())) = ifeq(c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a())), c_in(c_Pair(c_Tarski_Olub(v_S(), c_Tarski_Odual(v_cl(), t_a()), t_a()), v_x(), t_a(), t_a()), c_Tarski_Opotype_Oorder(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_prod(t_a(), t_a())), c_lessequals(v_S(), c_Tarski_Opotype_Opset(v_cl(), t_a(), tc_Product__Type_Ounit()), tc_set(t_a()))).
% 8.27/8.75 Proof: A critical pair between equations 61 and 56.
% 8.27/8.75
% 8.27/8.75 92: c_lessequals(v_S(), v_A(), tc_set(t_a())) = c_in(c_Pair(c_Tarski_Olub(v_S(), c_Tarski_Odual(v_cl(), t_a()), t_a()), v_x(), t_a(), t_a()), v_r(), tc_prod(t_a(), t_a())).
% 8.27/8.75 Proof: Rewrite equation 73,
% 8.27/8.75 lhs with equations [3]
% 8.27/8.75 rhs with equations [3,3,10,3,0].
% 8.27/8.75
% 8.27/8.75 106: c_lessequals(v_S(), v_A(), tc_set(t_a())) = true().
% 8.27/8.75 Proof: Rewrite equation 58,
% 8.27/8.75 lhs with equations [3]
% 8.27/8.75 rhs with equations [].
% 8.27/8.75
% 8.27/8.75 113: c_in(c_Pair(c_Tarski_Oglb(v_S(), v_cl(), t_a()), v_x(), t_a(), t_a()), v_r(), tc_prod(t_a(), t_a())) = true().
% 8.27/8.75 Proof: Rewrite lhs with equations [8,92]
% 8.27/8.75 rhs with equations [106].
% 8.27/8.75
% 8.27/8.75 % SZS output end Proof
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