TSTP Solution File: LAT268-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT268-2 : 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 : n024.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 06:28:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT268-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n024.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 05:00:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.41 Command-line arguments: --no-flatten-goal
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Take the following subset of the input axioms:
% 0.20/0.42 fof(cls_Tarski_OA_A_61_61_Apset_Acl_0, axiom, v_A=c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit)).
% 0.20/0.42 fof(cls_Tarski_OCL_Olub__upper_0, axiom, ![V_x, V_S, T_a, V_cl]: (~c_in(V_x, V_S, T_a) | (~c_in(V_cl, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) | (~c_in(V_cl, 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)) | 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))))))).
% 0.20/0.42 fof(cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0, axiom, ![V_y, T_a2, V_cl2, V_x2]: (~c_in(c_Pair(V_x2, V_y, T_a2, T_a2), c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl2, T_a2), T_a2, tc_Product__Type_Ounit), tc_prod(T_a2, T_a2)) | c_in(c_Pair(V_y, V_x2, T_a2, T_a2), c_Tarski_Opotype_Oorder(V_cl2, T_a2, tc_Product__Type_Ounit), tc_prod(T_a2, T_a2)))).
% 0.20/0.42 fof(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0, axiom, c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit))).
% 0.20/0.42 fof(cls_Tarski_Odual_Acl_A_58_APartialOrder_0, axiom, c_in(c_Tarski_Odual(v_cl, t_a), c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit))).
% 0.20/0.42 fof(cls_Tarski_Oglb__dual__lub_0, axiom, ![T_a2, V_cl2, V_S2]: c_Tarski_Oglb(V_S2, V_cl2, T_a2)=c_Tarski_Olub(V_S2, c_Tarski_Odual(V_cl2, T_a2), T_a2)).
% 0.20/0.42 fof(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0, axiom, ![T_a2, V_cl2]: c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl2, T_a2), T_a2, tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(V_cl2, T_a2, tc_Product__Type_Ounit)).
% 0.20/0.42 fof(cls_Tarski_Or_A_61_61_Aorder_Acl_0, axiom, v_r=c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)).
% 0.20/0.42 fof(cls_conjecture_0, negated_conjecture, c_lessequals(v_S, v_A, tc_set(t_a))).
% 0.20/0.42 fof(cls_conjecture_1, negated_conjecture, c_in(v_x, v_S, t_a)).
% 0.20/0.42 fof(cls_conjecture_2, negated_conjecture, ~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))).
% 0.20/0.42
% 0.20/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.42 fresh(y, y, x1...xn) = u
% 0.20/0.42 C => fresh(s, t, x1...xn) = v
% 0.20/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.42 variables of u and v.
% 0.20/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.42 input problem has no model of domain size 1).
% 0.20/0.42
% 0.20/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.42
% 0.20/0.42 Axiom 1 (cls_Tarski_OA_A_61_61_Apset_Acl_0): v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit).
% 0.20/0.42 Axiom 2 (cls_Tarski_Or_A_61_61_Aorder_Acl_0): v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit).
% 0.20/0.42 Axiom 3 (cls_conjecture_1): c_in(v_x, v_S, t_a) = true.
% 0.20/0.42 Axiom 4 (cls_conjecture_0): c_lessequals(v_S, v_A, tc_set(t_a)) = true.
% 0.20/0.42 Axiom 5 (cls_Tarski_Oglb__dual__lub_0): c_Tarski_Oglb(X, Y, Z) = c_Tarski_Olub(X, c_Tarski_Odual(Y, Z), Z).
% 0.20/0.42 Axiom 6 (cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0): c_Tarski_Opotype_Opset(c_Tarski_Odual(X, Y), Y, tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X, Y, tc_Product__Type_Ounit).
% 0.20/0.42 Axiom 7 (cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0): fresh(X, X, Y, Z, W, V) = true.
% 0.20/0.42 Axiom 8 (cls_Tarski_OCL_Olub__upper_0): fresh5(X, X, Y, Z, W, V) = true.
% 0.20/0.42 Axiom 9 (cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0): 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.
% 0.20/0.42 Axiom 10 (cls_Tarski_Odual_Acl_A_58_APartialOrder_0): 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.
% 0.20/0.42 Axiom 11 (cls_Tarski_OCL_Olub__upper_0): fresh3(X, X, Y, Z, W, V) = fresh4(c_in(Y, Z, W), true, Y, Z, W, V).
% 0.20/0.42 Axiom 12 (cls_Tarski_OCL_Olub__upper_0): fresh2(X, X, Y, Z, W, V) = fresh3(c_in(V, c_Tarski_OCompleteLattice, tc_Tarski_Opotype_Opotype__ext__type(W, tc_Product__Type_Ounit)), true, Y, Z, W, V).
% 0.20/0.42 Axiom 13 (cls_Tarski_OCL_Olub__upper_0): fresh4(X, X, Y, Z, W, V) = fresh5(c_lessequals(Z, c_Tarski_Opotype_Opset(V, W, tc_Product__Type_Ounit), tc_set(W)), true, Y, Z, W, V).
% 0.20/0.42 Axiom 14 (cls_Tarski_OCL_Olub__upper_0): fresh2(c_in(X, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y, tc_Product__Type_Ounit)), true, Z, W, Y, X) = c_in(c_Pair(Z, c_Tarski_Olub(W, X, Y), Y, Y), c_Tarski_Opotype_Oorder(X, Y, tc_Product__Type_Ounit), tc_prod(Y, Y)).
% 0.20/0.42 Axiom 15 (cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0): fresh(c_in(c_Pair(X, Y, Z, Z), c_Tarski_Opotype_Oorder(c_Tarski_Odual(W, Z), Z, tc_Product__Type_Ounit), tc_prod(Z, Z)), true, X, Y, Z, W) = c_in(c_Pair(Y, X, Z, Z), c_Tarski_Opotype_Oorder(W, Z, tc_Product__Type_Ounit), tc_prod(Z, Z)).
% 0.20/0.42
% 0.20/0.42 Goal 1 (cls_conjecture_2): 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.
% 0.20/0.42 Proof:
% 0.20/0.42 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))
% 0.20/0.42 = { by axiom 2 (cls_Tarski_Or_A_61_61_Aorder_Acl_0) }
% 0.20/0.42 c_in(c_Pair(c_Tarski_Oglb(v_S, v_cl, 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))
% 0.20/0.42 = { by axiom 5 (cls_Tarski_Oglb__dual__lub_0) }
% 0.20/0.42 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))
% 0.20/0.42 = { by axiom 15 (cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) R->L }
% 0.20/0.42 fresh(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)), true, v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 14 (cls_Tarski_OCL_Olub__upper_0) R->L }
% 0.20/0.42 fresh(fresh2(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, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Olub(v_S, c_Tarski_Odual(v_cl, t_a), t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 5 (cls_Tarski_Oglb__dual__lub_0) R->L }
% 0.20/0.42 fresh(fresh2(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, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 10 (cls_Tarski_Odual_Acl_A_58_APartialOrder_0) }
% 0.20/0.42 fresh(fresh2(true, true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 12 (cls_Tarski_OCL_Olub__upper_0) }
% 0.20/0.42 fresh(fresh3(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, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 9 (cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) }
% 0.20/0.42 fresh(fresh3(true, true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 11 (cls_Tarski_OCL_Olub__upper_0) }
% 0.20/0.42 fresh(fresh4(c_in(v_x, v_S, t_a), true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 3 (cls_conjecture_1) }
% 0.20/0.42 fresh(fresh4(true, true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 13 (cls_Tarski_OCL_Olub__upper_0) }
% 0.20/0.42 fresh(fresh5(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)), true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 6 (cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) }
% 0.20/0.42 fresh(fresh5(c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)), true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 1 (cls_Tarski_OA_A_61_61_Apset_Acl_0) R->L }
% 0.20/0.42 fresh(fresh5(c_lessequals(v_S, v_A, tc_set(t_a)), true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 4 (cls_conjecture_0) }
% 0.20/0.42 fresh(fresh5(true, true, v_x, v_S, t_a, c_Tarski_Odual(v_cl, t_a)), true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 8 (cls_Tarski_OCL_Olub__upper_0) }
% 0.20/0.42 fresh(true, true, v_x, c_Tarski_Oglb(v_S, v_cl, t_a), t_a, v_cl)
% 0.20/0.42 = { by axiom 7 (cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) }
% 0.20/0.42 true
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------