TSTP Solution File: LAT278-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT278-1 : 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 : n032.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 06:28:06 EDT 2023
% Result : Unsatisfiable 217.37s 28.40s
% Output : Proof 217.37s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT278-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 24 06:03:41 EDT 2023
% 0.10/0.30 % CPUTime :
% 217.37/28.40 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 217.37/28.40
% 217.37/28.40 % SZS status Unsatisfiable
% 217.37/28.40
% 217.37/28.41 % SZS output start Proof
% 217.37/28.41 Take the following subset of the input axioms:
% 217.37/28.41 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)).
% 217.37/28.41 fof(cls_Tarski_OPartialOrder__iff_0, axiom, ![T_a, V_P]: (~c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) | c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P, T_a, tc_Product__Type_Ounit), c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a))).
% 217.37/28.41 fof(cls_Tarski_Ocl_A_58_APartialOrder_0, axiom, c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit))).
% 217.37/28.41 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)).
% 217.37/28.41 fof(cls_conjecture_0, negated_conjecture, ~c_Relation_Orefl(v_A, v_r, t_a)).
% 217.37/28.41
% 217.37/28.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 217.37/28.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 217.37/28.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 217.37/28.41 fresh(y, y, x1...xn) = u
% 217.37/28.41 C => fresh(s, t, x1...xn) = v
% 217.37/28.41 where fresh is a fresh function symbol and x1..xn are the free
% 217.37/28.41 variables of u and v.
% 217.37/28.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 217.37/28.41 input problem has no model of domain size 1).
% 217.37/28.41
% 217.37/28.41 The encoding turns the above axioms into the following unit equations and goals:
% 217.37/28.41
% 217.37/28.41 Axiom 1 (cls_Tarski_Or_A_61_61_Aorder_Acl_0): v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit).
% 217.37/28.41 Axiom 2 (cls_Tarski_OA_A_61_61_Apset_Acl_0): v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit).
% 217.37/28.41 Axiom 3 (cls_Tarski_OPartialOrder__iff_0): fresh1086(X, X, Y, Z) = true2.
% 217.37/28.41 Axiom 4 (cls_Tarski_Ocl_A_58_APartialOrder_0): c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)) = true2.
% 217.37/28.41 Axiom 5 (cls_Tarski_OPartialOrder__iff_0): fresh1086(c_in(X, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y, tc_Product__Type_Ounit)), true2, X, Y) = c_Relation_Orefl(c_Tarski_Opotype_Opset(X, Y, tc_Product__Type_Ounit), c_Tarski_Opotype_Oorder(X, Y, tc_Product__Type_Ounit), Y).
% 217.37/28.41
% 217.37/28.41 Goal 1 (cls_conjecture_0): c_Relation_Orefl(v_A, v_r, t_a) = true2.
% 217.37/28.41 Proof:
% 217.37/28.41 c_Relation_Orefl(v_A, v_r, t_a)
% 217.37/28.41 = { by axiom 2 (cls_Tarski_OA_A_61_61_Apset_Acl_0) }
% 217.37/28.41 c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), v_r, t_a)
% 217.37/28.41 = { by axiom 1 (cls_Tarski_Or_A_61_61_Aorder_Acl_0) }
% 217.37/28.41 c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), t_a)
% 217.37/28.41 = { by axiom 5 (cls_Tarski_OPartialOrder__iff_0) R->L }
% 217.37/28.41 fresh1086(c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true2, v_cl, t_a)
% 217.37/28.41 = { by axiom 4 (cls_Tarski_Ocl_A_58_APartialOrder_0) }
% 217.37/28.41 fresh1086(true2, true2, v_cl, t_a)
% 217.37/28.41 = { by axiom 3 (cls_Tarski_OPartialOrder__iff_0) }
% 217.37/28.41 true2
% 217.37/28.41 % SZS output end Proof
% 217.37/28.41
% 217.37/28.41 RESULT: Unsatisfiable (the axioms are contradictory).
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