TSTP Solution File: LAT279-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT279-2 : 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 : n019.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 0.14s 0.36s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT279-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 04:24:28 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.14/0.36 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.36
% 0.14/0.36 % SZS status Unsatisfiable
% 0.14/0.36
% 0.14/0.36 % SZS output start Proof
% 0.14/0.36 Take the following subset of the input axioms:
% 0.14/0.36 fof(cls_Tarski_OPartialOrder__iff_1, axiom, ![V_P, T_a]: (~c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a, tc_Product__Type_Ounit)) | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a, tc_Product__Type_Ounit), T_a))).
% 0.14/0.36 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))).
% 0.14/0.36 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)).
% 0.14/0.36 fof(cls_conjecture_0, negated_conjecture, ~c_Relation_Oantisym(v_r, t_a)).
% 0.14/0.36
% 0.14/0.36 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.36 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.36 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.36 fresh(y, y, x1...xn) = u
% 0.14/0.36 C => fresh(s, t, x1...xn) = v
% 0.14/0.36 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.36 variables of u and v.
% 0.14/0.36 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.36 input problem has no model of domain size 1).
% 0.14/0.36
% 0.14/0.36 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.36
% 0.14/0.36 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).
% 0.14/0.36 Axiom 2 (cls_Tarski_OPartialOrder__iff_1): fresh(X, X, Y, Z) = true.
% 0.14/0.36 Axiom 3 (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)) = true.
% 0.14/0.36 Axiom 4 (cls_Tarski_OPartialOrder__iff_1): fresh(c_in(X, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(Y, tc_Product__Type_Ounit)), true, X, Y) = c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X, Y, tc_Product__Type_Ounit), Y).
% 0.14/0.36
% 0.14/0.36 Goal 1 (cls_conjecture_0): c_Relation_Oantisym(v_r, t_a) = true.
% 0.14/0.36 Proof:
% 0.14/0.36 c_Relation_Oantisym(v_r, t_a)
% 0.14/0.36 = { by axiom 1 (cls_Tarski_Or_A_61_61_Aorder_Acl_0) }
% 0.14/0.36 c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), t_a)
% 0.14/0.36 = { by axiom 4 (cls_Tarski_OPartialOrder__iff_1) R->L }
% 0.14/0.36 fresh(c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, v_cl, t_a)
% 0.14/0.36 = { by axiom 3 (cls_Tarski_Ocl_A_58_APartialOrder_0) }
% 0.14/0.36 fresh(true, true, v_cl, t_a)
% 0.14/0.36 = { by axiom 2 (cls_Tarski_OPartialOrder__iff_1) }
% 0.14/0.36 true
% 0.14/0.36 % SZS output end Proof
% 0.14/0.36
% 0.14/0.36 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------