TSTP Solution File: LAT259-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT259-2 : 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 06:27:58 EDT 2023
% Result : Unsatisfiable 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT259-2 : 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
% 0.17/0.35 % Computer : n019.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 09:46:14 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.17/0.39 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.17/0.39
% 0.17/0.39 % SZS status Unsatisfiable
% 0.17/0.39
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 Take the following subset of the input axioms:
% 0.17/0.39 fof(cls_Relation_Oantisym__def_0, axiom, ![V_r, T_a, V_V, V_U]: (~c_Relation_Oantisym(V_r, T_a) | (~c_in(c_Pair(V_V, V_U, T_a, T_a), V_r, tc_prod(T_a, T_a)) | (~c_in(c_Pair(V_U, V_V, T_a, T_a), V_r, tc_prod(T_a, T_a)) | V_U=V_V)))).
% 0.17/0.39 fof(cls_Tarski_OPartialOrder__iff_1, axiom, ![V_P, T_a2]: (~c_in(V_P, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(T_a2, tc_Product__Type_Ounit)) | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P, T_a2, tc_Product__Type_Ounit), T_a2))).
% 0.17/0.39 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))).
% 0.17/0.39 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)).
% 0.17/0.39 fof(cls_conjecture_0, negated_conjecture, c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a))).
% 0.17/0.39 fof(cls_conjecture_1, negated_conjecture, c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a))).
% 0.17/0.39 fof(cls_conjecture_2, negated_conjecture, v_a!=v_b).
% 0.17/0.39
% 0.17/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.39 fresh(y, y, x1...xn) = u
% 0.17/0.39 C => fresh(s, t, x1...xn) = v
% 0.17/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.39 variables of u and v.
% 0.17/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.39 input problem has no model of domain size 1).
% 0.17/0.39
% 0.17/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.39
% 0.17/0.39 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).
% 0.17/0.39 Axiom 2 (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.
% 0.17/0.39 Axiom 3 (cls_Relation_Oantisym__def_0): fresh4(X, X, Y, Z) = Y.
% 0.17/0.39 Axiom 4 (cls_Tarski_OPartialOrder__iff_1): fresh2(X, X, Y, Z) = true.
% 0.17/0.39 Axiom 5 (cls_Relation_Oantisym__def_0): fresh(X, X, Y, Z, W, V) = V.
% 0.17/0.39 Axiom 6 (cls_conjecture_0): c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true.
% 0.17/0.39 Axiom 7 (cls_conjecture_1): c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a)) = true.
% 0.17/0.39 Axiom 8 (cls_Tarski_OPartialOrder__iff_1): fresh2(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).
% 0.17/0.39 Axiom 9 (cls_Relation_Oantisym__def_0): fresh3(X, X, Y, Z, W, V) = fresh4(c_in(c_Pair(W, V, Z, Z), Y, tc_prod(Z, Z)), true, W, V).
% 0.17/0.39 Axiom 10 (cls_Relation_Oantisym__def_0): fresh3(c_Relation_Oantisym(X, Y), true, X, Y, Z, W) = fresh(c_in(c_Pair(W, Z, Y, Y), X, tc_prod(Y, Y)), true, X, Y, Z, W).
% 0.17/0.39
% 0.17/0.39 Goal 1 (cls_conjecture_2): v_a = v_b.
% 0.17/0.39 Proof:
% 0.17/0.39 v_a
% 0.17/0.39 = { by axiom 5 (cls_Relation_Oantisym__def_0) R->L }
% 0.17/0.39 fresh(true, true, v_r, t_a, v_b, v_a)
% 0.17/0.39 = { by axiom 6 (cls_conjecture_0) R->L }
% 0.17/0.39 fresh(c_in(c_Pair(v_a, v_b, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, v_r, t_a, v_b, v_a)
% 0.17/0.39 = { by axiom 10 (cls_Relation_Oantisym__def_0) R->L }
% 0.17/0.39 fresh3(c_Relation_Oantisym(v_r, t_a), true, v_r, t_a, v_b, v_a)
% 0.17/0.39 = { by axiom 1 (cls_Tarski_Or_A_61_61_Aorder_Acl_0) }
% 0.17/0.39 fresh3(c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), t_a), true, v_r, t_a, v_b, v_a)
% 0.17/0.39 = { by axiom 8 (cls_Tarski_OPartialOrder__iff_1) R->L }
% 0.17/0.39 fresh3(fresh2(c_in(v_cl, c_Tarski_OPartialOrder, tc_Tarski_Opotype_Opotype__ext__type(t_a, tc_Product__Type_Ounit)), true, v_cl, t_a), true, v_r, t_a, v_b, v_a)
% 0.17/0.39 = { by axiom 2 (cls_Tarski_Ocl_A_58_APartialOrder_0) }
% 0.17/0.39 fresh3(fresh2(true, true, v_cl, t_a), true, v_r, t_a, v_b, v_a)
% 0.17/0.39 = { by axiom 4 (cls_Tarski_OPartialOrder__iff_1) }
% 0.17/0.39 fresh3(true, true, v_r, t_a, v_b, v_a)
% 0.17/0.39 = { by axiom 9 (cls_Relation_Oantisym__def_0) }
% 0.17/0.39 fresh4(c_in(c_Pair(v_b, v_a, t_a, t_a), v_r, tc_prod(t_a, t_a)), true, v_b, v_a)
% 0.17/0.39 = { by axiom 7 (cls_conjecture_1) }
% 0.17/0.39 fresh4(true, true, v_b, v_a)
% 0.17/0.39 = { by axiom 3 (cls_Relation_Oantisym__def_0) }
% 0.17/0.39 v_b
% 0.17/0.39 % SZS output end Proof
% 0.17/0.39
% 0.17/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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