TSTP Solution File: LAT275-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT275-2 : 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 : n001.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 06:28:05 EDT 2023
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT275-2 : 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
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 09:18:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.37 Command-line arguments: --no-flatten-goal
% 0.20/0.37
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 Take the following subset of the input axioms:
% 0.20/0.38 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)).
% 0.20/0.38 fof(cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0, axiom, ![V_S]: (~c_lessequals(V_S, v_A, tc_set(t_a)) | c_in(c_Tarski_Olub(V_S, v_cl, t_a), v_A, t_a))).
% 0.20/0.38 fof(cls_conjecture_0, negated_conjecture, c_lessequals(v_S, v_A, tc_set(t_a))).
% 0.20/0.38 fof(cls_conjecture_2, negated_conjecture, ~c_in(c_Tarski_Olub(v_S, v_cl, t_a), c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)).
% 0.20/0.38
% 0.20/0.38 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.38 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.38 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.38 fresh(y, y, x1...xn) = u
% 0.20/0.38 C => fresh(s, t, x1...xn) = v
% 0.20/0.38 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.38 variables of u and v.
% 0.20/0.38 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.38 input problem has no model of domain size 1).
% 0.20/0.38
% 0.20/0.38 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.38
% 0.20/0.38 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).
% 0.20/0.38 Axiom 2 (cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0): fresh(X, X, Y) = true.
% 0.20/0.38 Axiom 3 (cls_conjecture_0): c_lessequals(v_S, v_A, tc_set(t_a)) = true.
% 0.20/0.38 Axiom 4 (cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0): fresh(c_lessequals(X, v_A, tc_set(t_a)), true, X) = c_in(c_Tarski_Olub(X, v_cl, t_a), v_A, t_a).
% 0.20/0.38
% 0.20/0.38 Goal 1 (cls_conjecture_2): c_in(c_Tarski_Olub(v_S, v_cl, t_a), c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) = true.
% 0.20/0.38 Proof:
% 0.20/0.38 c_in(c_Tarski_Olub(v_S, v_cl, t_a), c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)
% 0.20/0.38 = { by axiom 1 (cls_Tarski_OA_A_61_61_Apset_Acl_0) R->L }
% 0.20/0.38 c_in(c_Tarski_Olub(v_S, v_cl, t_a), v_A, t_a)
% 0.20/0.38 = { by axiom 4 (cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0) R->L }
% 0.20/0.38 fresh(c_lessequals(v_S, v_A, tc_set(t_a)), true, v_S)
% 0.20/0.38 = { by axiom 3 (cls_conjecture_0) }
% 0.20/0.38 fresh(true, true, v_S)
% 0.20/0.38 = { by axiom 2 (cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0) }
% 0.20/0.38 true
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38
% 0.20/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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