TSTP Solution File: LCL856-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL856-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n031.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 08:20:59 EDT 2023
% Result : Unsatisfiable 0.19s 0.79s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL856-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 22:54:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.19/0.79 Command-line arguments: --no-flatten-goal
% 0.19/0.79
% 0.19/0.79 % SZS status Unsatisfiable
% 0.19/0.79
% 0.19/0.79 % SZS output start Proof
% 0.19/0.79 Take the following subset of the input axioms:
% 0.19/0.79 fof(cls_IT__implies__termi_0, axiom, ![V_t]: (c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), V_t, tc_Lambda_OdB) | ~hBOOL(hAPP(c_InductTermi_OIT, V_t)))).
% 0.19/0.79 fof(cls_conjecture_0, negated_conjecture, c_Type_Otyping(v_e, v_t, v_T)).
% 0.19/0.79 fof(cls_conjecture_1, negated_conjecture, ~c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), v_t, tc_Lambda_OdB)).
% 0.19/0.79 fof(cls_type__implies__IT_0, axiom, ![V_T, V_e, V_t2]: (hBOOL(hAPP(c_InductTermi_OIT, V_t2)) | ~c_Type_Otyping(V_e, V_t2, V_T))).
% 0.19/0.79
% 0.19/0.79 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.79 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.79 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.79 fresh(y, y, x1...xn) = u
% 0.19/0.79 C => fresh(s, t, x1...xn) = v
% 0.19/0.79 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.79 variables of u and v.
% 0.19/0.79 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.79 input problem has no model of domain size 1).
% 0.19/0.79
% 0.19/0.79 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.79
% 0.19/0.79 Axiom 1 (cls_IT__implies__termi_0): fresh142(X, X, Y) = true2.
% 0.19/0.79 Axiom 2 (cls_type__implies__IT_0): fresh33(X, X, Y) = true2.
% 0.19/0.79 Axiom 3 (cls_conjecture_0): c_Type_Otyping(v_e, v_t, v_T) = true2.
% 0.19/0.79 Axiom 4 (cls_type__implies__IT_0): fresh33(c_Type_Otyping(X, Y, Z), true2, Y) = hBOOL(hAPP(c_InductTermi_OIT, Y)).
% 0.19/0.79 Axiom 5 (cls_IT__implies__termi_0): fresh142(hBOOL(hAPP(c_InductTermi_OIT, X)), true2, X) = c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), X, tc_Lambda_OdB).
% 0.19/0.79
% 0.19/0.79 Goal 1 (cls_conjecture_1): c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), v_t, tc_Lambda_OdB) = true2.
% 0.19/0.79 Proof:
% 0.19/0.79 c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), v_t, tc_Lambda_OdB)
% 0.19/0.79 = { by axiom 5 (cls_IT__implies__termi_0) R->L }
% 0.19/0.79 fresh142(hBOOL(hAPP(c_InductTermi_OIT, v_t)), true2, v_t)
% 0.19/0.79 = { by axiom 4 (cls_type__implies__IT_0) R->L }
% 0.19/0.79 fresh142(fresh33(c_Type_Otyping(v_e, v_t, v_T), true2, v_t), true2, v_t)
% 0.19/0.79 = { by axiom 3 (cls_conjecture_0) }
% 0.19/0.79 fresh142(fresh33(true2, true2, v_t), true2, v_t)
% 0.19/0.79 = { by axiom 2 (cls_type__implies__IT_0) }
% 0.19/0.79 fresh142(true2, true2, v_t)
% 0.19/0.79 = { by axiom 1 (cls_IT__implies__termi_0) }
% 0.19/0.79 true2
% 0.19/0.79 % SZS output end Proof
% 0.19/0.79
% 0.19/0.79 RESULT: Unsatisfiable (the axioms are contradictory).
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