TSTP Solution File: LCL858-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL858-1 : 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 : n015.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 2.75s 0.82s
% Output : Proof 2.75s
% 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 : LCL858-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 05:05:21 EDT 2023
% 0.14/0.34 % CPUTime :
% 2.75/0.82 Command-line arguments: --no-flatten-goal
% 2.75/0.82
% 2.75/0.82 % SZS status Unsatisfiable
% 2.75/0.82
% 2.75/0.82 % SZS output start Proof
% 2.75/0.82 Take the following subset of the input axioms:
% 2.75/0.82 fof(cls_CHAINED_0, axiom, hBOOL(hAPP(c_InductTermi_OIT, v_t))).
% 2.75/0.82 fof(cls_IT__implies__termi_0, axiom, ![V_t]: (hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), V_t)) | ~hBOOL(hAPP(c_InductTermi_OIT, V_t)))).
% 2.75/0.82 fof(cls_conjecture_0, negated_conjecture, ~hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), v_t))).
% 2.75/0.82
% 2.75/0.82 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.75/0.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.75/0.82 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.75/0.82 fresh(y, y, x1...xn) = u
% 2.75/0.82 C => fresh(s, t, x1...xn) = v
% 2.75/0.82 where fresh is a fresh function symbol and x1..xn are the free
% 2.75/0.82 variables of u and v.
% 2.75/0.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.75/0.82 input problem has no model of domain size 1).
% 2.75/0.82
% 2.75/0.83 The encoding turns the above axioms into the following unit equations and goals:
% 2.75/0.83
% 2.75/0.83 Axiom 1 (cls_IT__implies__termi_0): fresh145(X, X, Y) = true2.
% 2.75/0.83 Axiom 2 (cls_CHAINED_0): hBOOL(hAPP(c_InductTermi_OIT, v_t)) = true2.
% 2.75/0.83 Axiom 3 (cls_IT__implies__termi_0): fresh145(hBOOL(hAPP(c_InductTermi_OIT, X)), true2, X) = hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), X)).
% 2.75/0.83
% 2.75/0.83 Goal 1 (cls_conjecture_0): hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), v_t)) = true2.
% 2.75/0.83 Proof:
% 2.75/0.83 hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta, tc_Lambda_OdB, tc_Lambda_OdB), tc_Lambda_OdB), v_t))
% 2.75/0.83 = { by axiom 3 (cls_IT__implies__termi_0) R->L }
% 2.75/0.83 fresh145(hBOOL(hAPP(c_InductTermi_OIT, v_t)), true2, v_t)
% 2.75/0.83 = { by axiom 2 (cls_CHAINED_0) }
% 2.75/0.83 fresh145(true2, true2, v_t)
% 2.75/0.83 = { by axiom 1 (cls_IT__implies__termi_0) }
% 2.75/0.83 true2
% 2.75/0.83 % SZS output end Proof
% 2.75/0.83
% 2.75/0.83 RESULT: Unsatisfiable (the axioms are contradictory).
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