TSTP Solution File: LCL844-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL844-1 : 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 : n021.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 08:20:57 EDT 2023
% Result : Unsatisfiable 0.19s 0.47s
% 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
% 0.00/0.12 % Problem : LCL844-1 : 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
% 0.13/0.34 % Computer : n021.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 22:52:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Command-line arguments: --no-flatten-goal
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% 0.19/0.47 % SZS status Unsatisfiable
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% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 Take the following subset of the input axioms:
% 0.19/0.47 fof(cls_Abs_I2_J_0, axiom, c_InductTermi_OIT(v_ta______)).
% 0.19/0.47 fof(cls_Lambda_0, axiom, ![V_r]: (c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) | ~c_InductTermi_OIT(V_r))).
% 0.19/0.47 fof(cls_conjecture_0, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ta______))).
% 0.19/0.47
% 0.19/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.47 fresh(y, y, x1...xn) = u
% 0.19/0.47 C => fresh(s, t, x1...xn) = v
% 0.19/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.47 variables of u and v.
% 0.19/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.47 input problem has no model of domain size 1).
% 0.19/0.47
% 0.19/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.47
% 0.19/0.47 Axiom 1 (cls_Abs_I2_J_0): c_InductTermi_OIT(v_ta______) = true2.
% 0.19/0.47 Axiom 2 (cls_Lambda_0): fresh25(X, X, Y) = true2.
% 0.19/0.47 Axiom 3 (cls_Lambda_0): fresh25(c_InductTermi_OIT(X), true2, X) = c_InductTermi_OIT(c_Lambda_OdB_OAbs(X)).
% 0.19/0.47
% 0.19/0.47 Goal 1 (cls_conjecture_0): c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ta______)) = true2.
% 0.19/0.47 Proof:
% 0.19/0.47 c_InductTermi_OIT(c_Lambda_OdB_OAbs(v_ta______))
% 0.19/0.47 = { by axiom 3 (cls_Lambda_0) R->L }
% 0.19/0.47 fresh25(c_InductTermi_OIT(v_ta______), true2, v_ta______)
% 0.19/0.47 = { by axiom 1 (cls_Abs_I2_J_0) }
% 0.19/0.47 fresh25(true2, true2, v_ta______)
% 0.19/0.47 = { by axiom 2 (cls_Lambda_0) }
% 0.19/0.47 true2
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47
% 0.19/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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