TSTP Solution File: LCL756-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL756-1 : 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 : n022.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 08:20:28 EDT 2023
% Result : Unsatisfiable 29.46s 4.22s
% Output : Proof 29.46s
% 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 : LCL756-1 : 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
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 18:56:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 29.46/4.22 Command-line arguments: --no-flatten-goal
% 29.46/4.22
% 29.46/4.22 % SZS status Unsatisfiable
% 29.46/4.22
% 29.46/4.22 % SZS output start Proof
% 29.46/4.22 Take the following subset of the input axioms:
% 29.46/4.22 fof(cls_conjecture_1, negated_conjecture, ![V_i, V_j]: c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(V_i), V_j))).
% 29.46/4.22 fof(cls_conjecture_2, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))).
% 29.46/4.22
% 29.46/4.22 Now clausify the problem and encode Horn clauses using encoding 3 of
% 29.46/4.22 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 29.46/4.22 We repeatedly replace C & s=t => u=v by the two clauses:
% 29.46/4.22 fresh(y, y, x1...xn) = u
% 29.46/4.22 C => fresh(s, t, x1...xn) = v
% 29.46/4.22 where fresh is a fresh function symbol and x1..xn are the free
% 29.46/4.22 variables of u and v.
% 29.46/4.22 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 29.46/4.22 input problem has no model of domain size 1).
% 29.46/4.22
% 29.46/4.22 The encoding turns the above axioms into the following unit equations and goals:
% 29.46/4.22
% 29.46/4.22 Axiom 1 (cls_conjecture_1): c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(X), Y)) = true2.
% 29.46/4.22
% 29.46/4.22 Goal 1 (cls_conjecture_2): c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja))) = true2.
% 29.46/4.22 Proof:
% 29.46/4.22 c_InductTermi_OIT(c_Lambda_Osubst(v_ra, c_Lambda_OdB_OVar(c_Suc(v_ia)), c_Suc(v_ja)))
% 29.46/4.22 = { by axiom 1 (cls_conjecture_1) }
% 29.46/4.22 true2
% 29.46/4.22 % SZS output end Proof
% 29.46/4.22
% 29.46/4.22 RESULT: Unsatisfiable (the axioms are contradictory).
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