TSTP Solution File: LCL748-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL748-1 : 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 08:20:25 EDT 2023
% Result : Unsatisfiable 6.08s 1.20s
% Output : Proof 6.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL748-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14 % 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 : Fri Aug 25 05:19:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.08/1.20 Command-line arguments: --no-flatten-goal
% 6.08/1.20
% 6.08/1.20 % SZS status Unsatisfiable
% 6.08/1.20
% 6.08/1.20 % SZS output start Proof
% 6.68/1.20 Take the following subset of the input axioms:
% 6.68/1.20 fof(cls_Lambda_0, axiom, ![V_r]: (c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r)) | ~c_InductTermi_OIT(V_r))).
% 6.68/1.20 fof(cls_Suc__eq__plus1_0, axiom, ![V_n]: c_Suc(V_n)=c_HOL_Oplus__class_Oplus(V_n, c_HOL_Oone__class_Oone(tc_nat), tc_nat)).
% 6.68/1.20 fof(cls_conjecture_1, negated_conjecture, ![V_i]: c_InductTermi_OIT(c_Lambda_Olift(v_r, V_i))).
% 6.68/1.20 fof(cls_conjecture_2, negated_conjecture, ~c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r), v_ia))).
% 6.68/1.20 fof(cls_lift_Osimps_I3_J_0, axiom, ![V_s, V_k]: c_Lambda_Olift(c_Lambda_OdB_OAbs(V_s), V_k)=c_Lambda_OdB_OAbs(c_Lambda_Olift(V_s, c_HOL_Oplus__class_Oplus(V_k, c_HOL_Oone__class_Oone(tc_nat), tc_nat)))).
% 6.68/1.20
% 6.68/1.20 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.68/1.20 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.68/1.20 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.68/1.20 fresh(y, y, x1...xn) = u
% 6.68/1.20 C => fresh(s, t, x1...xn) = v
% 6.68/1.20 where fresh is a fresh function symbol and x1..xn are the free
% 6.68/1.20 variables of u and v.
% 6.68/1.20 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.68/1.20 input problem has no model of domain size 1).
% 6.68/1.20
% 6.68/1.20 The encoding turns the above axioms into the following unit equations and goals:
% 6.68/1.20
% 6.68/1.20 Axiom 1 (cls_Lambda_0): fresh244(X, X, Y) = true2.
% 6.68/1.20 Axiom 2 (cls_conjecture_1): c_InductTermi_OIT(c_Lambda_Olift(v_r, X)) = true2.
% 6.68/1.20 Axiom 3 (cls_Lambda_0): fresh244(c_InductTermi_OIT(X), true2, X) = c_InductTermi_OIT(c_Lambda_OdB_OAbs(X)).
% 6.68/1.20 Axiom 4 (cls_Suc__eq__plus1_0): c_Suc(X) = c_HOL_Oplus__class_Oplus(X, c_HOL_Oone__class_Oone(tc_nat), tc_nat).
% 6.68/1.20 Axiom 5 (cls_lift_Osimps_I3_J_0): c_Lambda_Olift(c_Lambda_OdB_OAbs(X), Y) = c_Lambda_OdB_OAbs(c_Lambda_Olift(X, c_HOL_Oplus__class_Oplus(Y, c_HOL_Oone__class_Oone(tc_nat), tc_nat))).
% 6.68/1.20
% 6.68/1.20 Goal 1 (cls_conjecture_2): c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r), v_ia)) = true2.
% 6.68/1.20 Proof:
% 6.68/1.20 c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r), v_ia))
% 6.68/1.20 = { by axiom 5 (cls_lift_Osimps_I3_J_0) }
% 6.68/1.20 c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r, c_HOL_Oplus__class_Oplus(v_ia, c_HOL_Oone__class_Oone(tc_nat), tc_nat))))
% 6.68/1.20 = { by axiom 4 (cls_Suc__eq__plus1_0) R->L }
% 6.68/1.20 c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r, c_Suc(v_ia))))
% 6.68/1.20 = { by axiom 3 (cls_Lambda_0) R->L }
% 6.68/1.20 fresh244(c_InductTermi_OIT(c_Lambda_Olift(v_r, c_Suc(v_ia))), true2, c_Lambda_Olift(v_r, c_Suc(v_ia)))
% 6.68/1.20 = { by axiom 2 (cls_conjecture_1) }
% 6.68/1.20 fresh244(true2, true2, c_Lambda_Olift(v_r, c_Suc(v_ia)))
% 6.68/1.20 = { by axiom 1 (cls_Lambda_0) }
% 6.68/1.20 true2
% 6.68/1.20 % SZS output end Proof
% 6.68/1.20
% 6.68/1.20 RESULT: Unsatisfiable (the axioms are contradictory).
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