TSTP Solution File: HWV009-4 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : HWV009-4 : TPTP v8.1.2. Released v2.5.0.
% 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 : n006.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 02:31:32 EDT 2023
% Result : Unsatisfiable 0.19s 0.49s
% 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
% 0.11/0.12 % Problem : HWV009-4 : TPTP v8.1.2. Released v2.5.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 14:18:36 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.49 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 Take the following subset of the input axioms:
% 0.19/0.49 fof(axiom_111, axiom, ![B_174, A_173]: (~p__pred_(B_174) | (~p__pred_(A_173) | ~p__pred_(f__xor_(A_173, B_174))))).
% 0.19/0.49 fof(axiom_115, axiom, ![A_181, B_182]: (~p__pred_(A_181) | (~p__pred_(B_182) | ~p__pred_(f__nand_(A_181, B_182))))).
% 0.19/0.49 fof(axiom_118, axiom, ![B_186, A_185]: (~p__pred_(B_186) | ~p__pred_(f__nor_(A_185, B_186)))).
% 0.19/0.49 fof(axiom_119, axiom, ![B_186_2, A_185_2]: (~p__pred_(A_185_2) | ~p__pred_(f__nor_(A_185_2, B_186_2)))).
% 0.19/0.49 fof(axiom_125, axiom, ![A_197]: (~p__pred_(A_197) | ~p__pred_(f__not_(A_197)))).
% 0.19/0.49 fof(axiom_127, axiom, ![B_199, A_198]: (~p_LES_EQU_(B_199, A_198) | ~p__pred_(f__lt_(A_198, B_199)))).
% 0.19/0.49 fof(axiom_13, axiom, ![T_5]: (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr__error_(f_ADD_(T_5, n1))) | ~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)))).
% 0.19/0.49 fof(axiom_131, axiom, ![A_202, B_203]: (~p_LES_EQU_(A_202, B_203) | ~p__pred_(f__gt_(A_202, B_203)))).
% 0.19/0.49 fof(axiom_14, axiom, ![T_5_2]: (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_5_2, n1))) | ~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5_2)))).
% 0.19/0.49 fof(axiom_15, axiom, ![I1_6, I2_7, T_5_2]: (~p__pred_(f__index_(f__index_(fwork_DOTfifo_DOTrtl_DOTmem_(f_ADD_(T_5_2, n1)), I1_6), I2_7)) | (~p_LES_EQU_(n0, I2_7) | (~p_LES_EQU_(I2_7, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__width_, n1)) | (~p_LES_EQU_(n0, I1_6) | (~p_LES_EQU_(I1_6, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1)) | ~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5_2)))))))).
% 0.19/0.49 fof(axiom_16, axiom, ![I1_10, T_5_2]: (~p__pred_(f__index_(fwork_DOTfifo_DOTrtl_DOTdata__out_(f_ADD_(T_5_2, n1)), I1_10)) | (~p_LES_EQU_(n0, I1_10) | (~p_LES_EQU_(I1_10, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__width_, n1)) | ~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5_2)))))).
% 0.19/0.49 fof(axiom_59, axiom, ![X_80]: f_ADD_(X_80, n1)!=n0).
% 0.19/0.49 fof(axiom_60, axiom, ![X_81]: ~p_LES_EQU_(f_ADD_(X_81, n1), n0)).
% 0.19/0.49 fof(axiom_64, axiom, ![Y_84, X_83]: (X_83!=Y_84 | ~def_89(Y_84, X_83))).
% 0.19/0.49 fof(quest_1, negated_conjecture, p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))).
% 0.19/0.49 fof(quest_2, negated_conjecture, p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))).
% 0.19/0.49
% 0.19/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.49 fresh(y, y, x1...xn) = u
% 0.19/0.49 C => fresh(s, t, x1...xn) = v
% 0.19/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.49 variables of u and v.
% 0.19/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.49 input problem has no model of domain size 1).
% 0.19/0.49
% 0.19/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.49
% 0.19/0.49 Axiom 1 (quest_1): p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) = true2.
% 0.19/0.49 Axiom 2 (quest_2): p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1))) = true2.
% 0.19/0.49
% 0.19/0.49 Goal 1 (axiom_14): tuple4(p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(X)), p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(X, n1)))) = tuple4(true2, true2).
% 0.19/0.49 The goal is true when:
% 0.19/0.49 X = t_206
% 0.19/0.49
% 0.19/0.49 Proof:
% 0.19/0.49 tuple4(p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)), p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1))))
% 0.19/0.49 = { by axiom 1 (quest_1) }
% 0.19/0.49 tuple4(true2, p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1))))
% 0.19/0.49 = { by axiom 2 (quest_2) }
% 0.19/0.49 tuple4(true2, true2)
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49
% 0.19/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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