TSTP Solution File: HWV009-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : HWV009-2 : 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 : n024.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 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HWV009-2 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.14 % 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 : n024.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
% 0.21/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Tue Aug 29 13:49:08 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.51 Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.51
% 0.21/0.51 % SZS status Unsatisfiable
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% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 Take the following subset of the input axioms:
% 0.21/0.51 fof(axiom_12, axiom, ![T_5]: (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1))=n0 | ~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)))).
% 0.21/0.51 fof(axiom_5, axiom, ![T_0]: fwork_DOTfifo_DOTrtl_DOTlevel_(T_0)=fwork_DOTfifo_DOTrtl_DOTint__level_(T_0)).
% 0.21/0.51 fof(quest_1, negated_conjecture, p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))).
% 0.21/0.51 fof(quest_2, negated_conjecture, fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1))!=n0).
% 0.21/0.51
% 0.21/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.51 fresh(y, y, x1...xn) = u
% 0.21/0.51 C => fresh(s, t, x1...xn) = v
% 0.21/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.51 variables of u and v.
% 0.21/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.51 input problem has no model of domain size 1).
% 0.21/0.51
% 0.21/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.51
% 0.21/0.51 Axiom 1 (axiom_5): fwork_DOTfifo_DOTrtl_DOTlevel_(X) = fwork_DOTfifo_DOTrtl_DOTint__level_(X).
% 0.21/0.51 Axiom 2 (quest_1): p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) = true2.
% 0.21/0.51 Axiom 3 (axiom_12): fresh29(X, X, Y) = n0.
% 0.21/0.51 Axiom 4 (axiom_12): fresh29(p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(X)), true2, X) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(X, n1)).
% 0.21/0.51
% 0.21/0.51 Goal 1 (quest_2): fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = n0.
% 0.21/0.51 Proof:
% 0.21/0.51 fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1))
% 0.21/0.51 = { by axiom 1 (axiom_5) }
% 0.21/0.51 fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))
% 0.21/0.51 = { by axiom 4 (axiom_12) R->L }
% 0.21/0.51 fresh29(p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)), true2, t_206)
% 0.21/0.51 = { by axiom 2 (quest_1) }
% 0.21/0.51 fresh29(true2, true2, t_206)
% 0.21/0.51 = { by axiom 3 (axiom_12) }
% 0.21/0.51 n0
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51
% 0.21/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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