TSTP Solution File: SWV817-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV817-1 : 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 : n027.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 23:06:23 EDT 2023
% Result : Unsatisfiable 0.13s 0.37s
% Output : Proof 0.13s
% 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 : SWV817-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.13 % 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 : n027.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 : Tue Aug 29 07:44:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.37 Command-line arguments: --no-flatten-goal
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable
% 0.13/0.37
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 Take the following subset of the input axioms:
% 0.13/0.37 fof(cls_conjecture_1, negated_conjecture, ![V_s]: V_s=v_x).
% 0.13/0.37 fof(cls_state__not__singleton__def_0, axiom, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1!=v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 | ~c_Hoare__Mirabelle_Ostate__not__singleton).
% 0.13/0.37 fof(cls_state__not__singleton__def__raw_0, axiom, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1!=v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 | ~c_Hoare__Mirabelle_Ostate__not__singleton).
% 0.13/0.37
% 0.13/0.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.37 fresh(y, y, x1...xn) = u
% 0.13/0.37 C => fresh(s, t, x1...xn) = v
% 0.13/0.37 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.37 variables of u and v.
% 0.13/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.37 input problem has no model of domain size 1).
% 0.13/0.37
% 0.13/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.37
% 0.13/0.38 Axiom 1 (cls_conjecture_1): X = v_x.
% 0.13/0.38
% 0.13/0.38 Lemma 2: Y = X.
% 0.13/0.38 Proof:
% 0.13/0.38 Y
% 0.13/0.38 = { by axiom 1 (cls_conjecture_1) }
% 0.13/0.38 v_x
% 0.13/0.38 = { by axiom 1 (cls_conjecture_1) R->L }
% 0.13/0.38 X
% 0.13/0.38
% 0.13/0.38 Goal 1 (cls_state__not__singleton__def_0): tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1, c_Hoare__Mirabelle_Ostate__not__singleton) = tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2, true).
% 0.13/0.38 Proof:
% 0.13/0.38 tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1, c_Hoare__Mirabelle_Ostate__not__singleton)
% 0.13/0.38 = { by lemma 2 }
% 0.13/0.38 tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2, true)
% 0.13/0.38
% 0.13/0.38 Goal 2 (cls_state__not__singleton__def__raw_0): tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1, c_Hoare__Mirabelle_Ostate__not__singleton) = tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, true).
% 0.13/0.38 Proof:
% 0.13/0.38 tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1, c_Hoare__Mirabelle_Ostate__not__singleton)
% 0.13/0.38 = { by lemma 2 }
% 0.13/0.38 tuple(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2, true)
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38
% 0.13/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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