TSTP Solution File: SWC405-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWC405-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n023.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 20:55:24 EDT 2023
% Result : Unsatisfiable 3.91s 0.89s
% Output : Proof 3.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC405-1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.12 % 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 : n023.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 : Mon Aug 28 18:16:10 EDT 2023
% 0.12/0.33 % CPUTime :
% 3.91/0.89 Command-line arguments: --ground-connectedness --complete-subsets
% 3.91/0.89
% 3.91/0.89 % SZS status Unsatisfiable
% 3.91/0.89
% 3.91/0.89 % SZS output start Proof
% 3.91/0.89 Take the following subset of the input axioms:
% 3.91/0.89 fof(co1_10, negated_conjecture, memberP(sk1, sk5)).
% 3.91/0.89 fof(co1_11, negated_conjecture, ~memberP(sk2, sk5)).
% 3.91/0.89 fof(co1_5, negated_conjecture, sk2=sk4).
% 3.91/0.89 fof(co1_6, negated_conjecture, sk1=sk3).
% 3.91/0.89 fof(co1_7, negated_conjecture, ![A2]: (~ssItem(A2) | (memberP(sk4, A2) | ~memberP(sk3, A2)))).
% 3.91/0.89 fof(co1_9, negated_conjecture, ssItem(sk5)).
% 3.91/0.89
% 3.91/0.89 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.91/0.89 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.91/0.89 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.91/0.89 fresh(y, y, x1...xn) = u
% 3.91/0.89 C => fresh(s, t, x1...xn) = v
% 3.91/0.89 where fresh is a fresh function symbol and x1..xn are the free
% 3.91/0.89 variables of u and v.
% 3.91/0.89 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.91/0.89 input problem has no model of domain size 1).
% 3.91/0.89
% 3.91/0.89 The encoding turns the above axioms into the following unit equations and goals:
% 3.91/0.89
% 3.91/0.89 Axiom 1 (co1_6): sk1 = sk3.
% 3.91/0.89 Axiom 2 (co1_5): sk2 = sk4.
% 3.91/0.89 Axiom 3 (co1_9): ssItem(sk5) = true2.
% 3.91/0.89 Axiom 4 (co1_10): memberP(sk1, sk5) = true2.
% 3.91/0.89 Axiom 5 (co1_7): fresh17(X, X, Y) = memberP(sk4, Y).
% 3.91/0.89 Axiom 6 (co1_7): fresh16(X, X, Y) = true2.
% 3.91/0.89 Axiom 7 (co1_7): fresh17(memberP(sk3, X), true2, X) = fresh16(ssItem(X), true2, X).
% 3.91/0.89
% 3.91/0.89 Goal 1 (co1_11): memberP(sk2, sk5) = true2.
% 3.91/0.89 Proof:
% 3.91/0.89 memberP(sk2, sk5)
% 3.91/0.89 = { by axiom 2 (co1_5) }
% 3.91/0.89 memberP(sk4, sk5)
% 3.91/0.89 = { by axiom 5 (co1_7) R->L }
% 3.91/0.89 fresh17(true2, true2, sk5)
% 3.91/0.89 = { by axiom 4 (co1_10) R->L }
% 3.91/0.89 fresh17(memberP(sk1, sk5), true2, sk5)
% 3.91/0.89 = { by axiom 1 (co1_6) }
% 3.91/0.89 fresh17(memberP(sk3, sk5), true2, sk5)
% 3.91/0.89 = { by axiom 7 (co1_7) }
% 3.91/0.89 fresh16(ssItem(sk5), true2, sk5)
% 3.91/0.89 = { by axiom 3 (co1_9) }
% 3.91/0.89 fresh16(true2, true2, sk5)
% 3.91/0.89 = { by axiom 6 (co1_7) }
% 3.91/0.89 true2
% 3.91/0.89 % SZS output end Proof
% 3.91/0.89
% 3.91/0.89 RESULT: Unsatisfiable (the axioms are contradictory).
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