TSTP Solution File: SWC408-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWC408-1 : 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 : n016.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 20:55:25 EDT 2023
% Result : Unsatisfiable 19.24s 2.78s
% Output : Proof 19.24s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC408-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n016.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 15:04:59 EDT 2023
% 0.10/0.29 % CPUTime :
% 19.24/2.78 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 19.24/2.78
% 19.24/2.78 % SZS status Unsatisfiable
% 19.24/2.78
% 19.24/2.78 % SZS output start Proof
% 19.24/2.78 Take the following subset of the input axioms:
% 19.24/2.78 fof(clause140, axiom, ![U, V, W]: (~memberP(U, V) | (~ssList(W) | (~ssList(U) | (~ssItem(V) | memberP(app(U, W), V)))))).
% 19.24/2.78 fof(co1_10, negated_conjecture, ~memberP(sk1, sk5)).
% 19.24/2.78 fof(co1_4, negated_conjecture, ssList(sk4)).
% 19.24/2.78 fof(co1_5, negated_conjecture, app(sk4, sk4)=sk3).
% 19.24/2.78 fof(co1_6, negated_conjecture, sk2=sk4).
% 19.24/2.78 fof(co1_7, negated_conjecture, sk1=sk3).
% 19.24/2.78 fof(co1_8, negated_conjecture, ssItem(sk5)).
% 19.24/2.78 fof(co1_9, negated_conjecture, memberP(sk2, sk5)).
% 19.24/2.78
% 19.24/2.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.24/2.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.24/2.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.24/2.78 fresh(y, y, x1...xn) = u
% 19.24/2.78 C => fresh(s, t, x1...xn) = v
% 19.24/2.78 where fresh is a fresh function symbol and x1..xn are the free
% 19.24/2.78 variables of u and v.
% 19.24/2.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.24/2.78 input problem has no model of domain size 1).
% 19.24/2.78
% 19.24/2.78 The encoding turns the above axioms into the following unit equations and goals:
% 19.24/2.78
% 19.24/2.78 Axiom 1 (co1_6): sk2 = sk4.
% 19.24/2.78 Axiom 2 (co1_7): sk1 = sk3.
% 19.24/2.78 Axiom 3 (co1_4): ssList(sk4) = true2.
% 19.24/2.78 Axiom 4 (co1_8): ssItem(sk5) = true2.
% 19.24/2.78 Axiom 5 (co1_5): app(sk4, sk4) = sk3.
% 19.24/2.78 Axiom 6 (co1_9): memberP(sk2, sk5) = true2.
% 19.24/2.78 Axiom 7 (clause140): fresh211(X, X, Y, Z, W) = true2.
% 19.24/2.78 Axiom 8 (clause140): fresh209(X, X, Y, Z, W) = memberP(app(Y, W), Z).
% 19.24/2.78 Axiom 9 (clause140): fresh210(X, X, Y, Z, W) = fresh211(ssList(Y), true2, Y, Z, W).
% 19.24/2.78 Axiom 10 (clause140): fresh208(X, X, Y, Z, W) = fresh209(ssList(W), true2, Y, Z, W).
% 19.24/2.78 Axiom 11 (clause140): fresh208(memberP(X, Y), true2, X, Y, Z) = fresh210(ssItem(Y), true2, X, Y, Z).
% 19.24/2.78
% 19.24/2.78 Goal 1 (co1_10): memberP(sk1, sk5) = true2.
% 19.24/2.78 Proof:
% 19.24/2.78 memberP(sk1, sk5)
% 19.24/2.78 = { by axiom 2 (co1_7) }
% 19.24/2.78 memberP(sk3, sk5)
% 19.24/2.78 = { by axiom 5 (co1_5) R->L }
% 19.24/2.78 memberP(app(sk4, sk4), sk5)
% 19.24/2.78 = { by axiom 8 (clause140) R->L }
% 19.24/2.78 fresh209(true2, true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 3 (co1_4) R->L }
% 19.24/2.78 fresh209(ssList(sk4), true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 10 (clause140) R->L }
% 19.24/2.78 fresh208(true2, true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 6 (co1_9) R->L }
% 19.24/2.78 fresh208(memberP(sk2, sk5), true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 1 (co1_6) }
% 19.24/2.78 fresh208(memberP(sk4, sk5), true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 11 (clause140) }
% 19.24/2.78 fresh210(ssItem(sk5), true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 4 (co1_8) }
% 19.24/2.78 fresh210(true2, true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 9 (clause140) }
% 19.24/2.78 fresh211(ssList(sk4), true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 3 (co1_4) }
% 19.24/2.78 fresh211(true2, true2, sk4, sk5, sk4)
% 19.24/2.78 = { by axiom 7 (clause140) }
% 19.24/2.78 true2
% 19.24/2.78 % SZS output end Proof
% 19.24/2.78
% 19.24/2.78 RESULT: Unsatisfiable (the axioms are contradictory).
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