TSTP Solution File: SWC404-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC404-1 : 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 : n009.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 94.29s 12.25s
% Output : Proof 94.29s
% 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 : SWC404-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 15:46:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 94.29/12.25 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 94.29/12.25
% 94.29/12.25 % SZS status Unsatisfiable
% 94.29/12.25
% 94.29/12.25 % SZS output start Proof
% 94.29/12.25 Take the following subset of the input axioms:
% 94.29/12.25 fof(clause140, axiom, ![U, V, W]: (~memberP(U, V) | (~ssList(W) | (~ssList(U) | (~ssItem(V) | memberP(app(U, W), V)))))).
% 94.29/12.25 fof(clause141, axiom, ![U2, V2, W2]: (~memberP(U2, V2) | (~ssList(U2) | (~ssList(W2) | (~ssItem(V2) | memberP(app(W2, U2), V2)))))).
% 94.29/12.25 fof(clause85, axiom, ![U2, V2]: (~ssList(U2) | (~ssList(V2) | ssList(app(V2, U2))))).
% 94.29/12.25 fof(co1_13, negated_conjecture, ssItem(sk7)).
% 94.29/12.25 fof(co1_14, negated_conjecture, memberP(sk1, sk7)).
% 94.29/12.25 fof(co1_15, negated_conjecture, ~memberP(sk2, sk7)).
% 94.29/12.25 fof(co1_3, negated_conjecture, ssList(sk3)).
% 94.29/12.25 fof(co1_5, negated_conjecture, sk2=sk4).
% 94.29/12.25 fof(co1_6, negated_conjecture, sk1=sk3).
% 94.29/12.25 fof(co1_7, negated_conjecture, ssList(sk5)).
% 94.29/12.25 fof(co1_8, negated_conjecture, ssList(sk6)).
% 94.29/12.25 fof(co1_9, negated_conjecture, app(app(sk5, sk3), sk6)=sk4).
% 94.29/12.25
% 94.29/12.25 Now clausify the problem and encode Horn clauses using encoding 3 of
% 94.29/12.25 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 94.29/12.25 We repeatedly replace C & s=t => u=v by the two clauses:
% 94.29/12.25 fresh(y, y, x1...xn) = u
% 94.29/12.25 C => fresh(s, t, x1...xn) = v
% 94.29/12.25 where fresh is a fresh function symbol and x1..xn are the free
% 94.29/12.25 variables of u and v.
% 94.29/12.25 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 94.29/12.25 input problem has no model of domain size 1).
% 94.29/12.25
% 94.29/12.25 The encoding turns the above axioms into the following unit equations and goals:
% 94.29/12.25
% 94.29/12.25 Axiom 1 (co1_5): sk2 = sk4.
% 94.29/12.25 Axiom 2 (co1_6): sk1 = sk3.
% 94.29/12.25 Axiom 3 (co1_3): ssList(sk3) = true2.
% 94.29/12.25 Axiom 4 (co1_7): ssList(sk5) = true2.
% 94.29/12.25 Axiom 5 (co1_8): ssList(sk6) = true2.
% 94.29/12.25 Axiom 6 (co1_13): ssItem(sk7) = true2.
% 94.29/12.25 Axiom 7 (co1_14): memberP(sk1, sk7) = true2.
% 94.29/12.25 Axiom 8 (co1_9): app(app(sk5, sk3), sk6) = sk4.
% 94.29/12.25 Axiom 9 (clause85): fresh34(X, X, Y, Z) = ssList(app(Z, Y)).
% 94.29/12.25 Axiom 10 (clause85): fresh33(X, X, Y, Z) = true2.
% 94.29/12.25 Axiom 11 (clause140): fresh212(X, X, Y, Z, W) = true2.
% 94.29/12.25 Axiom 12 (clause140): fresh210(X, X, Y, Z, W) = memberP(app(Y, W), Z).
% 94.29/12.25 Axiom 13 (clause141): fresh208(X, X, Y, Z, W) = true2.
% 94.29/12.25 Axiom 14 (clause141): fresh206(X, X, Y, Z, W) = memberP(app(W, Y), Z).
% 94.29/12.25 Axiom 15 (clause85): fresh34(ssList(X), true2, Y, X) = fresh33(ssList(Y), true2, Y, X).
% 94.29/12.25 Axiom 16 (clause140): fresh211(X, X, Y, Z, W) = fresh212(ssList(Y), true2, Y, Z, W).
% 94.29/12.25 Axiom 17 (clause140): fresh209(X, X, Y, Z, W) = fresh210(ssList(W), true2, Y, Z, W).
% 94.29/12.25 Axiom 18 (clause140): fresh209(memberP(X, Y), true2, X, Y, Z) = fresh211(ssItem(Y), true2, X, Y, Z).
% 94.29/12.25 Axiom 19 (clause141): fresh207(X, X, Y, Z, W) = fresh208(ssList(Y), true2, Y, Z, W).
% 94.29/12.25 Axiom 20 (clause141): fresh205(X, X, Y, Z, W) = fresh206(ssList(W), true2, Y, Z, W).
% 94.29/12.26 Axiom 21 (clause141): fresh205(memberP(X, Y), true2, X, Y, Z) = fresh207(ssItem(Y), true2, X, Y, Z).
% 94.29/12.26
% 94.29/12.26 Goal 1 (co1_15): memberP(sk2, sk7) = true2.
% 94.29/12.26 Proof:
% 94.29/12.26 memberP(sk2, sk7)
% 94.29/12.26 = { by axiom 1 (co1_5) }
% 94.29/12.26 memberP(sk4, sk7)
% 94.29/12.26 = { by axiom 8 (co1_9) R->L }
% 94.29/12.26 memberP(app(app(sk5, sk3), sk6), sk7)
% 94.29/12.26 = { by axiom 12 (clause140) R->L }
% 94.29/12.26 fresh210(true2, true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 5 (co1_8) R->L }
% 94.29/12.26 fresh210(ssList(sk6), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 17 (clause140) R->L }
% 94.29/12.26 fresh209(true2, true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 13 (clause141) R->L }
% 94.29/12.26 fresh209(fresh208(true2, true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 3 (co1_3) R->L }
% 94.29/12.26 fresh209(fresh208(ssList(sk3), true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 19 (clause141) R->L }
% 94.29/12.26 fresh209(fresh207(true2, true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 6 (co1_13) R->L }
% 94.29/12.26 fresh209(fresh207(ssItem(sk7), true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 21 (clause141) R->L }
% 94.29/12.26 fresh209(fresh205(memberP(sk3, sk7), true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 2 (co1_6) R->L }
% 94.29/12.26 fresh209(fresh205(memberP(sk1, sk7), true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 7 (co1_14) }
% 94.29/12.26 fresh209(fresh205(true2, true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 20 (clause141) }
% 94.29/12.26 fresh209(fresh206(ssList(sk5), true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 4 (co1_7) }
% 94.29/12.26 fresh209(fresh206(true2, true2, sk3, sk7, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 14 (clause141) }
% 94.29/12.26 fresh209(memberP(app(sk5, sk3), sk7), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 18 (clause140) }
% 94.29/12.26 fresh211(ssItem(sk7), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 6 (co1_13) }
% 94.29/12.26 fresh211(true2, true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 16 (clause140) }
% 94.29/12.26 fresh212(ssList(app(sk5, sk3)), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 9 (clause85) R->L }
% 94.29/12.26 fresh212(fresh34(true2, true2, sk3, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 4 (co1_7) R->L }
% 94.29/12.26 fresh212(fresh34(ssList(sk5), true2, sk3, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 15 (clause85) }
% 94.29/12.26 fresh212(fresh33(ssList(sk3), true2, sk3, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 3 (co1_3) }
% 94.29/12.26 fresh212(fresh33(true2, true2, sk3, sk5), true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 10 (clause85) }
% 94.29/12.26 fresh212(true2, true2, app(sk5, sk3), sk7, sk6)
% 94.29/12.26 = { by axiom 11 (clause140) }
% 94.29/12.26 true2
% 94.29/12.26 % SZS output end Proof
% 94.29/12.26
% 94.29/12.26 RESULT: Unsatisfiable (the axioms are contradictory).
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