TSTP Solution File: SWC008-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC008-1 : 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 : n012.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 20:53:23 EDT 2023
% Result : Unsatisfiable 242.99s 31.59s
% Output : Proof 243.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC008-1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 18:21:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 242.99/31.59 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 242.99/31.59
% 242.99/31.59 % SZS status Unsatisfiable
% 242.99/31.59
% 242.99/31.59 % SZS output start Proof
% 242.99/31.59 Take the following subset of the input axioms:
% 242.99/31.59 fof(clause110, axiom, ![U, V]: (~gt(U, V) | (~gt(V, U) | (~ssItem(U) | ~ssItem(V))))).
% 243.23/31.59 fof(clause111, axiom, ![U2, V2]: (U2!=V2 | (~lt(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 243.23/31.59 fof(clause114, axiom, ![U2, V2]: (~lt(U2, V2) | (~lt(V2, U2) | (~ssItem(U2) | ~ssItem(V2))))).
% 243.23/31.59 fof(clause115, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssList(V2) | ~ssList(U2))))).
% 243.23/31.59 fof(clause117, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 243.23/31.59 fof(clause132, axiom, ![U2, V2]: (~frontsegP(U2, V2) | (~ssList(V2) | (~ssList(U2) | app(V2, skaf45(U2, V2))=U2)))).
% 243.23/31.59 fof(clause179, axiom, ![W, X, Y, U2, V2]: (app(app(U2, cons(V2, W)), cons(V2, X))!=Y | (~ssList(X) | (~ssList(W) | (~ssList(U2) | (~ssItem(V2) | (~duplicatefreeP(Y) | ~ssList(Y)))))))).
% 243.23/31.59 fof(clause185, axiom, ![Z, U2, V2, W2, X2, Y2]: (~leq(U2, V2) | (~leq(V2, U2) | (app(app(W2, cons(U2, X2)), cons(V2, Y2))!=Z | (~ssList(Y2) | (~ssList(X2) | (~ssList(W2) | (~ssItem(V2) | (~ssItem(U2) | (~cyclefreeP(Z) | ~ssList(Z))))))))))).
% 243.23/31.59 fof(clause51, axiom, ![U2, V2]: ssList(skaf45(U2, V2))).
% 243.23/31.59 fof(clause63, axiom, ![U2]: (~lt(U2, U2) | ~ssItem(U2))).
% 243.23/31.59 fof(clause71, axiom, ![U2]: (~memberP(nil, U2) | ~ssItem(U2))).
% 243.23/31.59 fof(clause73, axiom, ![U2]: (~ssList(U2) | app(U2, nil)=U2)).
% 243.23/31.59 fof(clause8, axiom, ssList(nil)).
% 243.23/31.59 fof(clause98, axiom, ![U2, V2]: (cons(U2, V2)!=nil | (~ssItem(U2) | ~ssList(V2)))).
% 243.23/31.59 fof(clause99, axiom, ![U2, V2]: (cons(U2, V2)!=V2 | (~ssItem(U2) | ~ssList(V2)))).
% 243.23/31.59 fof(co1_10, negated_conjecture, ![A]: (~ssList(A) | (~neq(sk3, A) | (~frontsegP(sk4, A) | (~segmentP(A, sk3) | ~equalelemsP(A)))))).
% 243.23/31.59 fof(co1_2, negated_conjecture, ssList(sk2)).
% 243.23/31.59 fof(co1_3, negated_conjecture, ssList(sk3)).
% 243.23/31.59 fof(co1_5, negated_conjecture, sk2=sk4).
% 243.23/31.59 fof(co1_6, negated_conjecture, sk1=sk3).
% 243.23/31.59 fof(co1_7, negated_conjecture, frontsegP(sk4, sk3)).
% 243.23/31.59 fof(co1_9, negated_conjecture, ![B, C, A2]: (~ssList(A2) | (~ssList(B) | (~ssList(C) | (app(app(A2, B), C)!=sk2 | app(A2, C)!=sk1))))).
% 243.23/31.59
% 243.23/31.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 243.23/31.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 243.23/31.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 243.23/31.60 fresh(y, y, x1...xn) = u
% 243.23/31.60 C => fresh(s, t, x1...xn) = v
% 243.23/31.60 where fresh is a fresh function symbol and x1..xn are the free
% 243.23/31.60 variables of u and v.
% 243.23/31.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 243.23/31.60 input problem has no model of domain size 1).
% 243.23/31.60
% 243.23/31.60 The encoding turns the above axioms into the following unit equations and goals:
% 243.23/31.60
% 243.23/31.60 Axiom 1 (co1_6): sk1 = sk3.
% 243.23/31.60 Axiom 2 (co1_5): sk2 = sk4.
% 243.23/31.60 Axiom 3 (clause8): ssList(nil) = true2.
% 243.23/31.60 Axiom 4 (co1_3): ssList(sk3) = true2.
% 243.23/31.60 Axiom 5 (co1_2): ssList(sk2) = true2.
% 243.23/31.60 Axiom 6 (co1_7): frontsegP(sk4, sk3) = true2.
% 243.23/31.60 Axiom 7 (clause51): ssList(skaf45(X, Y)) = true2.
% 243.23/31.60 Axiom 8 (clause73): fresh13(X, X, Y) = Y.
% 243.23/31.60 Axiom 9 (clause132): fresh225(X, X, Y, Z) = Y.
% 243.23/31.60 Axiom 10 (clause132): fresh66(X, X, Y, Z) = app(Z, skaf45(Y, Z)).
% 243.23/31.60 Axiom 11 (clause73): fresh13(ssList(X), true2, X) = app(X, nil).
% 243.23/31.60 Axiom 12 (clause132): fresh224(X, X, Y, Z) = fresh225(ssList(Y), true2, Y, Z).
% 243.23/31.60 Axiom 13 (clause132): fresh224(frontsegP(X, Y), true2, X, Y) = fresh66(ssList(Y), true2, X, Y).
% 243.23/31.60
% 243.23/31.60 Goal 1 (co1_9): tuple7(app(X, Y), app(app(X, Z), Y), ssList(X), ssList(Z), ssList(Y)) = tuple7(sk1, sk2, true2, true2, true2).
% 243.23/31.60 The goal is true when:
% 243.23/31.60 X = sk3
% 243.23/31.60 Y = nil
% 243.23/31.60 Z = skaf45(sk2, sk3)
% 243.23/31.60
% 243.23/31.60 Proof:
% 243.23/31.60 tuple7(app(sk3, nil), app(app(sk3, skaf45(sk2, sk3)), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), ssList(nil))
% 243.23/31.60 = { by axiom 3 (clause8) }
% 243.23/31.60 tuple7(app(sk3, nil), app(app(sk3, skaf45(sk2, sk3)), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 10 (clause132) R->L }
% 243.23/31.60 tuple7(app(sk3, nil), app(fresh66(true2, true2, sk2, sk3), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 4 (co1_3) R->L }
% 243.23/31.60 tuple7(app(sk3, nil), app(fresh66(ssList(sk3), true2, sk2, sk3), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 13 (clause132) R->L }
% 243.23/31.60 tuple7(app(sk3, nil), app(fresh224(frontsegP(sk2, sk3), true2, sk2, sk3), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 2 (co1_5) }
% 243.23/31.60 tuple7(app(sk3, nil), app(fresh224(frontsegP(sk4, sk3), true2, sk2, sk3), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 6 (co1_7) }
% 243.23/31.60 tuple7(app(sk3, nil), app(fresh224(true2, true2, sk2, sk3), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 12 (clause132) }
% 243.23/31.60 tuple7(app(sk3, nil), app(fresh225(ssList(sk2), true2, sk2, sk3), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 5 (co1_2) }
% 243.23/31.60 tuple7(app(sk3, nil), app(fresh225(true2, true2, sk2, sk3), nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 9 (clause132) }
% 243.23/31.60 tuple7(app(sk3, nil), app(sk2, nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 11 (clause73) R->L }
% 243.23/31.60 tuple7(fresh13(ssList(sk3), true2, sk3), app(sk2, nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 4 (co1_3) }
% 243.23/31.60 tuple7(fresh13(true2, true2, sk3), app(sk2, nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 8 (clause73) }
% 243.23/31.60 tuple7(sk3, app(sk2, nil), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 11 (clause73) R->L }
% 243.23/31.60 tuple7(sk3, fresh13(ssList(sk2), true2, sk2), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 5 (co1_2) }
% 243.23/31.60 tuple7(sk3, fresh13(true2, true2, sk2), ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 8 (clause73) }
% 243.23/31.60 tuple7(sk3, sk2, ssList(sk3), ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 4 (co1_3) }
% 243.23/31.60 tuple7(sk3, sk2, true2, ssList(skaf45(sk2, sk3)), true2)
% 243.23/31.60 = { by axiom 7 (clause51) }
% 243.23/31.60 tuple7(sk3, sk2, true2, true2, true2)
% 243.23/31.60 = { by axiom 1 (co1_6) R->L }
% 243.23/31.60 tuple7(sk1, sk2, true2, true2, true2)
% 243.23/31.60 % SZS output end Proof
% 243.23/31.60
% 243.23/31.60 RESULT: Unsatisfiable (the axioms are contradictory).
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