TSTP Solution File: SWC082-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC082-1 : 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 : 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 20:53:46 EDT 2023
% Result : Unsatisfiable 4.27s 1.01s
% Output : Proof 4.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC082-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 18:59:52 EDT 2023
% 0.11/0.33 % CPUTime :
% 4.27/1.01 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 4.27/1.01
% 4.27/1.01 % SZS status Unsatisfiable
% 4.27/1.01
% 4.27/1.02 % SZS output start Proof
% 4.27/1.02 Take the following subset of the input axioms:
% 4.27/1.02 fof(clause110, axiom, ![U, V]: (~gt(U, V) | (~gt(V, U) | (~ssItem(U) | ~ssItem(V))))).
% 4.27/1.02 fof(clause111, axiom, ![U2, V2]: (U2!=V2 | (~lt(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 4.27/1.02 fof(clause114, axiom, ![U2, V2]: (~lt(U2, V2) | (~lt(V2, U2) | (~ssItem(U2) | ~ssItem(V2))))).
% 4.27/1.02 fof(clause115, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssList(V2) | ~ssList(U2))))).
% 4.27/1.02 fof(clause117, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 4.27/1.02 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)))))))).
% 4.27/1.02 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))))))))))).
% 4.27/1.02 fof(clause63, axiom, ![U2]: (~lt(U2, U2) | ~ssItem(U2))).
% 4.27/1.02 fof(clause71, axiom, ![U2]: (~memberP(nil, U2) | ~ssItem(U2))).
% 4.27/1.02 fof(clause98, axiom, ![U2, V2]: (cons(U2, V2)!=nil | (~ssItem(U2) | ~ssList(V2)))).
% 4.27/1.02 fof(clause99, axiom, ![U2, V2]: (cons(U2, V2)!=V2 | (~ssItem(U2) | ~ssList(V2)))).
% 4.27/1.02 fof(co1_10, negated_conjecture, ssList(sk5) | ~neq(sk4, nil)).
% 4.27/1.02 fof(co1_11, negated_conjecture, neq(sk5, nil) | ~neq(sk4, nil)).
% 4.27/1.02 fof(co1_12, negated_conjecture, segmentP(sk4, sk5) | ~neq(sk4, nil)).
% 4.27/1.02 fof(co1_13, negated_conjecture, segmentP(sk3, sk5) | ~neq(sk4, nil)).
% 4.27/1.02 fof(co1_5, negated_conjecture, sk2=sk4).
% 4.27/1.02 fof(co1_6, negated_conjecture, sk1=sk3).
% 4.27/1.02 fof(co1_7, negated_conjecture, neq(sk2, nil)).
% 4.27/1.02 fof(co1_8, negated_conjecture, ![A]: (~ssList(A) | (~neq(A, nil) | (~segmentP(sk2, A) | ~segmentP(sk1, A))))).
% 4.27/1.02
% 4.27/1.02 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.27/1.02 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.27/1.02 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.27/1.02 fresh(y, y, x1...xn) = u
% 4.27/1.02 C => fresh(s, t, x1...xn) = v
% 4.27/1.02 where fresh is a fresh function symbol and x1..xn are the free
% 4.27/1.02 variables of u and v.
% 4.27/1.02 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.27/1.02 input problem has no model of domain size 1).
% 4.27/1.02
% 4.27/1.02 The encoding turns the above axioms into the following unit equations and goals:
% 4.27/1.02
% 4.27/1.02 Axiom 1 (co1_5): sk2 = sk4.
% 4.27/1.02 Axiom 2 (co1_6): sk1 = sk3.
% 4.27/1.02 Axiom 3 (co1_7): neq(sk2, nil) = true2.
% 4.27/1.02 Axiom 4 (co1_10): fresh18(X, X) = true2.
% 4.27/1.02 Axiom 5 (co1_11): fresh17(X, X) = true2.
% 4.27/1.02 Axiom 6 (co1_12): fresh16(X, X) = true2.
% 4.27/1.02 Axiom 7 (co1_13): fresh15(X, X) = true2.
% 4.27/1.02 Axiom 8 (co1_10): fresh18(neq(sk4, nil), true2) = ssList(sk5).
% 4.27/1.02 Axiom 9 (co1_11): fresh17(neq(sk4, nil), true2) = neq(sk5, nil).
% 4.27/1.02 Axiom 10 (co1_12): fresh16(neq(sk4, nil), true2) = segmentP(sk4, sk5).
% 4.27/1.02 Axiom 11 (co1_13): fresh15(neq(sk4, nil), true2) = segmentP(sk3, sk5).
% 4.27/1.02
% 4.27/1.02 Lemma 12: neq(sk4, nil) = true2.
% 4.27/1.02 Proof:
% 4.27/1.02 neq(sk4, nil)
% 4.27/1.02 = { by axiom 1 (co1_5) R->L }
% 4.27/1.02 neq(sk2, nil)
% 4.27/1.02 = { by axiom 3 (co1_7) }
% 4.27/1.03 true2
% 4.27/1.03
% 4.27/1.03 Goal 1 (co1_8): tuple(ssList(X), segmentP(sk1, X), segmentP(sk2, X), neq(X, nil)) = tuple(true2, true2, true2, true2).
% 4.27/1.03 The goal is true when:
% 4.27/1.03 X = sk5
% 4.27/1.03
% 4.27/1.03 Proof:
% 4.27/1.03 tuple(ssList(sk5), segmentP(sk1, sk5), segmentP(sk2, sk5), neq(sk5, nil))
% 4.27/1.03 = { by axiom 2 (co1_6) }
% 4.27/1.03 tuple(ssList(sk5), segmentP(sk3, sk5), segmentP(sk2, sk5), neq(sk5, nil))
% 4.27/1.03 = { by axiom 1 (co1_5) }
% 4.27/1.03 tuple(ssList(sk5), segmentP(sk3, sk5), segmentP(sk4, sk5), neq(sk5, nil))
% 4.27/1.03 = { by axiom 8 (co1_10) R->L }
% 4.27/1.03 tuple(fresh18(neq(sk4, nil), true2), segmentP(sk3, sk5), segmentP(sk4, sk5), neq(sk5, nil))
% 4.27/1.03 = { by lemma 12 }
% 4.27/1.03 tuple(fresh18(true2, true2), segmentP(sk3, sk5), segmentP(sk4, sk5), neq(sk5, nil))
% 4.27/1.03 = { by axiom 4 (co1_10) }
% 4.27/1.03 tuple(true2, segmentP(sk3, sk5), segmentP(sk4, sk5), neq(sk5, nil))
% 4.27/1.03 = { by axiom 11 (co1_13) R->L }
% 4.27/1.03 tuple(true2, fresh15(neq(sk4, nil), true2), segmentP(sk4, sk5), neq(sk5, nil))
% 4.27/1.03 = { by lemma 12 }
% 4.27/1.03 tuple(true2, fresh15(true2, true2), segmentP(sk4, sk5), neq(sk5, nil))
% 4.27/1.03 = { by axiom 7 (co1_13) }
% 4.27/1.03 tuple(true2, true2, segmentP(sk4, sk5), neq(sk5, nil))
% 4.27/1.03 = { by axiom 10 (co1_12) R->L }
% 4.27/1.03 tuple(true2, true2, fresh16(neq(sk4, nil), true2), neq(sk5, nil))
% 4.27/1.03 = { by lemma 12 }
% 4.27/1.03 tuple(true2, true2, fresh16(true2, true2), neq(sk5, nil))
% 4.27/1.03 = { by axiom 6 (co1_12) }
% 4.27/1.03 tuple(true2, true2, true2, neq(sk5, nil))
% 4.27/1.03 = { by axiom 9 (co1_11) R->L }
% 4.27/1.03 tuple(true2, true2, true2, fresh17(neq(sk4, nil), true2))
% 4.27/1.03 = { by lemma 12 }
% 4.27/1.03 tuple(true2, true2, true2, fresh17(true2, true2))
% 4.27/1.03 = { by axiom 5 (co1_11) }
% 4.27/1.03 tuple(true2, true2, true2, true2)
% 4.27/1.03 % SZS output end Proof
% 4.27/1.03
% 4.27/1.03 RESULT: Unsatisfiable (the axioms are contradictory).
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