TSTP Solution File: SWC095-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWC095-1 : 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 : n018.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 20:53:50 EDT 2023
% Result : Unsatisfiable 3.76s 0.83s
% Output : Proof 3.76s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC095-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 15:22:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.76/0.83 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.76/0.83
% 3.76/0.83 % SZS status Unsatisfiable
% 3.76/0.83
% 3.76/0.84 % SZS output start Proof
% 3.76/0.84 Take the following subset of the input axioms:
% 3.76/0.84 fof(clause110, axiom, ![U, V]: (~gt(U, V) | (~gt(V, U) | (~ssItem(U) | ~ssItem(V))))).
% 3.76/0.84 fof(clause111, axiom, ![U2, V2]: (U2!=V2 | (~lt(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 3.76/0.84 fof(clause114, axiom, ![U2, V2]: (~lt(U2, V2) | (~lt(V2, U2) | (~ssItem(U2) | ~ssItem(V2))))).
% 3.76/0.84 fof(clause115, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssList(V2) | ~ssList(U2))))).
% 3.76/0.84 fof(clause117, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 3.76/0.84 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)))))))).
% 3.76/0.84 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))))))))))).
% 3.76/0.84 fof(clause63, axiom, ![U2]: (~lt(U2, U2) | ~ssItem(U2))).
% 3.76/0.84 fof(clause71, axiom, ![U2]: (~memberP(nil, U2) | ~ssItem(U2))).
% 3.76/0.84 fof(clause98, axiom, ![U2, V2]: (cons(U2, V2)!=nil | (~ssItem(U2) | ~ssList(V2)))).
% 3.76/0.84 fof(clause99, axiom, ![U2, V2]: (cons(U2, V2)!=V2 | (~ssItem(U2) | ~ssList(V2)))).
% 3.76/0.84 fof(co1_10, negated_conjecture, ssList(sk7)).
% 3.76/0.84 fof(co1_11, negated_conjecture, app(app(sk5, sk6), sk7)=sk3).
% 3.76/0.84 fof(co1_12, negated_conjecture, app(sk5, sk7)=sk4).
% 3.76/0.84 fof(co1_5, negated_conjecture, sk2=sk4).
% 3.76/0.84 fof(co1_6, negated_conjecture, sk1=sk3).
% 3.76/0.84 fof(co1_7, negated_conjecture, ![A, B, C]: (~ssList(A) | (~ssList(B) | (~ssList(C) | (app(app(A, B), C)!=sk1 | app(A, C)!=sk2))))).
% 3.76/0.84 fof(co1_8, negated_conjecture, ssList(sk5)).
% 3.76/0.84 fof(co1_9, negated_conjecture, ssList(sk6)).
% 3.76/0.84
% 3.76/0.84 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.76/0.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.76/0.84 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.76/0.84 fresh(y, y, x1...xn) = u
% 3.76/0.84 C => fresh(s, t, x1...xn) = v
% 3.76/0.84 where fresh is a fresh function symbol and x1..xn are the free
% 3.76/0.84 variables of u and v.
% 3.76/0.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.76/0.84 input problem has no model of domain size 1).
% 3.76/0.84
% 3.76/0.84 The encoding turns the above axioms into the following unit equations and goals:
% 3.76/0.84
% 3.76/0.84 Axiom 1 (co1_6): sk1 = sk3.
% 3.76/0.84 Axiom 2 (co1_5): sk2 = sk4.
% 3.76/0.84 Axiom 3 (co1_8): ssList(sk5) = true2.
% 3.76/0.84 Axiom 4 (co1_10): ssList(sk7) = true2.
% 3.76/0.84 Axiom 5 (co1_9): ssList(sk6) = true2.
% 3.76/0.84 Axiom 6 (co1_12): app(sk5, sk7) = sk4.
% 3.76/0.84 Axiom 7 (co1_11): app(app(sk5, sk6), sk7) = sk3.
% 3.76/0.84
% 3.76/0.84 Goal 1 (co1_7): tuple6(app(X, Y), app(app(X, Z), Y), ssList(X), ssList(Z), ssList(Y)) = tuple6(sk2, sk1, true2, true2, true2).
% 3.76/0.84 The goal is true when:
% 3.76/0.84 X = sk5
% 3.76/0.84 Y = sk7
% 3.76/0.84 Z = sk6
% 3.76/0.84
% 3.76/0.84 Proof:
% 3.76/0.84 tuple6(app(sk5, sk7), app(app(sk5, sk6), sk7), ssList(sk5), ssList(sk6), ssList(sk7))
% 3.76/0.84 = { by axiom 7 (co1_11) }
% 3.76/0.84 tuple6(app(sk5, sk7), sk3, ssList(sk5), ssList(sk6), ssList(sk7))
% 3.76/0.84 = { by axiom 1 (co1_6) R->L }
% 3.76/0.84 tuple6(app(sk5, sk7), sk1, ssList(sk5), ssList(sk6), ssList(sk7))
% 3.76/0.84 = { by axiom 6 (co1_12) }
% 3.76/0.84 tuple6(sk4, sk1, ssList(sk5), ssList(sk6), ssList(sk7))
% 3.76/0.84 = { by axiom 2 (co1_5) R->L }
% 3.76/0.84 tuple6(sk2, sk1, ssList(sk5), ssList(sk6), ssList(sk7))
% 3.76/0.84 = { by axiom 3 (co1_8) }
% 3.76/0.84 tuple6(sk2, sk1, true2, ssList(sk6), ssList(sk7))
% 3.76/0.84 = { by axiom 5 (co1_9) }
% 3.76/0.84 tuple6(sk2, sk1, true2, true2, ssList(sk7))
% 3.76/0.84 = { by axiom 4 (co1_10) }
% 3.76/0.84 tuple6(sk2, sk1, true2, true2, true2)
% 3.76/0.84 % SZS output end Proof
% 3.76/0.84
% 3.76/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
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