TSTP Solution File: SWC012-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC012-1 : 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 : n003.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 20:53:25 EDT 2023
% Result : Unsatisfiable 133.78s 17.41s
% Output : Proof 134.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC012-1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 16:31:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 133.78/17.41 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 133.78/17.41
% 133.78/17.41 % SZS status Unsatisfiable
% 133.78/17.41
% 133.78/17.42 % SZS output start Proof
% 133.78/17.42 Take the following subset of the input axioms:
% 134.07/17.43 fof(clause110, axiom, ![U, V]: (~gt(U, V) | (~gt(V, U) | (~ssItem(U) | ~ssItem(V))))).
% 134.07/17.43 fof(clause111, axiom, ![U2, V2]: (U2!=V2 | (~lt(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 134.07/17.43 fof(clause114, axiom, ![U2, V2]: (~lt(U2, V2) | (~lt(V2, U2) | (~ssItem(U2) | ~ssItem(V2))))).
% 134.07/17.43 fof(clause115, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssList(V2) | ~ssList(U2))))).
% 134.07/17.43 fof(clause117, axiom, ![U2, V2]: (U2!=V2 | (~neq(U2, V2) | (~ssItem(V2) | ~ssItem(U2))))).
% 134.07/17.43 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)))))))).
% 134.07/17.43 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))))))))))).
% 134.07/17.43 fof(clause63, axiom, ![U2]: (~lt(U2, U2) | ~ssItem(U2))).
% 134.07/17.43 fof(clause71, axiom, ![U2]: (~memberP(nil, U2) | ~ssItem(U2))).
% 134.07/17.43 fof(clause73, axiom, ![U2]: (~ssList(U2) | app(U2, nil)=U2)).
% 134.07/17.43 fof(clause8, axiom, ssList(nil)).
% 134.07/17.43 fof(clause98, axiom, ![U2, V2]: (cons(U2, V2)!=nil | (~ssItem(U2) | ~ssList(V2)))).
% 134.07/17.43 fof(clause99, axiom, ![U2, V2]: (cons(U2, V2)!=V2 | (~ssItem(U2) | ~ssList(V2)))).
% 134.07/17.43 fof(co1_1, negated_conjecture, ssList(sk1)).
% 134.07/17.43 fof(co1_12, negated_conjecture, ![A, B, C]: (~ssItem(A) | (~ssList(B) | (~ssList(C) | (app(app(B, cons(A, nil)), C)!=sk2 | (app(B, C)!=sk1 | ~neq(sk4, nil))))))).
% 134.07/17.43 fof(co1_13, negated_conjecture, ssItem(sk5) | ~neq(sk4, nil)).
% 134.07/17.43 fof(co1_14, negated_conjecture, app(sk3, cons(sk5, nil))=sk4 | ~neq(sk4, nil)).
% 134.07/17.43 fof(co1_2, negated_conjecture, ssList(sk2)).
% 134.07/17.43 fof(co1_5, negated_conjecture, sk2=sk4).
% 134.07/17.43 fof(co1_6, negated_conjecture, sk1=sk3).
% 134.07/17.43 fof(co1_7, negated_conjecture, neq(sk2, nil) | neq(sk2, nil)).
% 134.07/17.43
% 134.07/17.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 134.07/17.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 134.07/17.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 134.07/17.43 fresh(y, y, x1...xn) = u
% 134.07/17.43 C => fresh(s, t, x1...xn) = v
% 134.07/17.43 where fresh is a fresh function symbol and x1..xn are the free
% 134.07/17.43 variables of u and v.
% 134.07/17.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 134.07/17.43 input problem has no model of domain size 1).
% 134.07/17.43
% 134.07/17.43 The encoding turns the above axioms into the following unit equations and goals:
% 134.07/17.43
% 134.07/17.43 Axiom 1 (co1_5): sk2 = sk4.
% 134.07/17.43 Axiom 2 (co1_6): sk1 = sk3.
% 134.07/17.43 Axiom 3 (clause8): ssList(nil) = true2.
% 134.07/17.43 Axiom 4 (co1_2): ssList(sk2) = true2.
% 134.07/17.43 Axiom 5 (co1_1): ssList(sk1) = true2.
% 134.07/17.43 Axiom 6 (co1_7): neq(sk2, nil) = true2.
% 134.07/17.43 Axiom 7 (co1_13): fresh17(X, X) = true2.
% 134.07/17.43 Axiom 8 (co1_14): fresh16(X, X) = sk4.
% 134.07/17.43 Axiom 9 (clause73): fresh13(X, X, Y) = Y.
% 134.07/17.43 Axiom 10 (co1_13): fresh17(neq(sk4, nil), true2) = ssItem(sk5).
% 134.07/17.43 Axiom 11 (co1_14): fresh16(neq(sk4, nil), true2) = app(sk3, cons(sk5, nil)).
% 134.07/17.43 Axiom 12 (clause73): fresh13(ssList(X), true2, X) = app(X, nil).
% 134.07/17.43
% 134.07/17.43 Goal 1 (co1_12): tuple6(app(X, Y), app(app(X, cons(Z, nil)), Y), ssList(X), ssList(Y), ssItem(Z), neq(sk4, nil)) = tuple6(sk1, sk2, true2, true2, true2, true2).
% 134.07/17.43 The goal is true when:
% 134.07/17.43 X = sk1
% 134.07/17.43 Y = nil
% 134.07/17.43 Z = sk5
% 134.07/17.43
% 134.07/17.43 Proof:
% 134.07/17.43 tuple6(app(sk1, nil), app(app(sk1, cons(sk5, nil)), nil), ssList(sk1), ssList(nil), ssItem(sk5), neq(sk4, nil))
% 134.07/17.43 = { by axiom 1 (co1_5) R->L }
% 134.07/17.43 tuple6(app(sk1, nil), app(app(sk1, cons(sk5, nil)), nil), ssList(sk1), ssList(nil), ssItem(sk5), neq(sk2, nil))
% 134.07/17.43 = { by axiom 6 (co1_7) }
% 134.07/17.43 tuple6(app(sk1, nil), app(app(sk1, cons(sk5, nil)), nil), ssList(sk1), ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 2 (co1_6) }
% 134.07/17.43 tuple6(app(sk1, nil), app(app(sk3, cons(sk5, nil)), nil), ssList(sk1), ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 11 (co1_14) R->L }
% 134.07/17.43 tuple6(app(sk1, nil), app(fresh16(neq(sk4, nil), true2), nil), ssList(sk1), ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 1 (co1_5) R->L }
% 134.07/17.43 tuple6(app(sk1, nil), app(fresh16(neq(sk2, nil), true2), nil), ssList(sk1), ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 6 (co1_7) }
% 134.07/17.43 tuple6(app(sk1, nil), app(fresh16(true2, true2), nil), ssList(sk1), ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 8 (co1_14) }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk4, nil), ssList(sk1), ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 1 (co1_5) R->L }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk2, nil), ssList(sk1), ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 5 (co1_1) }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk2, nil), true2, ssList(nil), ssItem(sk5), true2)
% 134.07/17.43 = { by axiom 10 (co1_13) R->L }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk2, nil), true2, ssList(nil), fresh17(neq(sk4, nil), true2), true2)
% 134.07/17.43 = { by axiom 1 (co1_5) R->L }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk2, nil), true2, ssList(nil), fresh17(neq(sk2, nil), true2), true2)
% 134.07/17.43 = { by axiom 6 (co1_7) }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk2, nil), true2, ssList(nil), fresh17(true2, true2), true2)
% 134.07/17.43 = { by axiom 7 (co1_13) }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk2, nil), true2, ssList(nil), true2, true2)
% 134.07/17.43 = { by axiom 3 (clause8) }
% 134.07/17.43 tuple6(app(sk1, nil), app(sk2, nil), true2, true2, true2, true2)
% 134.07/17.43 = { by axiom 12 (clause73) R->L }
% 134.07/17.43 tuple6(fresh13(ssList(sk1), true2, sk1), app(sk2, nil), true2, true2, true2, true2)
% 134.07/17.43 = { by axiom 5 (co1_1) }
% 134.07/17.43 tuple6(fresh13(true2, true2, sk1), app(sk2, nil), true2, true2, true2, true2)
% 134.07/17.43 = { by axiom 9 (clause73) }
% 134.07/17.43 tuple6(sk1, app(sk2, nil), true2, true2, true2, true2)
% 134.07/17.43 = { by axiom 12 (clause73) R->L }
% 134.07/17.43 tuple6(sk1, fresh13(ssList(sk2), true2, sk2), true2, true2, true2, true2)
% 134.07/17.43 = { by axiom 4 (co1_2) }
% 134.07/17.43 tuple6(sk1, fresh13(true2, true2, sk2), true2, true2, true2, true2)
% 134.07/17.43 = { by axiom 9 (clause73) }
% 134.07/17.43 tuple6(sk1, sk2, true2, true2, true2, true2)
% 134.07/17.43 % SZS output end Proof
% 134.07/17.43
% 134.07/17.43 RESULT: Unsatisfiable (the axioms are contradictory).
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