TSTP Solution File: SWC189-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC189-1 : 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 : n024.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 20:54:20 EDT 2023
% Result : Unsatisfiable 32.92s 4.55s
% Output : Proof 32.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC189-1 : 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 : n024.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 18:52:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 32.92/4.55 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 32.92/4.55
% 32.92/4.55 % SZS status Unsatisfiable
% 32.92/4.55
% 32.92/4.56 % SZS output start Proof
% 32.92/4.56 Take the following subset of the input axioms:
% 32.92/4.56 fof(co1_10, negated_conjecture, ssList(sk7)).
% 32.92/4.56 fof(co1_11, negated_conjecture, ssList(sk8)).
% 32.92/4.56 fof(co1_12, negated_conjecture, app(app(app(sk7, cons(sk5, nil)), cons(sk6, nil)), sk8)=sk1).
% 32.92/4.56 fof(co1_13, negated_conjecture, sk5!=sk6).
% 32.92/4.56 fof(co1_6, negated_conjecture, sk1=sk3).
% 32.92/4.56 fof(co1_7, negated_conjecture, ![B, C, D, A2]: (~ssItem(A2) | (~ssItem(B) | (~ssList(C) | (~ssList(D) | (A2=B | app(app(app(C, cons(A2, nil)), cons(B, nil)), D)!=sk3)))))).
% 32.92/4.56 fof(co1_8, negated_conjecture, ssItem(sk5)).
% 32.92/4.56 fof(co1_9, negated_conjecture, ssItem(sk6)).
% 32.92/4.56
% 32.92/4.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 32.92/4.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 32.92/4.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 32.92/4.56 fresh(y, y, x1...xn) = u
% 32.92/4.56 C => fresh(s, t, x1...xn) = v
% 32.92/4.56 where fresh is a fresh function symbol and x1..xn are the free
% 32.92/4.56 variables of u and v.
% 32.92/4.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 32.92/4.56 input problem has no model of domain size 1).
% 32.92/4.56
% 32.92/4.56 The encoding turns the above axioms into the following unit equations and goals:
% 32.92/4.56
% 32.92/4.56 Axiom 1 (co1_6): sk1 = sk3.
% 32.92/4.56 Axiom 2 (co1_10): ssList(sk7) = true2.
% 32.92/4.56 Axiom 3 (co1_11): ssList(sk8) = true2.
% 32.92/4.56 Axiom 4 (co1_8): ssItem(sk5) = true2.
% 32.92/4.56 Axiom 5 (co1_9): ssItem(sk6) = true2.
% 32.92/4.56 Axiom 6 (co1_7): fresh(X, X, Y, Z) = Z.
% 32.92/4.56 Axiom 7 (co1_12): app(app(app(sk7, cons(sk5, nil)), cons(sk6, nil)), sk8) = sk1.
% 32.92/4.56 Axiom 8 (co1_7): fresh85(X, X, Y, Z, W, V) = Y.
% 32.92/4.56 Axiom 9 (co1_7): fresh84(X, X, Y, Z, W, V) = fresh85(ssList(W), true2, Y, Z, W, V).
% 32.92/4.56 Axiom 10 (co1_7): fresh83(X, X, Y, Z, W, V) = fresh84(ssList(V), true2, Y, Z, W, V).
% 32.92/4.56 Axiom 11 (co1_7): fresh82(X, X, Y, Z, W, V) = fresh83(ssItem(Y), true2, Y, Z, W, V).
% 32.92/4.56 Axiom 12 (co1_7): fresh82(ssItem(X), true2, Y, X, Z, W) = fresh(app(app(app(Z, cons(Y, nil)), cons(X, nil)), W), sk3, Y, X).
% 32.92/4.56
% 32.92/4.56 Goal 1 (co1_13): sk5 = sk6.
% 32.92/4.56 Proof:
% 32.92/4.56 sk5
% 32.92/4.56 = { by axiom 8 (co1_7) R->L }
% 32.92/4.56 fresh85(true2, true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 2 (co1_10) R->L }
% 32.92/4.56 fresh85(ssList(sk7), true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 9 (co1_7) R->L }
% 32.92/4.56 fresh84(true2, true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 3 (co1_11) R->L }
% 32.92/4.56 fresh84(ssList(sk8), true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 10 (co1_7) R->L }
% 32.92/4.56 fresh83(true2, true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 4 (co1_8) R->L }
% 32.92/4.56 fresh83(ssItem(sk5), true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 11 (co1_7) R->L }
% 32.92/4.56 fresh82(true2, true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 5 (co1_9) R->L }
% 32.92/4.56 fresh82(ssItem(sk6), true2, sk5, sk6, sk7, sk8)
% 32.92/4.56 = { by axiom 12 (co1_7) }
% 32.92/4.56 fresh(app(app(app(sk7, cons(sk5, nil)), cons(sk6, nil)), sk8), sk3, sk5, sk6)
% 32.92/4.56 = { by axiom 1 (co1_6) R->L }
% 32.92/4.56 fresh(app(app(app(sk7, cons(sk5, nil)), cons(sk6, nil)), sk8), sk1, sk5, sk6)
% 32.92/4.56 = { by axiom 7 (co1_12) }
% 32.92/4.56 fresh(sk1, sk1, sk5, sk6)
% 32.92/4.56 = { by axiom 6 (co1_7) }
% 32.92/4.56 sk6
% 32.92/4.56 % SZS output end Proof
% 32.92/4.56
% 32.92/4.56 RESULT: Unsatisfiable (the axioms are contradictory).
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