TSTP Solution File: SWC355+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC355+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 : n025.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 20:55:08 EDT 2023
% Result : Theorem 12.08s 1.93s
% Output : Proof 12.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC355+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % 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 : n025.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 16:25:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 12.08/1.93 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 12.08/1.93
% 12.08/1.93 % SZS status Theorem
% 12.08/1.93
% 12.26/1.94 % SZS output start Proof
% 12.26/1.94 Take the following subset of the input axioms:
% 12.26/1.94 fof(ax16, axiom, ![U]: (ssList(U) => ![V]: (ssItem(V) => ssList(cons(V, U))))).
% 12.26/1.94 fof(ax17, axiom, ssList(nil)).
% 12.26/1.94 fof(ax28, axiom, ![U2]: (ssList(U2) => app(nil, U2)=U2)).
% 12.26/1.94 fof(ax7, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (segmentP(U2, V2) <=> ?[W]: (ssList(W) & ?[X]: (ssList(X) & app(app(W, V2), X)=U2)))))).
% 12.26/1.94 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X2]: (ssList(X2) => (V2!=X2 | (U2!=W2 | ((~neq(V2, nil) | (![Y]: (ssItem(Y) => app(W2, cons(Y, nil))!=X2) | segmentP(V2, U2))) & (~neq(V2, nil) | neq(X2, nil)))))))))).
% 12.26/1.94
% 12.26/1.94 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.26/1.94 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.26/1.94 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.26/1.94 fresh(y, y, x1...xn) = u
% 12.26/1.94 C => fresh(s, t, x1...xn) = v
% 12.26/1.94 where fresh is a fresh function symbol and x1..xn are the free
% 12.26/1.94 variables of u and v.
% 12.26/1.94 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.26/1.94 input problem has no model of domain size 1).
% 12.26/1.94
% 12.26/1.94 The encoding turns the above axioms into the following unit equations and goals:
% 12.26/1.94
% 12.26/1.94 Axiom 1 (co1_2): v = x.
% 12.26/1.94 Axiom 2 (co1_1): u = w.
% 12.26/1.94 Axiom 3 (ax17): ssList(nil) = true2.
% 12.26/1.94 Axiom 4 (co1_6): ssList(v) = true2.
% 12.26/1.94 Axiom 5 (co1_5): ssList(u) = true2.
% 12.26/1.94 Axiom 6 (co1_4): neq(v, nil) = true2.
% 12.26/1.94 Axiom 7 (co1_10): fresh17(X, X) = true2.
% 12.26/1.94 Axiom 8 (co1_9): fresh14(X, X) = x.
% 12.26/1.94 Axiom 9 (ax28): fresh7(X, X, Y) = Y.
% 12.26/1.94 Axiom 10 (ax16): fresh80(X, X, Y, Z) = ssList(cons(Z, Y)).
% 12.26/1.94 Axiom 11 (ax16): fresh79(X, X, Y, Z) = true2.
% 12.26/1.94 Axiom 12 (ax7): fresh34(X, X, Y, Z) = true2.
% 12.26/1.94 Axiom 13 (co1_10): fresh17(neq(x, nil), true2) = ssItem(y).
% 12.26/1.94 Axiom 14 (co1_9): fresh14(neq(x, nil), true2) = app(w, cons(y, nil)).
% 12.26/1.94 Axiom 15 (ax28): fresh7(ssList(X), true2, X) = app(nil, X).
% 12.26/1.94 Axiom 16 (ax16): fresh80(ssList(X), true2, X, Y) = fresh79(ssItem(Y), true2, X, Y).
% 12.26/1.94 Axiom 17 (ax7): fresh255(X, X, Y, Z, W, V) = segmentP(Y, Z).
% 12.26/1.94 Axiom 18 (ax7): fresh254(X, X, Y, Z, W, V) = fresh255(ssList(Y), true2, Y, Z, W, V).
% 12.26/1.94 Axiom 19 (ax7): fresh253(X, X, Y, Z, W, V) = fresh254(ssList(Z), true2, Y, Z, W, V).
% 12.26/1.94 Axiom 20 (ax7): fresh252(X, X, Y, Z, W, V) = fresh253(ssList(W), true2, Y, Z, W, V).
% 12.26/1.94 Axiom 21 (ax7): fresh252(ssList(X), true2, Y, Z, W, X) = fresh34(app(app(W, Z), X), Y, Y, Z).
% 12.26/1.94
% 12.26/1.94 Goal 1 (co1_12): tuple2(neq(x, nil), segmentP(v, u)) = tuple2(true2, true2).
% 12.26/1.94 Proof:
% 12.26/1.94 tuple2(neq(x, nil), segmentP(v, u))
% 12.26/1.94 = { by axiom 1 (co1_2) R->L }
% 12.26/1.94 tuple2(neq(v, nil), segmentP(v, u))
% 12.26/1.94 = { by axiom 6 (co1_4) }
% 12.26/1.94 tuple2(true2, segmentP(v, u))
% 12.26/1.94 = { by axiom 17 (ax7) R->L }
% 12.26/1.94 tuple2(true2, fresh255(true2, true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 4 (co1_6) R->L }
% 12.26/1.94 tuple2(true2, fresh255(ssList(v), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 18 (ax7) R->L }
% 12.26/1.94 tuple2(true2, fresh254(true2, true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 5 (co1_5) R->L }
% 12.26/1.94 tuple2(true2, fresh254(ssList(u), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 19 (ax7) R->L }
% 12.26/1.94 tuple2(true2, fresh253(true2, true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 3 (ax17) R->L }
% 12.26/1.94 tuple2(true2, fresh253(ssList(nil), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 20 (ax7) R->L }
% 12.26/1.94 tuple2(true2, fresh252(true2, true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 11 (ax16) R->L }
% 12.26/1.94 tuple2(true2, fresh252(fresh79(true2, true2, nil, y), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 7 (co1_10) R->L }
% 12.26/1.94 tuple2(true2, fresh252(fresh79(fresh17(true2, true2), true2, nil, y), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 6 (co1_4) R->L }
% 12.26/1.94 tuple2(true2, fresh252(fresh79(fresh17(neq(v, nil), true2), true2, nil, y), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 1 (co1_2) }
% 12.26/1.94 tuple2(true2, fresh252(fresh79(fresh17(neq(x, nil), true2), true2, nil, y), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 13 (co1_10) }
% 12.26/1.94 tuple2(true2, fresh252(fresh79(ssItem(y), true2, nil, y), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 16 (ax16) R->L }
% 12.26/1.94 tuple2(true2, fresh252(fresh80(ssList(nil), true2, nil, y), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 3 (ax17) }
% 12.26/1.94 tuple2(true2, fresh252(fresh80(true2, true2, nil, y), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 10 (ax16) }
% 12.26/1.94 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, v, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 1 (co1_2) }
% 12.26/1.94 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, x, u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 8 (co1_9) R->L }
% 12.26/1.94 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, fresh14(true2, true2), u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 6 (co1_4) R->L }
% 12.26/1.94 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, fresh14(neq(v, nil), true2), u, nil, cons(y, nil)))
% 12.26/1.94 = { by axiom 1 (co1_2) }
% 12.26/1.94 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, fresh14(neq(x, nil), true2), u, nil, cons(y, nil)))
% 12.26/1.95 = { by axiom 14 (co1_9) }
% 12.26/1.95 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, app(w, cons(y, nil)), u, nil, cons(y, nil)))
% 12.26/1.95 = { by axiom 2 (co1_1) R->L }
% 12.26/1.95 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, app(u, cons(y, nil)), u, nil, cons(y, nil)))
% 12.26/1.95 = { by axiom 9 (ax28) R->L }
% 12.26/1.95 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, app(fresh7(true2, true2, u), cons(y, nil)), u, nil, cons(y, nil)))
% 12.26/1.95 = { by axiom 5 (co1_5) R->L }
% 12.26/1.95 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, app(fresh7(ssList(u), true2, u), cons(y, nil)), u, nil, cons(y, nil)))
% 12.26/1.95 = { by axiom 15 (ax28) }
% 12.26/1.95 tuple2(true2, fresh252(ssList(cons(y, nil)), true2, app(app(nil, u), cons(y, nil)), u, nil, cons(y, nil)))
% 12.26/1.95 = { by axiom 21 (ax7) }
% 12.26/1.95 tuple2(true2, fresh34(app(app(nil, u), cons(y, nil)), app(app(nil, u), cons(y, nil)), app(app(nil, u), cons(y, nil)), u))
% 12.26/1.95 = { by axiom 12 (ax7) }
% 12.26/1.95 tuple2(true2, true2)
% 12.26/1.95 % SZS output end Proof
% 12.26/1.95
% 12.26/1.95 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------