TSTP Solution File: SWC331+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC331+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 20:55:01 EDT 2023
% Result : Theorem 11.90s 1.87s
% Output : Proof 11.90s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC331+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % 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 : n003.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 15:58:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 11.90/1.87 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 11.90/1.87
% 11.90/1.87 % SZS status Theorem
% 11.90/1.87
% 11.90/1.87 % SZS output start Proof
% 11.90/1.87 Take the following subset of the input axioms:
% 11.90/1.88 fof(ax17, axiom, ssList(nil)).
% 11.90/1.88 fof(ax28, axiom, ![U]: (ssList(U) => app(nil, U)=U)).
% 11.90/1.88 fof(ax7, axiom, ![U2]: (ssList(U2) => ![V]: (ssList(V) => (segmentP(U2, V) <=> ?[W]: (ssList(W) & ?[X]: (ssList(X) & app(app(W, V), X)=U2)))))).
% 11.90/1.88 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X3]: (ssList(X3) => (V2!=X3 | (U2!=W2 | (![Y]: (ssList(Y) => (app(W2, Y)!=X3 | (~equalelemsP(W2) | ?[Z]: (ssItem(Z) & ?[X1]: (ssList(X1) & (app(cons(Z, nil), X1)=Y & ?[X2]: (ssList(X2) & app(X2, cons(Z, nil))=W2))))))) | ((nil!=X3 & nil=W2) | (segmentP(V2, U2) & equalelemsP(U2))))))))))).
% 11.90/1.88
% 11.90/1.88 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.90/1.88 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.90/1.88 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.90/1.88 fresh(y, y, x1...xn) = u
% 11.90/1.88 C => fresh(s, t, x1...xn) = v
% 11.90/1.88 where fresh is a fresh function symbol and x1..xn are the free
% 11.90/1.88 variables of u and v.
% 11.90/1.88 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.90/1.88 input problem has no model of domain size 1).
% 11.90/1.88
% 11.90/1.88 The encoding turns the above axioms into the following unit equations and goals:
% 11.90/1.88
% 11.90/1.88 Axiom 1 (co1_1): u = w.
% 11.90/1.88 Axiom 2 (co1_2): v = x.
% 11.90/1.88 Axiom 3 (ax17): ssList(nil) = true2.
% 11.90/1.88 Axiom 4 (co1_3): ssList(u) = true2.
% 11.90/1.88 Axiom 5 (co1_4): ssList(v) = true2.
% 11.90/1.88 Axiom 6 (co1_7): ssList(y) = true2.
% 11.90/1.88 Axiom 7 (co1_8): equalelemsP(w) = true2.
% 11.90/1.88 Axiom 8 (co1): app(w, y) = x.
% 11.90/1.88 Axiom 9 (ax28): fresh7(X, X, Y) = Y.
% 11.90/1.88 Axiom 10 (ax7): fresh31(X, X, Y, Z) = true2.
% 11.90/1.88 Axiom 11 (ax28): fresh7(ssList(X), true2, X) = app(nil, X).
% 11.90/1.88 Axiom 12 (ax7): fresh252(X, X, Y, Z, W, V) = segmentP(Y, Z).
% 11.90/1.88 Axiom 13 (ax7): fresh251(X, X, Y, Z, W, V) = fresh252(ssList(Y), true2, Y, Z, W, V).
% 11.90/1.88 Axiom 14 (ax7): fresh250(X, X, Y, Z, W, V) = fresh251(ssList(Z), true2, Y, Z, W, V).
% 11.90/1.88 Axiom 15 (ax7): fresh249(X, X, Y, Z, W, V) = fresh250(ssList(W), true2, Y, Z, W, V).
% 11.90/1.88 Axiom 16 (ax7): fresh249(ssList(X), true2, Y, Z, W, X) = fresh31(app(app(W, Z), X), Y, Y, Z).
% 11.90/1.88
% 11.90/1.88 Goal 1 (co1_11): tuple2(segmentP(v, u), equalelemsP(u)) = tuple2(true2, true2).
% 11.90/1.88 Proof:
% 11.90/1.88 tuple2(segmentP(v, u), equalelemsP(u))
% 11.90/1.88 = { by axiom 1 (co1_1) }
% 11.90/1.88 tuple2(segmentP(v, u), equalelemsP(w))
% 11.90/1.88 = { by axiom 7 (co1_8) }
% 11.90/1.88 tuple2(segmentP(v, u), true2)
% 11.90/1.88 = { by axiom 12 (ax7) R->L }
% 11.90/1.88 tuple2(fresh252(true2, true2, v, u, nil, y), true2)
% 11.90/1.88 = { by axiom 5 (co1_4) R->L }
% 11.90/1.88 tuple2(fresh252(ssList(v), true2, v, u, nil, y), true2)
% 11.90/1.88 = { by axiom 13 (ax7) R->L }
% 11.90/1.88 tuple2(fresh251(true2, true2, v, u, nil, y), true2)
% 11.90/1.88 = { by axiom 2 (co1_2) }
% 11.90/1.88 tuple2(fresh251(true2, true2, x, u, nil, y), true2)
% 11.90/1.88 = { by axiom 8 (co1) R->L }
% 11.90/1.88 tuple2(fresh251(true2, true2, app(w, y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 1 (co1_1) R->L }
% 11.90/1.88 tuple2(fresh251(true2, true2, app(u, y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 4 (co1_3) R->L }
% 11.90/1.88 tuple2(fresh251(ssList(u), true2, app(u, y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 14 (ax7) R->L }
% 11.90/1.88 tuple2(fresh250(true2, true2, app(u, y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 3 (ax17) R->L }
% 11.90/1.88 tuple2(fresh250(ssList(nil), true2, app(u, y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 15 (ax7) R->L }
% 11.90/1.88 tuple2(fresh249(true2, true2, app(u, y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 6 (co1_7) R->L }
% 11.90/1.88 tuple2(fresh249(ssList(y), true2, app(u, y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 9 (ax28) R->L }
% 11.90/1.88 tuple2(fresh249(ssList(y), true2, app(fresh7(true2, true2, u), y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 4 (co1_3) R->L }
% 11.90/1.88 tuple2(fresh249(ssList(y), true2, app(fresh7(ssList(u), true2, u), y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 11 (ax28) }
% 11.90/1.88 tuple2(fresh249(ssList(y), true2, app(app(nil, u), y), u, nil, y), true2)
% 11.90/1.88 = { by axiom 16 (ax7) }
% 11.90/1.88 tuple2(fresh31(app(app(nil, u), y), app(app(nil, u), y), app(app(nil, u), y), u), true2)
% 11.90/1.88 = { by axiom 10 (ax7) }
% 11.90/1.88 tuple2(true2, true2)
% 11.90/1.88 % SZS output end Proof
% 11.90/1.88
% 11.90/1.88 RESULT: Theorem (the conjecture is true).
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