TSTP Solution File: SWC006+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWC006+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 : n006.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 20:53:22 EDT 2023
% Result : Theorem 3.36s 0.84s
% Output : Proof 3.69s
% 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 : SWC006+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 : n006.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 18:12:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.36/0.84 Command-line arguments: --ground-connectedness --complete-subsets
% 3.36/0.84
% 3.36/0.84 % SZS status Theorem
% 3.36/0.84
% 3.69/0.85 % SZS output start Proof
% 3.69/0.85 Take the following subset of the input axioms:
% 3.69/0.86 fof(ax1, axiom, ![U]: (ssItem(U) => ![V]: (ssItem(V) => (neq(U, V) <=> U!=V)))).
% 3.69/0.86 fof(ax13, axiom, ![U2]: (ssList(U2) => (duplicatefreeP(U2) <=> ![V2]: (ssItem(V2) => ![W]: (ssItem(W) => ![X]: (ssList(X) => ![Y]: (ssList(Y) => ![Z]: (ssList(Z) => (app(app(X, cons(V2, Y)), cons(W, Z))=U2 => V2!=W))))))))).
% 3.69/0.86 fof(ax15, axiom, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => (neq(U2, V2) <=> U2!=V2)))).
% 3.69/0.86 fof(ax18, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => cons(V2, U2)!=U2))).
% 3.69/0.86 fof(ax21, axiom, ![U2]: (ssList(U2) => ![V2]: (ssItem(V2) => nil!=cons(V2, U2)))).
% 3.69/0.86 fof(ax33, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) => ~lt(V2, U2))))).
% 3.69/0.86 fof(ax38, axiom, ![U2]: (ssItem(U2) => ~memberP(nil, U2))).
% 3.69/0.86 fof(ax8, axiom, ![U2]: (ssList(U2) => (cyclefreeP(U2) <=> ![V2]: (ssItem(V2) => ![W2]: (ssItem(W2) => ![X5]: (ssList(X5) => ![Y2]: (ssList(Y2) => ![Z2]: (ssList(Z2) => (app(app(X5, cons(V2, Y2)), cons(W2, Z2))=U2 => ~(leq(V2, W2) & leq(W2, V2))))))))))).
% 3.69/0.86 fof(ax90, axiom, ![U2]: (ssItem(U2) => ~lt(U2, U2))).
% 3.69/0.86 fof(ax93, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (lt(U2, V2) <=> (U2!=V2 & leq(U2, V2)))))).
% 3.69/0.86 fof(ax94, axiom, ![U2]: (ssItem(U2) => ![V2]: (ssItem(V2) => (gt(U2, V2) => ~gt(V2, U2))))).
% 3.69/0.86 fof(co1, conjecture, ![U2]: (ssList(U2) => ![V2]: (ssList(V2) => ![W2]: (ssList(W2) => ![X5]: (~ssList(X5) | (V2!=X5 | (U2!=W2 | (?[Y2]: (ssList(Y2) & ?[Z2]: (ssList(Z2) & ?[X1]: (ssList(X1) & (app(app(Y2, Z2), X1)=V2 & app(Y2, X1)=U2)))) | ![X2]: (ssList(X2) => ![X3]: (ssList(X3) => ![X4]: (~ssList(X4) | (app(app(X2, X3), X4)!=X5 | app(X2, X4)!=W2)))))))))))).
% 3.69/0.86
% 3.69/0.86 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.69/0.86 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.69/0.86 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.69/0.86 fresh(y, y, x1...xn) = u
% 3.69/0.86 C => fresh(s, t, x1...xn) = v
% 3.69/0.86 where fresh is a fresh function symbol and x1..xn are the free
% 3.69/0.86 variables of u and v.
% 3.69/0.86 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.69/0.86 input problem has no model of domain size 1).
% 3.69/0.86
% 3.69/0.86 The encoding turns the above axioms into the following unit equations and goals:
% 3.69/0.86
% 3.69/0.86 Axiom 1 (co1_2): u = w.
% 3.69/0.86 Axiom 2 (co1_3): v = x.
% 3.69/0.86 Axiom 3 (co1_9): ssList(x3) = true2.
% 3.69/0.86 Axiom 4 (co1_8): ssList(x2) = true2.
% 3.69/0.86 Axiom 5 (co1_10): ssList(x4) = true2.
% 3.69/0.86 Axiom 6 (co1_1): app(x2, x4) = w.
% 3.69/0.86 Axiom 7 (co1): app(app(x2, x3), x4) = x.
% 3.69/0.86
% 3.69/0.86 Goal 1 (co1_11): tuple6(app(X, Y), app(app(X, Z), Y), ssList(X), ssList(Z), ssList(Y)) = tuple6(u, v, true2, true2, true2).
% 3.69/0.86 The goal is true when:
% 3.69/0.86 X = x2
% 3.69/0.86 Y = x4
% 3.69/0.86 Z = x3
% 3.69/0.86
% 3.69/0.86 Proof:
% 3.69/0.86 tuple6(app(x2, x4), app(app(x2, x3), x4), ssList(x2), ssList(x3), ssList(x4))
% 3.69/0.86 = { by axiom 7 (co1) }
% 3.69/0.86 tuple6(app(x2, x4), x, ssList(x2), ssList(x3), ssList(x4))
% 3.69/0.86 = { by axiom 6 (co1_1) }
% 3.69/0.86 tuple6(w, x, ssList(x2), ssList(x3), ssList(x4))
% 3.69/0.86 = { by axiom 4 (co1_8) }
% 3.69/0.86 tuple6(w, x, true2, ssList(x3), ssList(x4))
% 3.69/0.86 = { by axiom 3 (co1_9) }
% 3.69/0.86 tuple6(w, x, true2, true2, ssList(x4))
% 3.69/0.86 = { by axiom 5 (co1_10) }
% 3.69/0.86 tuple6(w, x, true2, true2, true2)
% 3.69/0.86 = { by axiom 2 (co1_3) R->L }
% 3.69/0.86 tuple6(w, v, true2, true2, true2)
% 3.69/0.86 = { by axiom 1 (co1_2) R->L }
% 3.69/0.86 tuple6(u, v, true2, true2, true2)
% 3.69/0.86 % SZS output end Proof
% 3.69/0.86
% 3.69/0.86 RESULT: Theorem (the conjecture is true).
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