TSTP Solution File: GEO500+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO500+1 : TPTP v8.1.2. Released v7.0.0.
% 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 : n004.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 : Wed Aug 30 23:29:06 EDT 2023
% Result : Theorem 12.83s 2.10s
% Output : Proof 13.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO500+1 : TPTP v8.1.2. Released v7.0.0.
% 0.08/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 21:48:52 EDT 2023
% 0.15/0.37 % CPUTime :
% 12.83/2.10 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 12.83/2.10
% 12.83/2.10 % SZS status Theorem
% 12.83/2.10
% 13.56/2.11 % SZS output start Proof
% 13.56/2.11 Take the following subset of the input axioms:
% 13.56/2.11 fof(aSatz7_10a, axiom, ![Xa, Xp]: (s(Xa, Xp)!=Xp | Xp=Xa)).
% 13.56/2.11 fof(aSatz7_10b, axiom, ![Xa2, Xp2]: (s(Xa2, Xp2)=Xp2 | Xp2!=Xa2)).
% 13.56/2.11 fof(aSatz7_13, axiom, ![Xq, Xa2, Xp2]: s_e(Xp2, Xq, s(Xa2, Xp2), s(Xa2, Xq))).
% 13.56/2.11 fof(aSatz7_15a, axiom, ![Xr, Xa2, Xp2, Xq2]: (~s_t(Xp2, Xq2, Xr) | s_t(s(Xa2, Xp2), s(Xa2, Xq2), s(Xa2, Xr)))).
% 13.56/2.11 fof(aSatz7_16a, axiom, ![Xcs, Xa2, Xp2, Xq2, Xr2]: (~s_e(Xp2, Xq2, Xr2, Xcs) | s_e(s(Xa2, Xp2), s(Xa2, Xq2), s(Xa2, Xr2), s(Xa2, Xcs)))).
% 13.56/2.11 fof(aSatz7_17, axiom, ![Xb, Xa2, Xp2, Xq2]: (~s_m(Xp2, Xa2, Xq2) | (~s_m(Xp2, Xb, Xq2) | Xa2=Xb))).
% 13.56/2.11 fof(aSatz7_19, conjecture, ![Xa2, Xb2, Xp2]: (s(Xa2, s(Xb2, Xp2))!=s(Xb2, s(Xa2, Xp2)) | Xa2=Xb2)).
% 13.56/2.11 fof(aSatz7_4a, axiom, ![Xa2, Xp2]: s_m(Xp2, Xa2, s(Xa2, Xp2))).
% 13.56/2.11 fof(aSatz7_7, axiom, ![Xa2, Xp2]: s(Xa2, s(Xa2, Xp2))=Xp2).
% 13.56/2.11 fof(d_Defn7_1, axiom, ![Xm, Xa2, Xb2]: ((~s_m(Xa2, Xm, Xb2) | s_t(Xa2, Xm, Xb2)) & ((~s_m(Xa2, Xm, Xb2) | s_e(Xm, Xa2, Xm, Xb2)) & (~s_t(Xa2, Xm, Xb2) | (~s_e(Xm, Xa2, Xm, Xb2) | s_m(Xa2, Xm, Xb2)))))).
% 13.56/2.11
% 13.56/2.11 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.56/2.11 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.56/2.11 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.56/2.11 fresh(y, y, x1...xn) = u
% 13.56/2.11 C => fresh(s, t, x1...xn) = v
% 13.56/2.11 where fresh is a fresh function symbol and x1..xn are the free
% 13.56/2.11 variables of u and v.
% 13.56/2.11 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.56/2.11 input problem has no model of domain size 1).
% 13.56/2.11
% 13.56/2.11 The encoding turns the above axioms into the following unit equations and goals:
% 13.56/2.11
% 13.56/2.11 Axiom 1 (aSatz7_10b): s(X, X) = X.
% 13.56/2.11 Axiom 2 (aSatz7_7): s(X, s(X, Y)) = Y.
% 13.56/2.11 Axiom 3 (aSatz7_19): s(xa, s(xb2, xp)) = s(xb2, s(xa, xp)).
% 13.56/2.11 Axiom 4 (aSatz7_17): fresh9(X, X, Y, Z) = Z.
% 13.56/2.11 Axiom 5 (aSatz7_10a): fresh4(X, X, Y, Z) = Y.
% 13.56/2.11 Axiom 6 (aSatz7_4a): s_m(X, Y, s(Y, X)) = true2.
% 13.56/2.11 Axiom 7 (d_Defn7_1): fresh31(X, X, Y, Z, W) = s_m(Y, Z, W).
% 13.56/2.11 Axiom 8 (d_Defn7_1): fresh30(X, X, Y, Z, W) = true2.
% 13.56/2.11 Axiom 9 (d_Defn7_1_1): fresh29(X, X, Y, Z, W) = true2.
% 13.56/2.11 Axiom 10 (aSatz7_15a): fresh63(X, X, Y, Z, W, V) = true2.
% 13.56/2.11 Axiom 11 (aSatz7_17): fresh10(X, X, Y, Z, W, V) = Z.
% 13.56/2.11 Axiom 12 (aSatz7_10a): fresh4(s(X, Y), Y, X, Y) = Y.
% 13.56/2.11 Axiom 13 (aSatz7_16a): fresh61(X, X, Y, Z, W, V, U) = true2.
% 13.56/2.11 Axiom 14 (aSatz7_13): s_e(X, Y, s(Z, X), s(Z, Y)) = true2.
% 13.56/2.11 Axiom 15 (d_Defn7_1_1): fresh29(s_m(X, Y, Z), true2, X, Y, Z) = s_t(X, Y, Z).
% 13.56/2.11 Axiom 16 (aSatz7_15a): fresh63(s_t(X, Y, Z), true2, X, Y, Z, W) = s_t(s(W, X), s(W, Y), s(W, Z)).
% 13.56/2.11 Axiom 17 (d_Defn7_1): fresh31(s_t(X, Y, Z), true2, X, Y, Z) = fresh30(s_e(Y, X, Y, Z), true2, X, Y, Z).
% 13.56/2.11 Axiom 18 (aSatz7_17): fresh10(s_m(X, Y, Z), true2, X, W, Z, Y) = fresh9(s_m(X, W, Z), true2, W, Y).
% 13.56/2.11 Axiom 19 (aSatz7_16a): fresh61(s_e(X, Y, Z, W), true2, X, Y, Z, W, V) = s_e(s(V, X), s(V, Y), s(V, Z), s(V, W)).
% 13.56/2.11
% 13.56/2.11 Lemma 20: s(xb2, s(xa, s(xb2, xp))) = s(xa, xp).
% 13.56/2.11 Proof:
% 13.56/2.11 s(xb2, s(xa, s(xb2, xp)))
% 13.56/2.11 = { by axiom 3 (aSatz7_19) }
% 13.56/2.11 s(xb2, s(xb2, s(xa, xp)))
% 13.56/2.11 = { by axiom 2 (aSatz7_7) }
% 13.56/2.11 s(xa, xp)
% 13.56/2.11
% 13.56/2.11 Goal 1 (aSatz7_19_1): xa = xb2.
% 13.56/2.11 Proof:
% 13.56/2.11 xa
% 13.56/2.11 = { by axiom 12 (aSatz7_10a) R->L }
% 13.56/2.11 fresh4(s(xb2, xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 11 (aSatz7_17) R->L }
% 13.56/2.11 fresh4(fresh10(true2, true2, xp, s(xb2, xa), s(xa, xp), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 6 (aSatz7_4a) R->L }
% 13.56/2.11 fresh4(fresh10(s_m(xp, xa, s(xa, xp)), true2, xp, s(xb2, xa), s(xa, xp), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 18 (aSatz7_17) }
% 13.56/2.11 fresh4(fresh9(s_m(xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 7 (d_Defn7_1) R->L }
% 13.56/2.11 fresh4(fresh9(fresh31(true2, true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 10 (aSatz7_15a) R->L }
% 13.56/2.11 fresh4(fresh9(fresh31(fresh63(true2, true2, s(xb2, xp), xa, s(xa, s(xb2, xp)), xb2), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 9 (d_Defn7_1_1) R->L }
% 13.56/2.11 fresh4(fresh9(fresh31(fresh63(fresh29(true2, true2, s(xb2, xp), xa, s(xa, s(xb2, xp))), true2, s(xb2, xp), xa, s(xa, s(xb2, xp)), xb2), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 6 (aSatz7_4a) R->L }
% 13.56/2.11 fresh4(fresh9(fresh31(fresh63(fresh29(s_m(s(xb2, xp), xa, s(xa, s(xb2, xp))), true2, s(xb2, xp), xa, s(xa, s(xb2, xp))), true2, s(xb2, xp), xa, s(xa, s(xb2, xp)), xb2), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 15 (d_Defn7_1_1) }
% 13.56/2.11 fresh4(fresh9(fresh31(fresh63(s_t(s(xb2, xp), xa, s(xa, s(xb2, xp))), true2, s(xb2, xp), xa, s(xa, s(xb2, xp)), xb2), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 16 (aSatz7_15a) }
% 13.56/2.11 fresh4(fresh9(fresh31(s_t(s(xb2, s(xb2, xp)), s(xb2, xa), s(xb2, s(xa, s(xb2, xp)))), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by lemma 20 }
% 13.56/2.11 fresh4(fresh9(fresh31(s_t(s(xb2, s(xb2, xp)), s(xb2, xa), s(xa, xp)), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 2 (aSatz7_7) }
% 13.56/2.11 fresh4(fresh9(fresh31(s_t(xp, s(xb2, xa), s(xa, xp)), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 17 (d_Defn7_1) }
% 13.56/2.11 fresh4(fresh9(fresh30(s_e(s(xb2, xa), xp, s(xb2, xa), s(xa, xp)), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 2 (aSatz7_7) R->L }
% 13.56/2.11 fresh4(fresh9(fresh30(s_e(s(xb2, xa), s(xb2, s(xb2, xp)), s(xb2, xa), s(xa, xp)), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by lemma 20 R->L }
% 13.56/2.11 fresh4(fresh9(fresh30(s_e(s(xb2, xa), s(xb2, s(xb2, xp)), s(xb2, xa), s(xb2, s(xa, s(xb2, xp)))), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 19 (aSatz7_16a) R->L }
% 13.56/2.11 fresh4(fresh9(fresh30(fresh61(s_e(xa, s(xb2, xp), xa, s(xa, s(xb2, xp))), true2, xa, s(xb2, xp), xa, s(xa, s(xb2, xp)), xb2), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 1 (aSatz7_10b) R->L }
% 13.56/2.11 fresh4(fresh9(fresh30(fresh61(s_e(xa, s(xb2, xp), s(xa, xa), s(xa, s(xb2, xp))), true2, xa, s(xb2, xp), xa, s(xa, s(xb2, xp)), xb2), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 14 (aSatz7_13) }
% 13.56/2.11 fresh4(fresh9(fresh30(fresh61(true2, true2, xa, s(xb2, xp), xa, s(xa, s(xb2, xp)), xb2), true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.11 = { by axiom 13 (aSatz7_16a) }
% 13.56/2.12 fresh4(fresh9(fresh30(true2, true2, xp, s(xb2, xa), s(xa, xp)), true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.12 = { by axiom 8 (d_Defn7_1) }
% 13.56/2.12 fresh4(fresh9(true2, true2, s(xb2, xa), xa), xa, xb2, xa)
% 13.56/2.12 = { by axiom 4 (aSatz7_17) }
% 13.56/2.12 fresh4(xa, xa, xb2, xa)
% 13.56/2.12 = { by axiom 5 (aSatz7_10a) }
% 13.56/2.12 xb2
% 13.56/2.12 % SZS output end Proof
% 13.56/2.12
% 13.56/2.12 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------