TSTP Solution File: GEO504+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO504+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 : n031.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 23:29:07 EDT 2023
% Result : Theorem 61.09s 8.05s
% Output : Proof 61.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO504+1 : TPTP v8.1.2. Released v7.0.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n031.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 29 22:33:11 EDT 2023
% 0.11/0.32 % CPUTime :
% 61.09/8.05 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 61.09/8.05
% 61.09/8.05 % SZS status Theorem
% 61.09/8.05
% 61.09/8.05 % SZS output start Proof
% 61.09/8.05 Take the following subset of the input axioms:
% 61.09/8.05 fof(aSatz2_14, axiom, ![Xa, Xc, Xb, Xd]: (~s_e(Xa, Xb, Xc, Xd) | s_e(Xb, Xa, Xd, Xc))).
% 61.09/8.05 fof(aSatz2_3, axiom, ![Xe, Xf, Xb2, Xa2, Xc2, Xd2]: (~s_e(Xa2, Xb2, Xc2, Xd2) | (~s_e(Xc2, Xd2, Xe, Xf) | s_e(Xa2, Xb2, Xe, Xf)))).
% 61.09/8.05 fof(aSatz7_13, axiom, ![Xp, Xq, Xa2]: s_e(Xp, Xq, s(Xa2, Xp), s(Xa2, Xq))).
% 61.09/8.05 fof(aSatz7_7, axiom, ![Xa2, Xp2]: s(Xa2, s(Xa2, Xp2))=Xp2).
% 61.09/8.05 fof(aSatz8_2, conjecture, ![Xb2, Xa2, Xc2]: (~s_r(Xa2, Xb2, Xc2) | s_r(Xc2, Xb2, Xa2))).
% 61.09/8.05 fof(d_Defn8_1, axiom, ![Xb2, Xa2, Xc2]: ((~s_r(Xa2, Xb2, Xc2) | s_e(Xa2, Xc2, Xa2, s(Xb2, Xc2))) & (s_r(Xa2, Xb2, Xc2) | ~s_e(Xa2, Xc2, Xa2, s(Xb2, Xc2))))).
% 61.09/8.05
% 61.09/8.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 61.09/8.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 61.09/8.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 61.09/8.05 fresh(y, y, x1...xn) = u
% 61.09/8.05 C => fresh(s, t, x1...xn) = v
% 61.09/8.05 where fresh is a fresh function symbol and x1..xn are the free
% 61.09/8.05 variables of u and v.
% 61.09/8.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 61.09/8.05 input problem has no model of domain size 1).
% 61.09/8.05
% 61.09/8.05 The encoding turns the above axioms into the following unit equations and goals:
% 61.09/8.05
% 61.09/8.05 Axiom 1 (aSatz8_2): s_r(xa, xb2, xc) = true2.
% 61.09/8.05 Axiom 2 (aSatz7_7): s(X, s(X, Y)) = Y.
% 61.09/8.05 Axiom 3 (d_Defn8_1): fresh28(X, X, Y, Z, W) = true2.
% 61.09/8.05 Axiom 4 (d_Defn8_1_1): fresh22(X, X, Y, Z, W) = true2.
% 61.09/8.05 Axiom 5 (aSatz2_14): fresh136(X, X, Y, Z, W, V) = true2.
% 61.09/8.05 Axiom 6 (aSatz2_3): fresh132(X, X, Y, Z, W, V) = true2.
% 61.09/8.05 Axiom 7 (aSatz7_13): s_e(X, Y, s(Z, X), s(Z, Y)) = true2.
% 61.09/8.05 Axiom 8 (aSatz2_3): fresh133(X, X, Y, Z, W, V, U, T) = s_e(Y, Z, U, T).
% 61.09/8.05 Axiom 9 (d_Defn8_1_1): fresh22(s_r(X, Y, Z), true2, X, Y, Z) = s_e(X, Z, X, s(Y, Z)).
% 61.09/8.05 Axiom 10 (aSatz2_14): fresh136(s_e(X, Y, Z, W), true2, X, Y, Z, W) = s_e(Y, X, W, Z).
% 61.09/8.05 Axiom 11 (d_Defn8_1): fresh28(s_e(X, Y, X, s(Z, Y)), true2, X, Z, Y) = s_r(X, Z, Y).
% 61.09/8.05 Axiom 12 (aSatz2_3): fresh133(s_e(X, Y, Z, W), true2, V, U, X, Y, Z, W) = fresh132(s_e(V, U, X, Y), true2, V, U, Z, W).
% 61.09/8.05
% 61.09/8.05 Goal 1 (aSatz8_2_1): s_r(xc, xb2, xa) = true2.
% 61.09/8.05 Proof:
% 61.09/8.05 s_r(xc, xb2, xa)
% 61.09/8.05 = { by axiom 11 (d_Defn8_1) R->L }
% 61.09/8.05 fresh28(s_e(xc, xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 8 (aSatz2_3) R->L }
% 61.09/8.05 fresh28(fresh133(true2, true2, xc, xa, s(xb2, xc), xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 7 (aSatz7_13) R->L }
% 61.09/8.05 fresh28(fresh133(s_e(s(xb2, xc), xa, s(xb2, s(xb2, xc)), s(xb2, xa)), true2, xc, xa, s(xb2, xc), xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 2 (aSatz7_7) }
% 61.09/8.05 fresh28(fresh133(s_e(s(xb2, xc), xa, xc, s(xb2, xa)), true2, xc, xa, s(xb2, xc), xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 12 (aSatz2_3) }
% 61.09/8.05 fresh28(fresh132(s_e(xc, xa, s(xb2, xc), xa), true2, xc, xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 10 (aSatz2_14) R->L }
% 61.09/8.05 fresh28(fresh132(fresh136(s_e(xa, xc, xa, s(xb2, xc)), true2, xa, xc, xa, s(xb2, xc)), true2, xc, xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 9 (d_Defn8_1_1) R->L }
% 61.09/8.05 fresh28(fresh132(fresh136(fresh22(s_r(xa, xb2, xc), true2, xa, xb2, xc), true2, xa, xc, xa, s(xb2, xc)), true2, xc, xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 1 (aSatz8_2) }
% 61.09/8.05 fresh28(fresh132(fresh136(fresh22(true2, true2, xa, xb2, xc), true2, xa, xc, xa, s(xb2, xc)), true2, xc, xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 4 (d_Defn8_1_1) }
% 61.09/8.05 fresh28(fresh132(fresh136(true2, true2, xa, xc, xa, s(xb2, xc)), true2, xc, xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 5 (aSatz2_14) }
% 61.09/8.05 fresh28(fresh132(true2, true2, xc, xa, xc, s(xb2, xa)), true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 6 (aSatz2_3) }
% 61.09/8.05 fresh28(true2, true2, xc, xb2, xa)
% 61.09/8.05 = { by axiom 3 (d_Defn8_1) }
% 61.09/8.05 true2
% 61.09/8.05 % SZS output end Proof
% 61.09/8.05
% 61.09/8.05 RESULT: Theorem (the conjecture is true).
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