TSTP Solution File: GEO502+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO502+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 : n027.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 230.31s 29.69s
% Output : Proof 230.31s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO502+1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 21:41:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 230.31/29.69 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 230.31/29.69
% 230.31/29.69 % SZS status Theorem
% 230.31/29.70
% 230.31/29.70 % SZS output start Proof
% 230.31/29.70 Take the following subset of the input axioms:
% 230.31/29.70 fof(aSatz7_22, conjecture, ![Xc, Xa1, Xb1, Xm1, Xb2, Xm2, Xa2]: (~s_t(Xa1, Xc, Xa2) | (~s_t(Xb1, Xc, Xb2) | (~s_e(Xc, Xa1, Xc, Xb1) | (~s_e(Xc, Xa2, Xc, Xb2) | (~s_m(Xa1, Xm1, Xb1) | (~s_m(Xa2, Xm2, Xb2) | s_t(Xm1, Xc, Xm2)))))))).
% 230.31/29.70 fof(aSatz7_22b, axiom, ![Xc2, Xa1_2, Xb1_2, Xm1_2, Xb2_2, Xm2_2, Xa2_2]: (~s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2) | s_t(Xm1_2, Xc2, Xm2_2))).
% 230.31/29.71 fof(d_Defn7_23, axiom, ![Xc2, Xa1_2, Xb1_2, Xm1_2, Xb2_2, Xm2_2, Xa2_2]: ((~s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2) | s_t(Xa1_2, Xc2, Xa2_2)) & ((~s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2) | s_t(Xb1_2, Xc2, Xb2_2)) & ((~s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2) | s_e(Xc2, Xa1_2, Xc2, Xb1_2)) & ((~s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2) | s_e(Xc2, Xa2_2, Xc2, Xb2_2)) & ((~s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2) | s_m(Xa1_2, Xm1_2, Xb1_2)) & ((~s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2) | s_m(Xa2_2, Xm2_2, Xb2_2)) & (~s_t(Xa1_2, Xc2, Xa2_2) | (~s_t(Xb1_2, Xc2, Xb2_2) | (~s_e(Xc2, Xa1_2, Xc2, Xb1_2) | (~s_e(Xc2, Xa2_2, Xc2, Xb2_2) | (~s_m(Xa1_2, Xm1_2, Xb1_2) | (~s_m(Xa2_2, Xm2_2, Xb2_2) | s_kf(Xa1_2, Xm1_2, Xb1_2, Xc2, Xb2_2, Xm2_2, Xa2_2)))))))))))))).
% 230.31/29.71
% 230.31/29.71 Now clausify the problem and encode Horn clauses using encoding 3 of
% 230.31/29.71 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 230.31/29.71 We repeatedly replace C & s=t => u=v by the two clauses:
% 230.31/29.71 fresh(y, y, x1...xn) = u
% 230.31/29.71 C => fresh(s, t, x1...xn) = v
% 230.31/29.71 where fresh is a fresh function symbol and x1..xn are the free
% 230.31/29.71 variables of u and v.
% 230.31/29.71 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 230.31/29.71 input problem has no model of domain size 1).
% 230.31/29.71
% 230.31/29.71 The encoding turns the above axioms into the following unit equations and goals:
% 230.31/29.71
% 230.31/29.71 Axiom 1 (aSatz7_22_2): s_t(xb1, xc, xb2) = true2.
% 230.31/29.71 Axiom 2 (aSatz7_22_3): s_t(xa1, xc, xa2) = true2.
% 230.31/29.71 Axiom 3 (aSatz7_22_4): s_m(xa2, xm2, xb2) = true2.
% 230.31/29.71 Axiom 4 (aSatz7_22_5): s_m(xa1, xm1, xb1) = true2.
% 230.31/29.71 Axiom 5 (aSatz7_22): s_e(xc, xa2, xc, xb2) = true2.
% 230.31/29.71 Axiom 6 (aSatz7_22_1): s_e(xc, xa1, xc, xb1) = true2.
% 230.31/29.71 Axiom 7 (aSatz7_22b): fresh60(X, X, Y, Z, W) = true2.
% 230.31/29.71 Axiom 8 (d_Defn7_23): fresh140(X, X, Y, Z, W, V, U, T, S) = true2.
% 230.31/29.71 Axiom 9 (d_Defn7_23): fresh28(X, X, Y, Z, W, V, U, T, S) = s_kf(T, S, Y, Z, W, V, U).
% 230.31/29.71 Axiom 10 (d_Defn7_23): fresh138(X, X, Y, Z, W, V, U, T, S) = fresh139(s_t(Y, Z, W), true2, Y, Z, W, V, U, T, S).
% 230.31/29.71 Axiom 11 (d_Defn7_23): fresh137(X, X, Y, Z, W, V, U, T, S) = fresh138(s_t(T, Z, U), true2, Y, Z, W, V, U, T, S).
% 230.31/29.71 Axiom 12 (d_Defn7_23): fresh136(X, X, Y, Z, W, V, U, T, S) = fresh137(s_m(U, V, W), true2, Y, Z, W, V, U, T, S).
% 230.31/29.71 Axiom 13 (aSatz7_22b): fresh60(s_kf(X, Y, Z, W, V, U, T), true2, Y, W, U) = s_t(Y, W, U).
% 230.31/29.71 Axiom 14 (d_Defn7_23): fresh139(X, X, Y, Z, W, V, U, T, S) = fresh140(s_e(Z, U, Z, W), true2, Y, Z, W, V, U, T, S).
% 230.31/29.71 Axiom 15 (d_Defn7_23): fresh136(s_m(X, Y, Z), true2, Z, W, V, U, T, X, Y) = fresh28(s_e(W, X, W, Z), true2, Z, W, V, U, T, X, Y).
% 230.31/29.71
% 230.31/29.71 Goal 1 (aSatz7_22_6): s_t(xm1, xc, xm2) = true2.
% 230.31/29.71 Proof:
% 230.31/29.71 s_t(xm1, xc, xm2)
% 230.31/29.71 = { by axiom 13 (aSatz7_22b) R->L }
% 230.31/29.71 fresh60(s_kf(xa1, xm1, xb1, xc, xb2, xm2, xa2), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 9 (d_Defn7_23) R->L }
% 230.31/29.71 fresh60(fresh28(true2, true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 6 (aSatz7_22_1) R->L }
% 230.31/29.71 fresh60(fresh28(s_e(xc, xa1, xc, xb1), true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 15 (d_Defn7_23) R->L }
% 230.31/29.71 fresh60(fresh136(s_m(xa1, xm1, xb1), true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 4 (aSatz7_22_5) }
% 230.31/29.71 fresh60(fresh136(true2, true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 12 (d_Defn7_23) }
% 230.31/29.71 fresh60(fresh137(s_m(xa2, xm2, xb2), true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 3 (aSatz7_22_4) }
% 230.31/29.71 fresh60(fresh137(true2, true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 11 (d_Defn7_23) }
% 230.31/29.71 fresh60(fresh138(s_t(xa1, xc, xa2), true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 2 (aSatz7_22_3) }
% 230.31/29.71 fresh60(fresh138(true2, true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 10 (d_Defn7_23) }
% 230.31/29.71 fresh60(fresh139(s_t(xb1, xc, xb2), true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 1 (aSatz7_22_2) }
% 230.31/29.71 fresh60(fresh139(true2, true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 14 (d_Defn7_23) }
% 230.31/29.71 fresh60(fresh140(s_e(xc, xa2, xc, xb2), true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 5 (aSatz7_22) }
% 230.31/29.71 fresh60(fresh140(true2, true2, xb1, xc, xb2, xm2, xa2, xa1, xm1), true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 8 (d_Defn7_23) }
% 230.31/29.71 fresh60(true2, true2, xm1, xc, xm2)
% 230.31/29.71 = { by axiom 7 (aSatz7_22b) }
% 230.31/29.71 true2
% 230.31/29.71 % SZS output end Proof
% 230.31/29.71
% 230.31/29.71 RESULT: Theorem (the conjecture is true).
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