TSTP Solution File: MGT006+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT006+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n024.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 09:16:57 EDT 2023
% Result : Theorem 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT006+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 06:11:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.55 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.55
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55
% 0.20/0.58 % SZS output start Proof
% 0.20/0.58 Take the following subset of the input axioms:
% 0.20/0.59 fof(a2_FOL, hypothesis, ![X, Y, T1, T2, R1, R2, A1, A2, Rp1, Rp2]: ((organization(X, T1) & (organization(Y, T2) & (reliability(X, R1, T1) & (reliability(Y, R2, T2) & (accountability(X, A1, T1) & (accountability(Y, A2, T2) & (reproducibility(X, Rp1, T1) & reproducibility(Y, Rp2, T2)))))))) => (greater(Rp2, Rp1) <=> (greater(R2, R1) & greater(A2, A1))))).
% 0.20/0.59 fof(a4_FOL, hypothesis, ![X2, T1_2, T2_2, Rp1_2, Rp2_2]: ((organization(X2, T1_2) & (organization(X2, T2_2) & (reorganization_free(X2, T1_2, T2_2) & (reproducibility(X2, Rp1_2, T1_2) & (reproducibility(X2, Rp2_2, T2_2) & greater(T2_2, T1_2)))))) => greater(Rp2_2, Rp1_2))).
% 0.20/0.59 fof(mp3, axiom, ![T, X2]: (organization(X2, T) => ?[Rp]: reproducibility(X2, Rp, T))).
% 0.20/0.59 fof(t6_FOL, conjecture, ![X2, T1_2, T2_2, R1_2, R2_2, A1_2, A2_2]: ((organization(X2, T1_2) & (organization(X2, T2_2) & (reorganization_free(X2, T1_2, T2_2) & (reliability(X2, R1_2, T1_2) & (reliability(X2, R2_2, T2_2) & (accountability(X2, A1_2, T1_2) & (accountability(X2, A2_2, T2_2) & greater(T2_2, T1_2)))))))) => (greater(R2_2, R1_2) & greater(A2_2, A1_2)))).
% 0.20/0.59
% 0.20/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.59 fresh(y, y, x1...xn) = u
% 0.20/0.59 C => fresh(s, t, x1...xn) = v
% 0.20/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.59 variables of u and v.
% 0.20/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.59 input problem has no model of domain size 1).
% 0.20/0.59
% 0.20/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.59
% 0.20/0.59 Axiom 1 (t6_FOL_6): greater(t2, t1) = true.
% 0.20/0.59 Axiom 2 (t6_FOL): organization(x, t1) = true.
% 0.20/0.59 Axiom 3 (t6_FOL_1): organization(x, t2) = true.
% 0.20/0.59 Axiom 4 (t6_FOL_2): reliability(x, r1, t1) = true.
% 0.20/0.59 Axiom 5 (t6_FOL_3): reliability(x, r2, t2) = true.
% 0.20/0.59 Axiom 6 (t6_FOL_4): accountability(x, a1, t1) = true.
% 0.20/0.59 Axiom 7 (t6_FOL_5): accountability(x, a2, t2) = true.
% 0.20/0.59 Axiom 8 (t6_FOL_7): reorganization_free(x, t1, t2) = true.
% 0.20/0.59 Axiom 9 (mp3): fresh(X, X, Y, Z) = true.
% 0.20/0.59 Axiom 10 (a2_FOL_2): fresh35(X, X, Y, Z) = true.
% 0.20/0.59 Axiom 11 (a2_FOL_1): fresh26(X, X, Y, Z) = true.
% 0.20/0.59 Axiom 12 (a4_FOL): fresh7(X, X, Y, Z) = true.
% 0.20/0.59 Axiom 13 (mp3): fresh(organization(X, Y), true, X, Y) = reproducibility(X, rp(X, Y), Y).
% 0.20/0.59 Axiom 14 (a2_FOL_2): fresh33(X, X, Y, Z, W, V) = greater(W, Z).
% 0.20/0.59 Axiom 15 (a2_FOL_1): fresh24(X, X, Y, Z, W, V) = greater(W, Z).
% 0.20/0.59 Axiom 16 (a4_FOL): fresh5(X, X, Y, Z, W, V) = greater(W, Z).
% 0.20/0.59 Axiom 17 (a4_FOL): fresh6(X, X, Y, Z, W, V, U) = fresh7(organization(Y, V), true, Z, W).
% 0.20/0.59 Axiom 18 (a2_FOL_2): fresh34(X, X, Y, Z, W, V, U, T) = fresh35(organization(Y, T), true, V, U).
% 0.20/0.59 Axiom 19 (a2_FOL_1): fresh25(X, X, Y, Z, W, V, U, T) = fresh26(organization(Y, T), true, V, U).
% 0.20/0.59 Axiom 20 (a4_FOL): fresh4(X, X, Y, Z, W, V, U) = fresh5(organization(Y, U), true, Y, Z, W, V).
% 0.20/0.59 Axiom 21 (a2_FOL_2): fresh32(X, X, Y, Z, W, V, U, T, S) = fresh33(organization(Z, W), true, Y, V, U, S).
% 0.20/0.59 Axiom 22 (a2_FOL_1): fresh23(X, X, Y, Z, W, V, U, T, S) = fresh24(organization(Z, W), true, Y, V, U, S).
% 0.20/0.59 Axiom 23 (a4_FOL): fresh2(X, X, Y, Z, W, V, U) = fresh3(greater(U, V), true, Y, Z, W, V, U).
% 0.20/0.59 Axiom 24 (a4_FOL): fresh3(X, X, Y, Z, W, V, U) = fresh6(reproducibility(Y, Z, V), true, Y, Z, W, V, U).
% 0.20/0.59 Axiom 25 (a4_FOL): fresh2(reorganization_free(X, Y, Z), true, X, W, V, Y, Z) = fresh4(reproducibility(X, V, Z), true, X, W, V, Y, Z).
% 0.20/0.59 Axiom 26 (a2_FOL_2): fresh31(X, X, Y, Z, W, V, U, T, S, X2) = fresh34(reproducibility(Y, T, X2), true, Y, Z, W, V, U, X2).
% 0.20/0.59 Axiom 27 (a2_FOL_1): fresh22(X, X, Y, Z, W, V, U, T, S, X2) = fresh25(reproducibility(Y, T, X2), true, Y, Z, W, V, U, X2).
% 0.20/0.59 Axiom 28 (a2_FOL_2): fresh30(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh32(reproducibility(Z, X2, W), true, Y, Z, W, U, T, S, Y2).
% 0.20/0.59 Axiom 29 (a2_FOL_1): fresh21(X, X, Y, Z, W, V, U, T, S, X2) = fresh23(reproducibility(Z, S, W), true, Y, Z, W, V, U, T, X2).
% 0.20/0.59 Axiom 30 (a2_FOL_2): fresh29(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh31(reliability(Y, V, Z2), true, Y, Z, W, T, S, X2, Y2, Z2).
% 0.20/0.59 Axiom 31 (a2_FOL_1): fresh20(X, X, Y, Z, W, V, U, T, S, X2) = fresh22(reliability(Y, V, X2), true, Y, Z, W, V, U, T, S, X2).
% 0.20/0.59 Axiom 32 (a2_FOL_1): fresh19(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh21(reliability(Z, U, W), true, Y, Z, W, V, U, S, X2, Y2).
% 0.20/0.59 Axiom 33 (a2_FOL_1): fresh18(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh20(accountability(Y, T, Z2), true, Y, Z, W, V, U, X2, Y2, Z2).
% 0.20/0.59 Axiom 34 (a2_FOL_2): fresh28(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh30(reliability(Z, U, W), true, Y, Z, W, V, T, S, X2, Y2, Z2).
% 0.20/0.59 Axiom 35 (a2_FOL_1): fresh18(greater(X, Y), true, Z, W, V, U, T, S, X2, Y, X, Y2) = fresh19(accountability(W, X2, V), true, Z, W, V, U, T, S, Y, X, Y2).
% 0.20/0.59 Axiom 36 (a2_FOL_2): fresh27(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2) = fresh29(accountability(Y, T, Z2), true, Y, Z, W, V, U, T, S, X2, Y2, Z2).
% 0.20/0.59 Axiom 37 (a2_FOL_2): fresh27(greater(X, Y), true, Z, W, V, U, T, S, X2, Y, X, Y2) = fresh28(accountability(W, X2, V), true, Z, W, V, U, T, S, X2, Y, X, Y2).
% 0.20/0.59
% 0.20/0.59 Lemma 38: reproducibility(x, rp(x, t1), t1) = true.
% 0.20/0.59 Proof:
% 0.20/0.59 reproducibility(x, rp(x, t1), t1)
% 0.20/0.59 = { by axiom 13 (mp3) R->L }
% 0.20/0.59 fresh(organization(x, t1), true, x, t1)
% 0.20/0.59 = { by axiom 2 (t6_FOL) }
% 0.20/0.59 fresh(true, true, x, t1)
% 0.20/0.59 = { by axiom 9 (mp3) }
% 0.20/0.59 true
% 0.20/0.59
% 0.20/0.59 Lemma 39: reproducibility(x, rp(x, t2), t2) = true.
% 0.20/0.59 Proof:
% 0.20/0.59 reproducibility(x, rp(x, t2), t2)
% 0.20/0.59 = { by axiom 13 (mp3) R->L }
% 0.20/0.59 fresh(organization(x, t2), true, x, t2)
% 0.20/0.59 = { by axiom 3 (t6_FOL_1) }
% 0.20/0.59 fresh(true, true, x, t2)
% 0.20/0.59 = { by axiom 9 (mp3) }
% 0.20/0.59 true
% 0.20/0.59
% 0.20/0.59 Lemma 40: greater(rp(x, t2), rp(x, t1)) = true.
% 0.20/0.59 Proof:
% 0.20/0.59 greater(rp(x, t2), rp(x, t1))
% 0.20/0.59 = { by axiom 16 (a4_FOL) R->L }
% 0.20/0.59 fresh5(true, true, x, rp(x, t1), rp(x, t2), t1)
% 0.20/0.59 = { by axiom 3 (t6_FOL_1) R->L }
% 0.20/0.59 fresh5(organization(x, t2), true, x, rp(x, t1), rp(x, t2), t1)
% 0.20/0.59 = { by axiom 20 (a4_FOL) R->L }
% 0.20/0.59 fresh4(true, true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by lemma 39 R->L }
% 0.20/0.59 fresh4(reproducibility(x, rp(x, t2), t2), true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by axiom 25 (a4_FOL) R->L }
% 0.20/0.59 fresh2(reorganization_free(x, t1, t2), true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by axiom 8 (t6_FOL_7) }
% 0.20/0.59 fresh2(true, true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by axiom 23 (a4_FOL) }
% 0.20/0.59 fresh3(greater(t2, t1), true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by axiom 1 (t6_FOL_6) }
% 0.20/0.59 fresh3(true, true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by axiom 24 (a4_FOL) }
% 0.20/0.59 fresh6(reproducibility(x, rp(x, t1), t1), true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by lemma 38 }
% 0.20/0.59 fresh6(true, true, x, rp(x, t1), rp(x, t2), t1, t2)
% 0.20/0.59 = { by axiom 17 (a4_FOL) }
% 0.20/0.59 fresh7(organization(x, t1), true, rp(x, t1), rp(x, t2))
% 0.20/0.59 = { by axiom 2 (t6_FOL) }
% 0.20/0.59 fresh7(true, true, rp(x, t1), rp(x, t2))
% 0.20/0.59 = { by axiom 12 (a4_FOL) }
% 0.20/0.60 true
% 0.20/0.60
% 0.20/0.60 Goal 1 (t6_FOL_8): tuple(greater(r2, r1), greater(a2, a1)) = tuple(true, true).
% 0.20/0.60 Proof:
% 0.20/0.60 tuple(greater(r2, r1), greater(a2, a1))
% 0.20/0.60 = { by axiom 14 (a2_FOL_2) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh33(true, true, x, a1, a2, t1))
% 0.20/0.60 = { by axiom 3 (t6_FOL_1) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh33(organization(x, t2), true, x, a1, a2, t1))
% 0.20/0.60 = { by axiom 21 (a2_FOL_2) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh32(true, true, x, x, t2, a1, a2, rp(x, t1), t1))
% 0.20/0.60 = { by lemma 39 R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh32(reproducibility(x, rp(x, t2), t2), true, x, x, t2, a1, a2, rp(x, t1), t1))
% 0.20/0.60 = { by axiom 28 (a2_FOL_2) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh30(true, true, x, x, t2, r1, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 5 (t6_FOL_3) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh30(reliability(x, r2, t2), true, x, x, t2, r1, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 34 (a2_FOL_2) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh28(true, true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 7 (t6_FOL_5) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh28(accountability(x, a2, t2), true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 37 (a2_FOL_2) R->L }
% 0.20/0.60 tuple(greater(r2, r1), fresh27(greater(rp(x, t2), rp(x, t1)), true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by lemma 40 }
% 0.20/0.60 tuple(greater(r2, r1), fresh27(true, true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 36 (a2_FOL_2) }
% 0.20/0.60 tuple(greater(r2, r1), fresh29(accountability(x, a1, t1), true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 6 (t6_FOL_4) }
% 0.20/0.60 tuple(greater(r2, r1), fresh29(true, true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 30 (a2_FOL_2) }
% 0.20/0.60 tuple(greater(r2, r1), fresh31(reliability(x, r1, t1), true, x, x, t2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 4 (t6_FOL_2) }
% 0.20/0.60 tuple(greater(r2, r1), fresh31(true, true, x, x, t2, a1, a2, rp(x, t1), rp(x, t2), t1))
% 0.20/0.60 = { by axiom 26 (a2_FOL_2) }
% 0.20/0.60 tuple(greater(r2, r1), fresh34(reproducibility(x, rp(x, t1), t1), true, x, x, t2, a1, a2, t1))
% 0.20/0.60 = { by lemma 38 }
% 0.20/0.60 tuple(greater(r2, r1), fresh34(true, true, x, x, t2, a1, a2, t1))
% 0.20/0.60 = { by axiom 18 (a2_FOL_2) }
% 0.20/0.60 tuple(greater(r2, r1), fresh35(organization(x, t1), true, a1, a2))
% 0.20/0.60 = { by axiom 2 (t6_FOL) }
% 0.20/0.60 tuple(greater(r2, r1), fresh35(true, true, a1, a2))
% 0.20/0.60 = { by axiom 10 (a2_FOL_2) }
% 0.20/0.60 tuple(greater(r2, r1), true)
% 0.20/0.60 = { by axiom 15 (a2_FOL_1) R->L }
% 0.20/0.60 tuple(fresh24(true, true, x, r1, r2, t1), true)
% 0.20/0.60 = { by axiom 3 (t6_FOL_1) R->L }
% 0.20/0.60 tuple(fresh24(organization(x, t2), true, x, r1, r2, t1), true)
% 0.20/0.60 = { by axiom 22 (a2_FOL_1) R->L }
% 0.20/0.60 tuple(fresh23(true, true, x, x, t2, r1, r2, rp(x, t1), t1), true)
% 0.20/0.60 = { by lemma 39 R->L }
% 0.20/0.60 tuple(fresh23(reproducibility(x, rp(x, t2), t2), true, x, x, t2, r1, r2, rp(x, t1), t1), true)
% 0.20/0.60 = { by axiom 29 (a2_FOL_1) R->L }
% 0.20/0.60 tuple(fresh21(true, true, x, x, t2, r1, r2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 5 (t6_FOL_3) R->L }
% 0.20/0.60 tuple(fresh21(reliability(x, r2, t2), true, x, x, t2, r1, r2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 32 (a2_FOL_1) R->L }
% 0.20/0.60 tuple(fresh19(true, true, x, x, t2, r1, r2, a1, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 7 (t6_FOL_5) R->L }
% 0.20/0.60 tuple(fresh19(accountability(x, a2, t2), true, x, x, t2, r1, r2, a1, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 35 (a2_FOL_1) R->L }
% 0.20/0.60 tuple(fresh18(greater(rp(x, t2), rp(x, t1)), true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by lemma 40 }
% 0.20/0.60 tuple(fresh18(true, true, x, x, t2, r1, r2, a1, a2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 33 (a2_FOL_1) }
% 0.20/0.60 tuple(fresh20(accountability(x, a1, t1), true, x, x, t2, r1, r2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 6 (t6_FOL_4) }
% 0.20/0.60 tuple(fresh20(true, true, x, x, t2, r1, r2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 31 (a2_FOL_1) }
% 0.20/0.60 tuple(fresh22(reliability(x, r1, t1), true, x, x, t2, r1, r2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 4 (t6_FOL_2) }
% 0.20/0.60 tuple(fresh22(true, true, x, x, t2, r1, r2, rp(x, t1), rp(x, t2), t1), true)
% 0.20/0.60 = { by axiom 27 (a2_FOL_1) }
% 0.20/0.60 tuple(fresh25(reproducibility(x, rp(x, t1), t1), true, x, x, t2, r1, r2, t1), true)
% 0.20/0.60 = { by lemma 38 }
% 0.20/0.60 tuple(fresh25(true, true, x, x, t2, r1, r2, t1), true)
% 0.20/0.60 = { by axiom 19 (a2_FOL_1) }
% 0.20/0.60 tuple(fresh26(organization(x, t1), true, r1, r2), true)
% 0.20/0.60 = { by axiom 2 (t6_FOL) }
% 0.20/0.60 tuple(fresh26(true, true, r1, r2), true)
% 0.20/0.60 = { by axiom 11 (a2_FOL_1) }
% 0.20/0.60 tuple(true, true)
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60
% 0.20/0.60 RESULT: Theorem (the conjecture is true).
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