TSTP Solution File: MGT012+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : MGT012+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 : n021.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 09:16:59 EDT 2023
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT012+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 06:27:43 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.45 Command-line arguments: --no-flatten-goal
% 0.21/0.45
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Take the following subset of the input axioms:
% 0.21/0.49 fof(a12_FOL, hypothesis, ![X, Y, C, T1, T2, C1, C2, I1, I2]: ((organization(X, T1) & (organization(Y, T2) & (class(X, C, T1) & (class(Y, C, T2) & (complexity(X, C1, T1) & (complexity(Y, C2, T2) & (inertia(X, I1, T1) & (inertia(Y, I2, T2) & greater(C2, C1))))))))) => greater(I2, I1))).
% 0.21/0.49 fof(mp10, axiom, ![X2, T1_2, T2_2, C1_2, C2_2]: ((organization(X2, T1_2) & (organization(X2, T2_2) & (reorganization_free(X2, T1_2, T2_2) & (class(X2, C1_2, T1_2) & class(X2, C2_2, T2_2))))) => C1_2=C2_2)).
% 0.21/0.49 fof(mp5, axiom, ![T, X2]: (organization(X2, T) => ?[I]: inertia(X2, I, T))).
% 0.21/0.49 fof(mp6_1, axiom, ![X2, Y2]: ~(greater(X2, Y2) & X2=Y2)).
% 0.21/0.49 fof(mp6_2, axiom, ![X2, Y2]: ~(greater(X2, Y2) & greater(Y2, X2))).
% 0.21/0.49 fof(mp9, axiom, ![X2, T3]: (organization(X2, T3) => ?[C3]: class(X2, C3, T3))).
% 0.21/0.49 fof(t12_FOL, conjecture, ![X2, T1_2, T2_2, C1_2, C2_2]: ((organization(X2, T1_2) & (organization(X2, T2_2) & (reorganization_free(X2, T1_2, T2_2) & (complexity(X2, C1_2, T1_2) & (complexity(X2, C2_2, T2_2) & greater(T2_2, T1_2)))))) => ~greater(C1_2, C2_2))).
% 0.21/0.49 fof(t2_FOL, hypothesis, ![X2, T1_2, T2_2, I1_2, I2_2]: ((organization(X2, T1_2) & (organization(X2, T2_2) & (reorganization_free(X2, T1_2, T2_2) & (inertia(X2, I1_2, T1_2) & (inertia(X2, I2_2, T2_2) & greater(T2_2, T1_2)))))) => greater(I2_2, I1_2))).
% 0.21/0.49
% 0.21/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.49 fresh(y, y, x1...xn) = u
% 0.21/0.49 C => fresh(s, t, x1...xn) = v
% 0.21/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.49 variables of u and v.
% 0.21/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.49 input problem has no model of domain size 1).
% 0.21/0.49
% 0.21/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.49
% 0.21/0.49 Axiom 1 (t12_FOL_2): greater(c1, c2) = true2.
% 0.21/0.49 Axiom 2 (t12_FOL_3): greater(t2, t1) = true2.
% 0.21/0.49 Axiom 3 (t12_FOL): organization(x, t1) = true2.
% 0.21/0.49 Axiom 4 (t12_FOL_1): organization(x, t2) = true2.
% 0.21/0.49 Axiom 5 (t12_FOL_4): reorganization_free(x, t1, t2) = true2.
% 0.21/0.49 Axiom 6 (t12_FOL_5): complexity(x, c1, t1) = true2.
% 0.21/0.49 Axiom 7 (t12_FOL_6): complexity(x, c2, t2) = true2.
% 0.21/0.49 Axiom 8 (mp9): fresh(X, X, Y, Z) = true2.
% 0.21/0.49 Axiom 9 (mp10): fresh22(X, X, Y, Z) = Z.
% 0.21/0.49 Axiom 10 (a12_FOL): fresh17(X, X, Y, Z) = true2.
% 0.21/0.49 Axiom 11 (t2_FOL): fresh8(X, X, Y, Z) = true2.
% 0.21/0.49 Axiom 12 (mp5): fresh2(X, X, Y, Z) = true2.
% 0.21/0.49 Axiom 13 (mp9): fresh(organization(X, Y), true2, X, Y) = class(X, c(X, Y), Y).
% 0.21/0.49 Axiom 14 (mp10): fresh20(X, X, Y, Z, W, V) = W.
% 0.21/0.49 Axiom 15 (a12_FOL): fresh15(X, X, Y, Z, W, V) = greater(W, Z).
% 0.21/0.49 Axiom 16 (t2_FOL): fresh6(X, X, Y, Z, W, V) = greater(W, Z).
% 0.21/0.49 Axiom 17 (mp5): fresh2(organization(X, Y), true2, X, Y) = inertia(X, i(X, Y), Y).
% 0.21/0.49 Axiom 18 (mp10): fresh21(X, X, Y, Z, W, V, U) = fresh22(organization(Y, Z), true2, V, U).
% 0.21/0.49 Axiom 19 (t2_FOL): fresh7(X, X, Y, Z, W, V, U) = fresh8(organization(Y, V), true2, Z, W).
% 0.21/0.49 Axiom 20 (mp10): fresh19(X, X, Y, Z, W, V, U) = fresh20(organization(Y, W), true2, Y, Z, V, U).
% 0.21/0.49 Axiom 21 (a12_FOL): fresh16(X, X, Y, Z, W, V, U, T) = fresh17(organization(Y, T), true2, W, V).
% 0.21/0.49 Axiom 22 (a12_FOL): fresh14(X, X, Y, Z, W, V, U, T) = fresh15(organization(Z, U), true2, Y, W, V, T).
% 0.21/0.49 Axiom 23 (t2_FOL): fresh5(X, X, Y, Z, W, V, U) = fresh6(organization(Y, U), true2, Y, Z, W, V).
% 0.21/0.49 Axiom 24 (t2_FOL): fresh3(X, X, Y, Z, W, V, U) = fresh4(greater(U, V), true2, Y, Z, W, V, U).
% 0.21/0.49 Axiom 25 (mp10): fresh18(X, X, Y, Z, W, V, U) = fresh21(class(Y, V, Z), true2, Y, Z, W, V, U).
% 0.21/0.49 Axiom 26 (mp10): fresh18(reorganization_free(X, Y, Z), true2, X, Y, Z, W, V) = fresh19(class(X, V, Z), true2, X, Y, Z, W, V).
% 0.21/0.49 Axiom 27 (a12_FOL): fresh12(X, X, Y, Z, W, V, U, T, S, X2) = fresh13(greater(V, W), true2, Y, Z, U, T, S, X2).
% 0.21/0.49 Axiom 28 (t2_FOL): fresh4(X, X, Y, Z, W, V, U) = fresh7(inertia(Y, Z, V), true2, Y, Z, W, V, U).
% 0.21/0.49 Axiom 29 (t2_FOL): fresh3(reorganization_free(X, Y, Z), true2, X, W, V, Y, Z) = fresh5(inertia(X, V, Z), true2, X, W, V, Y, Z).
% 0.21/0.49 Axiom 30 (a12_FOL): fresh13(X, X, Y, Z, W, V, U, T) = fresh16(inertia(Y, W, T), true2, Y, Z, W, V, U, T).
% 0.21/0.49 Axiom 31 (a12_FOL): fresh11(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh14(inertia(Z, S, X2), true2, Y, Z, T, S, X2, Y2).
% 0.21/0.49 Axiom 32 (a12_FOL): fresh10(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh12(class(Y, W, Y2), true2, Y, Z, V, U, T, S, X2, Y2).
% 0.21/0.49 Axiom 33 (a12_FOL): fresh9(X, X, Y, Z, W, V, U, T, S, X2, Y2) = fresh11(class(Z, W, X2), true2, Y, Z, W, V, U, T, S, X2, Y2).
% 0.21/0.49 Axiom 34 (a12_FOL): fresh9(complexity(X, Y, Z), true2, W, X, V, U, Y, T, S, Z, X2) = fresh10(complexity(W, U, X2), true2, W, X, V, U, Y, T, S, Z, X2).
% 0.21/0.49
% 0.21/0.49 Lemma 35: inertia(x, i(x, t1), t1) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 inertia(x, i(x, t1), t1)
% 0.21/0.49 = { by axiom 17 (mp5) R->L }
% 0.21/0.49 fresh2(organization(x, t1), true2, x, t1)
% 0.21/0.49 = { by axiom 3 (t12_FOL) }
% 0.21/0.49 fresh2(true2, true2, x, t1)
% 0.21/0.49 = { by axiom 12 (mp5) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Lemma 36: inertia(x, i(x, t2), t2) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 inertia(x, i(x, t2), t2)
% 0.21/0.49 = { by axiom 17 (mp5) R->L }
% 0.21/0.49 fresh2(organization(x, t2), true2, x, t2)
% 0.21/0.49 = { by axiom 4 (t12_FOL_1) }
% 0.21/0.49 fresh2(true2, true2, x, t2)
% 0.21/0.49 = { by axiom 12 (mp5) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Lemma 37: class(x, c(x, t1), t1) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 class(x, c(x, t1), t1)
% 0.21/0.49 = { by axiom 13 (mp9) R->L }
% 0.21/0.49 fresh(organization(x, t1), true2, x, t1)
% 0.21/0.49 = { by axiom 3 (t12_FOL) }
% 0.21/0.49 fresh(true2, true2, x, t1)
% 0.21/0.49 = { by axiom 8 (mp9) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Lemma 38: class(x, c(x, t2), t2) = true2.
% 0.21/0.49 Proof:
% 0.21/0.49 class(x, c(x, t2), t2)
% 0.21/0.49 = { by axiom 13 (mp9) R->L }
% 0.21/0.49 fresh(organization(x, t2), true2, x, t2)
% 0.21/0.49 = { by axiom 4 (t12_FOL_1) }
% 0.21/0.49 fresh(true2, true2, x, t2)
% 0.21/0.49 = { by axiom 8 (mp9) }
% 0.21/0.49 true2
% 0.21/0.49
% 0.21/0.49 Goal 1 (mp6_2): tuple(greater(X, Y), greater(Y, X)) = tuple(true2, true2).
% 0.21/0.49 The goal is true when:
% 0.21/0.49 X = i(x, t1)
% 0.21/0.49 Y = i(x, t2)
% 0.21/0.49
% 0.21/0.49 Proof:
% 0.21/0.49 tuple(greater(i(x, t1), i(x, t2)), greater(i(x, t2), i(x, t1)))
% 0.21/0.49 = { by axiom 15 (a12_FOL) R->L }
% 0.21/0.49 tuple(fresh15(true2, true2, x, i(x, t2), i(x, t1), t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.49 = { by axiom 3 (t12_FOL) R->L }
% 0.21/0.49 tuple(fresh15(organization(x, t1), true2, x, i(x, t2), i(x, t1), t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.49 = { by axiom 22 (a12_FOL) R->L }
% 0.21/0.49 tuple(fresh14(true2, true2, x, x, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.49 = { by lemma 35 R->L }
% 0.21/0.49 tuple(fresh14(inertia(x, i(x, t1), t1), true2, x, x, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.49 = { by axiom 31 (a12_FOL) R->L }
% 0.21/0.49 tuple(fresh11(true2, true2, x, x, c(x, t1), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.49 = { by lemma 37 R->L }
% 0.21/0.49 tuple(fresh11(class(x, c(x, t1), t1), true2, x, x, c(x, t1), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.49 = { by axiom 33 (a12_FOL) R->L }
% 0.21/0.50 tuple(fresh9(true2, true2, x, x, c(x, t1), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 6 (t12_FOL_5) R->L }
% 0.21/0.50 tuple(fresh9(complexity(x, c1, t1), true2, x, x, c(x, t1), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 34 (a12_FOL) }
% 0.21/0.50 tuple(fresh10(complexity(x, c2, t2), true2, x, x, c(x, t1), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 7 (t12_FOL_6) }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, c(x, t1), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 14 (mp10) R->L }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh20(true2, true2, x, t1, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 4 (t12_FOL_1) R->L }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh20(organization(x, t2), true2, x, t1, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 20 (mp10) R->L }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh19(true2, true2, x, t1, t2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by lemma 38 R->L }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh19(class(x, c(x, t2), t2), true2, x, t1, t2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 26 (mp10) R->L }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh18(reorganization_free(x, t1, t2), true2, x, t1, t2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 5 (t12_FOL_4) }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh18(true2, true2, x, t1, t2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 25 (mp10) }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh21(class(x, c(x, t1), t1), true2, x, t1, t2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by lemma 37 }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh21(true2, true2, x, t1, t2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 18 (mp10) }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh22(organization(x, t1), true2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 3 (t12_FOL) }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, fresh22(true2, true2, c(x, t1), c(x, t2)), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 9 (mp10) }
% 0.21/0.50 tuple(fresh10(true2, true2, x, x, c(x, t2), c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 32 (a12_FOL) }
% 0.21/0.50 tuple(fresh12(class(x, c(x, t2), t2), true2, x, x, c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by lemma 38 }
% 0.21/0.50 tuple(fresh12(true2, true2, x, x, c2, c1, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 27 (a12_FOL) }
% 0.21/0.50 tuple(fresh13(greater(c1, c2), true2, x, x, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 1 (t12_FOL_2) }
% 0.21/0.50 tuple(fresh13(true2, true2, x, x, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 30 (a12_FOL) }
% 0.21/0.50 tuple(fresh16(inertia(x, i(x, t2), t2), true2, x, x, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by lemma 36 }
% 0.21/0.50 tuple(fresh16(true2, true2, x, x, i(x, t2), i(x, t1), t1, t2), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 21 (a12_FOL) }
% 0.21/0.50 tuple(fresh17(organization(x, t2), true2, i(x, t2), i(x, t1)), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 4 (t12_FOL_1) }
% 0.21/0.50 tuple(fresh17(true2, true2, i(x, t2), i(x, t1)), greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 10 (a12_FOL) }
% 0.21/0.50 tuple(true2, greater(i(x, t2), i(x, t1)))
% 0.21/0.50 = { by axiom 16 (t2_FOL) R->L }
% 0.21/0.50 tuple(true2, fresh6(true2, true2, x, i(x, t1), i(x, t2), t1))
% 0.21/0.50 = { by axiom 4 (t12_FOL_1) R->L }
% 0.21/0.50 tuple(true2, fresh6(organization(x, t2), true2, x, i(x, t1), i(x, t2), t1))
% 0.21/0.50 = { by axiom 23 (t2_FOL) R->L }
% 0.21/0.50 tuple(true2, fresh5(true2, true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by lemma 36 R->L }
% 0.21/0.50 tuple(true2, fresh5(inertia(x, i(x, t2), t2), true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by axiom 29 (t2_FOL) R->L }
% 0.21/0.50 tuple(true2, fresh3(reorganization_free(x, t1, t2), true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by axiom 5 (t12_FOL_4) }
% 0.21/0.50 tuple(true2, fresh3(true2, true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by axiom 24 (t2_FOL) }
% 0.21/0.50 tuple(true2, fresh4(greater(t2, t1), true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by axiom 2 (t12_FOL_3) }
% 0.21/0.50 tuple(true2, fresh4(true2, true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by axiom 28 (t2_FOL) }
% 0.21/0.50 tuple(true2, fresh7(inertia(x, i(x, t1), t1), true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by lemma 35 }
% 0.21/0.50 tuple(true2, fresh7(true2, true2, x, i(x, t1), i(x, t2), t1, t2))
% 0.21/0.50 = { by axiom 19 (t2_FOL) }
% 0.21/0.50 tuple(true2, fresh8(organization(x, t1), true2, i(x, t1), i(x, t2)))
% 0.21/0.50 = { by axiom 3 (t12_FOL) }
% 0.21/0.50 tuple(true2, fresh8(true2, true2, i(x, t1), i(x, t2)))
% 0.21/0.50 = { by axiom 11 (t2_FOL) }
% 0.21/0.50 tuple(true2, true2)
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------