0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.11/0.31 % Computer : n019.cluster.edu 0.11/0.31 % Model : x86_64 x86_64 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.31 % Memory : 8042.1875MB 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.31 % CPULimit : 180 0.11/0.31 % DateTime : Thu Aug 29 15:23:52 EDT 2019 0.11/0.31 % CPUTime : 45.96/46.15 % SZS status Theorem 45.96/46.15 45.96/46.15 % SZS output start Proof 45.96/46.15 Take the following subset of the input axioms: 46.53/46.72 fof(goals_13, conjecture, ![X17, X18, X19]: (('>='('==>'(X17, X18), X17) & '==>'(X19, X18)=X19) => '>='(X19, X17))). 46.53/46.72 fof(sos_01, axiom, ![A, B, C]: '+'(A, '+'(B, C))='+'('+'(A, B), C)). 46.53/46.72 fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)). 46.53/46.72 fof(sos_03, axiom, ![A]: A='+'(A, '0')). 46.53/46.72 fof(sos_04, axiom, ![A]: '>='(A, A)). 46.53/46.72 fof(sos_06, axiom, ![X3, X4]: (X3=X4 <= ('>='(X4, X3) & '>='(X3, X4)))). 46.53/46.72 fof(sos_07, axiom, ![X5, X6, X7]: ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))). 46.53/46.72 fof(sos_08, axiom, ![A]: '>='(A, '0')). 46.53/46.72 fof(sos_09, axiom, ![X8, X9, X10]: ('>='('+'(X8, X10), '+'(X9, X10)) <= '>='(X8, X9))). 46.53/46.72 fof(sos_10, axiom, ![X11, X12, X13]: ('>='('==>'(X12, X13), '==>'(X11, X13)) <= '>='(X11, X12))). 46.53/46.72 fof(sos_11, axiom, ![X14, X15, X16]: ('>='('==>'(X16, X14), '==>'(X16, X15)) <= '>='(X14, X15))). 46.53/46.72 fof(sos_12, axiom, ![A, B]: '+'(B, '==>'(B, A))='+'(A, '==>'(A, B))). 46.53/46.72 46.53/46.72 Now clausify the problem and encode Horn clauses using encoding 3 of 46.53/46.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 46.53/46.72 We repeatedly replace C & s=t => u=v by the two clauses: 46.53/46.72 fresh(y, y, x1...xn) = u 46.53/46.72 C => fresh(s, t, x1...xn) = v 46.53/46.72 where fresh is a fresh function symbol and x1..xn are the free 46.53/46.72 variables of u and v. 46.53/46.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the 46.53/46.72 input problem has no model of domain size 1). 46.53/46.72 46.53/46.72 The encoding turns the above axioms into the following unit equations and goals: 46.53/46.72 46.53/46.72 Axiom 1 (sos_06): fresh2(X, X, Y, Z) = Y. 46.53/46.72 Axiom 2 (sos_06): fresh(X, X, Y, Z) = Z. 46.53/46.72 Axiom 3 (sos_07): fresh6(X, X, Y, Z, W) = true. 46.53/46.72 Axiom 4 (sos_07_1): fresh5(X, X, Y, Z, W) = true. 46.53/46.72 Axiom 5 (sos_09): fresh4(X, X, Y, Z, W) = true. 46.53/46.72 Axiom 6 (sos_10): fresh3(X, X, Y, Z, W) = true. 46.53/46.72 Axiom 7 (sos_11): fresh9(X, X, Y, Z, W) = true. 46.53/46.72 Axiom 8 (sos_11): fresh9(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y). 46.53/46.72 Axiom 9 (sos_09): fresh4(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z). 46.53/46.72 Axiom 10 (sos_10): fresh3(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z). 46.53/46.72 Axiom 11 (sos_06): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X). 46.53/46.72 Axiom 12 (sos_02): X + Y = Y + X. 46.53/46.72 Axiom 13 (sos_04): X >= X = true. 46.53/46.72 Axiom 14 (sos_08): X >= 0 = true. 46.53/46.72 Axiom 15 (sos_01): X + (Y + Z) = (X + Y) + Z. 46.53/46.72 Axiom 16 (sos_07_1): fresh5((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z). 46.53/46.72 Axiom 17 (sos_07): fresh6(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z. 46.53/46.72 Axiom 18 (sos_03): X = X + 0. 46.53/46.72 Axiom 19 (sos_12): X + (X ==> Y) = Y + (Y ==> X). 46.53/46.72 Axiom 20 (goals_13): sK2_goals_13_X19 ==> sK3_goals_13_X18 = sK2_goals_13_X19. 46.53/46.72 Axiom 21 (goals_13_1): (sK1_goals_13_X17 ==> sK3_goals_13_X18) >= sK1_goals_13_X17 = true. 46.53/46.72 46.53/46.72 Lemma 22: 0 + X = X. 46.53/46.72 Proof: 46.53/46.72 0 + X 46.53/46.72 = { by axiom 12 (sos_02) } 46.53/46.72 X + 0 46.53/46.72 = { by axiom 18 (sos_03) } 46.53/46.72 X 46.53/46.72 46.53/46.72 Lemma 23: (X + Y) >= X = true. 46.53/46.72 Proof: 46.53/46.72 (X + Y) >= X 46.53/46.72 = { by axiom 12 (sos_02) } 46.53/46.72 (Y + X) >= X 46.53/46.72 = { by lemma 22 } 46.53/46.72 (Y + X) >= (0 + X) 46.53/46.72 = { by axiom 9 (sos_09) } 46.53/46.72 fresh4(Y >= 0, true, Y, 0, X) 46.53/46.72 = { by axiom 14 (sos_08) } 46.53/46.72 fresh4(true, true, Y, 0, X) 46.53/46.72 = { by axiom 5 (sos_09) } 47.06/47.29 true 47.06/47.29 47.06/47.29 Goal 1 (goals_13_2): sK2_goals_13_X19 >= sK1_goals_13_X17 = true. 47.06/47.29 Proof: 47.06/47.29 sK2_goals_13_X19 >= sK1_goals_13_X17 47.06/47.29 = { by axiom 18 (sos_03) } 47.06/47.29 (sK2_goals_13_X19 + 0) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 2 (sos_06) } 47.06/47.29 (sK2_goals_13_X19 + fresh(true, true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 14 (sos_08) } 47.06/47.29 (sK2_goals_13_X19 + fresh((sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17)) >= 0, true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 11 (sos_06) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(0 >= (sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17)), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 16 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5((sK2_goals_13_X19 + 0) >= ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 18 (sos_03) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(sK2_goals_13_X19 >= ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 16 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(fresh5(((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) + sK2_goals_13_X19) >= sK1_goals_13_X17, true, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19, sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 12 (sos_02) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(fresh5((sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18))) >= sK1_goals_13_X17, true, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19, sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 17 (sos_07) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(fresh5(fresh6((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) >= (sK2_goals_13_X19 ==> sK1_goals_13_X17), true, sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK1_goals_13_X17), true, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19, sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 8 (sos_11) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(fresh5(fresh6(fresh9((sK1_goals_13_X17 ==> sK3_goals_13_X18) >= sK1_goals_13_X17, true, sK1_goals_13_X17 ==> sK3_goals_13_X18, sK1_goals_13_X17, sK2_goals_13_X19), true, sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK1_goals_13_X17), true, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19, sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 21 (goals_13_1) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(fresh5(fresh6(fresh9(true, true, sK1_goals_13_X17 ==> sK3_goals_13_X18, sK1_goals_13_X17, sK2_goals_13_X19), true, sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK1_goals_13_X17), true, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19, sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 7 (sos_11) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(fresh5(fresh6(true, true, sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK1_goals_13_X17), true, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19, sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 3 (sos_07) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(fresh5(true, true, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19, sK1_goals_13_X17), true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 4 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(fresh5(true, true, sK2_goals_13_X19, 0, (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 4 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + fresh2(true, true, sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17), 0)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 1 (sos_06) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 2 (sos_06) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(true, true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 4 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(true, true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 4 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5(true, true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 3 (sos_07) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5(fresh6(true, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by lemma 23 } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5(fresh6((sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) >= sK2_goals_13_X19, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 19 (sos_12) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5(fresh6((sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)) >= sK2_goals_13_X19, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 20 (goals_13) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5(fresh6((sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 17 (sos_07) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5((sK2_goals_13_X19 + (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19))) >= sK3_goals_13_X18, true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 12 (sos_02) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5(((sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)) + sK2_goals_13_X19) >= sK3_goals_13_X18, true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 15 (sos_01) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5((sK1_goals_13_X17 + ((sK1_goals_13_X17 ==> sK2_goals_13_X19) + sK2_goals_13_X19)) >= sK3_goals_13_X18, true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 12 (sos_02) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5(fresh5((sK1_goals_13_X17 + (sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19))) >= sK3_goals_13_X18, true, sK1_goals_13_X17, sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19), sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 16 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh(fresh5((sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)) >= (sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 16 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 11 (sos_06) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) >= (sK1_goals_13_X17 ==> sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 16 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5((sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18))) >= sK2_goals_13_X19, true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 20 (goals_13) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5((sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18))) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 16 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5((sK2_goals_13_X19 + (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 15 (sos_01) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5(((sK2_goals_13_X19 + sK1_goals_13_X17) + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 12 (sos_02) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5(((sK1_goals_13_X17 + sK2_goals_13_X19) + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 15 (sos_01) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5((sK1_goals_13_X17 + (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 19 (sos_12) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5((sK1_goals_13_X17 + ((sK1_goals_13_X17 ==> sK3_goals_13_X18) + ((sK1_goals_13_X17 ==> sK3_goals_13_X18) ==> sK2_goals_13_X19))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 15 (sos_01) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5(((sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK3_goals_13_X18)) + ((sK1_goals_13_X17 ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 19 (sos_12) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5(((sK3_goals_13_X18 + (sK3_goals_13_X18 ==> sK1_goals_13_X17)) + ((sK1_goals_13_X17 ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 15 (sos_01) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5((sK3_goals_13_X18 + ((sK3_goals_13_X18 ==> sK1_goals_13_X17) + ((sK1_goals_13_X17 ==> sK3_goals_13_X18) ==> sK2_goals_13_X19))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 12 (sos_02) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5((sK3_goals_13_X18 + (((sK1_goals_13_X17 ==> sK3_goals_13_X18) ==> sK2_goals_13_X19) + (sK3_goals_13_X18 ==> sK1_goals_13_X17))) >= sK3_goals_13_X18, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by lemma 23 } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(fresh5(true, true, sK2_goals_13_X19, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), sK3_goals_13_X18), true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 4 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(fresh5(true, true, sK1_goals_13_X17, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 4 (sos_07_1) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (fresh2(true, true, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 1 (sos_06) } 47.06/47.29 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17))) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 19 (sos_12) } 47.06/47.29 (((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) + (((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 12 (sos_02) } 47.06/47.29 ((((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) + ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17)) >= sK1_goals_13_X17 47.06/47.29 = { by axiom 17 (sos_07) } 47.06/47.29 fresh6(((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) >= ((((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by axiom 10 (sos_10) } 47.06/47.29 fresh6(fresh3((((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19) >= (sK1_goals_13_X17 ==> sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by axiom 10 (sos_10) } 47.06/47.29 fresh6(fresh3(fresh3(sK1_goals_13_X17 >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by axiom 2 (sos_06) } 47.06/47.29 fresh6(fresh3(fresh3(fresh(true, true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by lemma 23 } 47.06/47.29 fresh6(fresh3(fresh3(fresh((sK1_goals_13_X17 + (sK1_goals_13_X17 ==> 0)) >= sK1_goals_13_X17, true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by axiom 19 (sos_12) } 47.06/47.29 fresh6(fresh3(fresh3(fresh((0 + (0 ==> sK1_goals_13_X17)) >= sK1_goals_13_X17, true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by lemma 22 } 47.06/47.29 fresh6(fresh3(fresh3(fresh((0 ==> sK1_goals_13_X17) >= sK1_goals_13_X17, true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by axiom 11 (sos_06) } 47.06/47.29 fresh6(fresh3(fresh3(fresh2(sK1_goals_13_X17 >= (0 ==> sK1_goals_13_X17), true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.29 = { by axiom 18 (sos_03) } 47.06/47.30 fresh6(fresh3(fresh3(fresh2(sK1_goals_13_X17 >= (0 ==> (sK1_goals_13_X17 + 0)), true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.30 = { by axiom 12 (sos_02) } 47.06/47.30 fresh6(fresh3(fresh3(fresh2(sK1_goals_13_X17 >= (0 ==> (0 + sK1_goals_13_X17)), true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.30 = { by axiom 16 (sos_07_1) } 47.06/47.30 fresh6(fresh3(fresh3(fresh2(fresh5((0 + sK1_goals_13_X17) >= (0 + sK1_goals_13_X17), true, 0, sK1_goals_13_X17, 0 + sK1_goals_13_X17), true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.30 = { by axiom 13 (sos_04) } 47.06/47.30 fresh6(fresh3(fresh3(fresh2(fresh5(true, true, 0, sK1_goals_13_X17, 0 + sK1_goals_13_X17), true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.06/47.30 = { by axiom 4 (sos_07_1) } 47.13/47.30 fresh6(fresh3(fresh3(fresh2(true, true, 0 ==> sK1_goals_13_X17, sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.13/47.30 = { by axiom 1 (sos_06) } 47.13/47.30 fresh6(fresh3(fresh3((0 ==> sK1_goals_13_X17) >= ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.13/47.30 = { by axiom 10 (sos_10) } 47.13/47.30 fresh6(fresh3(fresh3(fresh3((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= 0, true, sK1_goals_13_X17 ==> sK2_goals_13_X19, 0, sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.13/47.30 = { by axiom 14 (sos_08) } 47.13/47.30 fresh6(fresh3(fresh3(fresh3(true, true, sK1_goals_13_X17 ==> sK2_goals_13_X19, 0, sK1_goals_13_X17), true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.13/47.30 = { by axiom 6 (sos_10) } 47.13/47.30 fresh6(fresh3(fresh3(true, true, sK1_goals_13_X17, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK2_goals_13_X19), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.13/47.30 = { by axiom 6 (sos_10) } 47.13/47.30 fresh6(fresh3(true, true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17), true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.13/47.30 = { by axiom 6 (sos_10) } 47.13/47.30 fresh6(true, true, ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17) ==> sK2_goals_13_X19, (sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK1_goals_13_X17, sK1_goals_13_X17) 47.13/47.30 = { by axiom 3 (sos_07) } 47.13/47.30 true 47.13/47.30 % SZS output end Proof 47.13/47.30 47.13/47.30 RESULT: Theorem (the conjecture is true). 47.13/47.31 EOF