0.11/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.14/0.35 % Computer : n006.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 : 180 0.14/0.35 % DateTime : Thu Aug 29 16:09:09 EDT 2019 0.14/0.35 % CPUTime : 79.39/79.61 % SZS status Theorem 79.39/79.61 79.39/79.61 % SZS output start Proof 79.39/79.61 Take the following subset of the input axioms: 79.82/80.05 fof(goals_14, conjecture, ![X17, X18, X19]: ('>='(X19, X17) <= ('==>'(X19, X18)=X19 & '>='('==>'(X17, X18), X17)))). 79.82/80.05 fof(sos_01, axiom, ![A, B, C]: '+'(A, '+'(B, C))='+'('+'(A, B), C)). 79.82/80.05 fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)). 79.82/80.05 fof(sos_03, axiom, ![A]: '+'(A, '0')=A). 79.82/80.05 fof(sos_05, axiom, ![A]: '>='(A, A)). 79.82/80.05 fof(sos_07, axiom, ![X3, X4]: (('>='(X4, X3) & '>='(X3, X4)) => X3=X4)). 79.82/80.05 fof(sos_08, axiom, ![X5, X6, X7]: ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))). 79.82/80.05 fof(sos_09, axiom, ![A]: '>='(A, '0')). 79.82/80.05 fof(sos_10, axiom, ![X8, X9, X10]: ('>='(X8, X9) => '>='('+'(X8, X10), '+'(X9, X10)))). 79.82/80.05 fof(sos_11, axiom, ![X11, X12, X13]: ('>='('==>'(X12, X13), '==>'(X11, X13)) <= '>='(X11, X12))). 79.82/80.05 fof(sos_12, axiom, ![X14, X15, X16]: ('>='(X14, X15) => '>='('==>'(X16, X14), '==>'(X16, X15)))). 79.82/80.05 fof(sos_13, axiom, ![A, B]: '+'(B, '==>'(B, A))='+'(A, '==>'(A, B))). 79.82/80.05 79.82/80.05 Now clausify the problem and encode Horn clauses using encoding 3 of 79.82/80.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 79.82/80.05 We repeatedly replace C & s=t => u=v by the two clauses: 79.82/80.05 fresh(y, y, x1...xn) = u 79.82/80.05 C => fresh(s, t, x1...xn) = v 79.82/80.05 where fresh is a fresh function symbol and x1..xn are the free 79.82/80.05 variables of u and v. 79.82/80.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the 79.82/80.05 input problem has no model of domain size 1). 79.82/80.05 79.82/80.05 The encoding turns the above axioms into the following unit equations and goals: 79.82/80.05 79.82/80.05 Axiom 1 (sos_07): fresh(X, X, Y, Z) = Y. 79.82/80.05 Axiom 2 (sos_07): fresh8(X, X, Y, Z) = Z. 79.82/80.05 Axiom 3 (sos_08): fresh5(X, X, Y, Z, W) = true. 79.82/80.05 Axiom 4 (sos_08_1): fresh4(X, X, Y, Z, W) = true. 79.82/80.05 Axiom 5 (sos_10): fresh3(X, X, Y, Z, W) = true. 79.82/80.05 Axiom 6 (sos_11): fresh2(X, X, Y, Z, W) = true. 79.82/80.05 Axiom 7 (sos_12): fresh9(X, X, Y, Z, W) = true. 79.82/80.05 Axiom 8 (sos_12): fresh9(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y). 79.82/80.05 Axiom 9 (sos_07): fresh(X >= Y, true, Y, X) = fresh8(Y >= X, true, Y, X). 79.82/80.05 Axiom 10 (sos_03): X + 0 = X. 79.82/80.05 Axiom 11 (sos_13): X + (X ==> Y) = Y + (Y ==> X). 79.82/80.05 Axiom 12 (sos_02): X + Y = Y + X. 79.82/80.05 Axiom 13 (sos_01): X + (Y + Z) = (X + Y) + Z. 79.82/80.05 Axiom 14 (sos_11): fresh2(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z). 79.82/80.05 Axiom 15 (sos_09): X >= 0 = true. 79.82/80.05 Axiom 16 (sos_08_1): fresh4((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z). 79.82/80.05 Axiom 17 (sos_08): fresh5(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z. 79.82/80.05 Axiom 18 (sos_10): fresh3(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z). 79.82/80.05 Axiom 19 (sos_05): X >= X = true. 79.82/80.05 Axiom 20 (goals_14): sK2_goals_14_X19 ==> sK3_goals_14_X18 = sK2_goals_14_X19. 79.82/80.05 Axiom 21 (goals_14_1): (sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17 = true. 79.82/80.05 79.82/80.05 Lemma 22: 0 + X = X. 79.82/80.05 Proof: 79.82/80.05 0 + X 79.82/80.05 = { by axiom 12 (sos_02) } 79.82/80.05 X + 0 79.82/80.05 = { by axiom 10 (sos_03) } 79.82/80.05 X 79.82/80.05 79.82/80.05 Lemma 23: (X + Y) >= X = true. 79.82/80.05 Proof: 79.82/80.05 (X + Y) >= X 79.82/80.05 = { by axiom 12 (sos_02) } 79.82/80.05 (Y + X) >= X 79.82/80.05 = { by lemma 22 } 79.82/80.05 (Y + X) >= (0 + X) 79.82/80.05 = { by axiom 18 (sos_10) } 79.82/80.05 fresh3(Y >= 0, true, Y, 0, X) 79.82/80.05 = { by axiom 15 (sos_09) } 79.82/80.05 fresh3(true, true, Y, 0, X) 79.82/80.05 = { by axiom 5 (sos_10) } 79.82/80.05 true 79.82/80.05 79.82/80.05 Lemma 24: (X + (X ==> Y)) >= Y = true. 79.82/80.05 Proof: 79.82/80.05 (X + (X ==> Y)) >= Y 79.82/80.05 = { by axiom 11 (sos_13) } 79.82/80.05 (Y + (Y ==> X)) >= Y 79.82/80.05 = { by lemma 23 } 80.27/80.50 true 80.27/80.50 80.27/80.50 Goal 1 (goals_14_2): sK2_goals_14_X19 >= sK1_goals_14_X17 = true. 80.27/80.50 Proof: 80.27/80.50 sK2_goals_14_X19 >= sK1_goals_14_X17 80.27/80.50 = { by axiom 10 (sos_03) } 80.27/80.50 (sK2_goals_14_X19 + 0) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 1 (sos_07) } 80.27/80.50 (sK2_goals_14_X19 + fresh(true, true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 15 (sos_09) } 80.27/80.50 (sK2_goals_14_X19 + fresh((sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)) >= 0, true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 9 (sos_07) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(0 >= (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17)), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 16 (sos_08_1) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4((sK2_goals_14_X19 + 0) >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 10 (sos_03) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(sK2_goals_14_X19 >= ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 16 (sos_08_1) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(fresh4(((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) + sK2_goals_14_X19) >= sK1_goals_14_X17, true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19, sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 12 (sos_02) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(fresh4((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19, sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 17 (sos_08) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(fresh4(fresh5((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true, sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19, sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 8 (sos_12) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(fresh4(fresh5(fresh9((sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17, true, sK1_goals_14_X17 ==> sK3_goals_14_X18, sK1_goals_14_X17, sK2_goals_14_X19), true, sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19, sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 21 (goals_14_1) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(fresh4(fresh5(fresh9(true, true, sK1_goals_14_X17 ==> sK3_goals_14_X18, sK1_goals_14_X17, sK2_goals_14_X19), true, sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19, sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 7 (sos_12) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(fresh4(fresh5(true, true, sK2_goals_14_X19, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19, sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 3 (sos_08) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(fresh4(true, true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19, sK1_goals_14_X17), true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 4 (sos_08_1) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(fresh4(true, true, sK2_goals_14_X19, 0, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17), true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 4 (sos_08_1) } 80.27/80.50 (sK2_goals_14_X19 + fresh8(true, true, 0, sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 2 (sos_07) } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 1 (sos_07) } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(true, true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 4 (sos_08_1) } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(true, true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 4 (sos_08_1) } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4(true, true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 3 (sos_08) } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4(fresh5(true, true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by lemma 24 } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4(fresh5((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= sK2_goals_14_X19, true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 20 (goals_14) } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4(fresh5((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 17 (sos_08) } 80.27/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4((sK2_goals_14_X19 + (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.27/80.50 = { by axiom 12 (sos_02) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4(((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 13 (sos_01) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4((sK1_goals_14_X17 + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) + sK2_goals_14_X19)) >= sK3_goals_14_X18, true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 12 (sos_02) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4(fresh4((sK1_goals_14_X17 + (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 16 (sos_08_1) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh(fresh4((sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 16 (sos_08_1) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 9 (sos_07) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 16 (sos_08_1) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4((sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK2_goals_14_X19, true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 20 (goals_14) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4((sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 16 (sos_08_1) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(fresh4((sK2_goals_14_X19 + (sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)))) >= sK3_goals_14_X18, true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 13 (sos_01) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(fresh4(((sK2_goals_14_X19 + sK1_goals_14_X17) + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK3_goals_14_X18, true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 12 (sos_02) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(fresh4(((sK1_goals_14_X17 + sK2_goals_14_X19) + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK3_goals_14_X18, true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 13 (sos_01) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(fresh4((sK1_goals_14_X17 + (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)))) >= sK3_goals_14_X18, true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 17 (sos_08) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(fresh4(fresh5((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= (sK1_goals_14_X17 ==> sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by lemma 24 } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(fresh4(fresh5(true, true, sK1_goals_14_X17, sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 3 (sos_08) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(fresh4(true, true, sK2_goals_14_X19, sK1_goals_14_X17 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK3_goals_14_X18), true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 4 (sos_08_1) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(fresh4(true, true, sK1_goals_14_X17, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK2_goals_14_X19), true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 4 (sos_08_1) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (fresh8(true, true, sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 2 (sos_07) } 80.31/80.50 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 11 (sos_13) } 80.31/80.50 (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) + (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19)) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 12 (sos_02) } 80.31/80.50 ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17 80.31/80.50 = { by axiom 17 (sos_08) } 80.31/80.50 fresh5(((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 14 (sos_11) } 80.31/80.50 fresh5(fresh2((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 14 (sos_11) } 80.31/80.50 fresh5(fresh2(fresh2(sK1_goals_14_X17 >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 1 (sos_07) } 80.31/80.50 fresh5(fresh2(fresh2(fresh(true, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by lemma 23 } 80.31/80.50 fresh5(fresh2(fresh2(fresh((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 0)) >= sK1_goals_14_X17, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 11 (sos_13) } 80.31/80.50 fresh5(fresh2(fresh2(fresh((0 + (0 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by lemma 22 } 80.31/80.50 fresh5(fresh2(fresh2(fresh((0 ==> sK1_goals_14_X17) >= sK1_goals_14_X17, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 9 (sos_07) } 80.31/80.50 fresh5(fresh2(fresh2(fresh8(sK1_goals_14_X17 >= (0 ==> sK1_goals_14_X17), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 10 (sos_03) } 80.31/80.50 fresh5(fresh2(fresh2(fresh8(sK1_goals_14_X17 >= (0 ==> (sK1_goals_14_X17 + 0)), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 12 (sos_02) } 80.31/80.50 fresh5(fresh2(fresh2(fresh8(sK1_goals_14_X17 >= (0 ==> (0 + sK1_goals_14_X17)), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 16 (sos_08_1) } 80.31/80.50 fresh5(fresh2(fresh2(fresh8(fresh4((0 + sK1_goals_14_X17) >= (0 + sK1_goals_14_X17), true, 0, sK1_goals_14_X17, 0 + sK1_goals_14_X17), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 19 (sos_05) } 80.31/80.50 fresh5(fresh2(fresh2(fresh8(fresh4(true, true, 0, sK1_goals_14_X17, 0 + sK1_goals_14_X17), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 4 (sos_08_1) } 80.31/80.50 fresh5(fresh2(fresh2(fresh8(true, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 2 (sos_07) } 80.31/80.50 fresh5(fresh2(fresh2((0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 14 (sos_11) } 80.31/80.50 fresh5(fresh2(fresh2(fresh2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= 0, true, sK1_goals_14_X17 ==> sK2_goals_14_X19, 0, sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 15 (sos_09) } 80.31/80.50 fresh5(fresh2(fresh2(fresh2(true, true, sK1_goals_14_X17 ==> sK2_goals_14_X19, 0, sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 6 (sos_11) } 80.31/80.50 fresh5(fresh2(fresh2(true, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 6 (sos_11) } 80.31/80.50 fresh5(fresh2(true, true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, sK1_goals_14_X17 ==> sK2_goals_14_X19, sK1_goals_14_X17), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 6 (sos_11) } 80.31/80.50 fresh5(true, true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19, (sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17, sK1_goals_14_X17) 80.31/80.50 = { by axiom 3 (sos_08) } 80.31/80.50 true 80.31/80.50 % SZS output end Proof 80.31/80.50 80.31/80.50 RESULT: Theorem (the conjecture is true). 80.31/80.52 EOF