0.02/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.11 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.10/0.32 % Computer : n018.cluster.edu 0.10/0.32 % Model : x86_64 x86_64 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.32 % Memory : 8042.1875MB 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.32 % CPULimit : 960 0.10/0.32 % WCLimit : 120 0.10/0.32 % DateTime : Thu Jul 2 09:12:22 EDT 2020 0.10/0.32 % CPUTime : 237.90/30.29 % SZS status Theorem 237.90/30.29 237.90/30.29 % SZS output start Proof 237.90/30.29 Take the following subset of the input axioms: 249.84/31.75 fof(goals_13, conjecture, ![X17, X18, X19]: ('>='(X17, X19) <= (X19='==>'(X19, X18) & '>='(X17, '==>'(X17, X18))))). 249.84/31.75 fof(sos_01, axiom, ![A, B, C]: '+'('+'(A, B), C)='+'(A, '+'(B, C))). 249.84/31.75 fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)). 249.84/31.75 fof(sos_03, axiom, ![A]: '+'(A, '0')=A). 249.84/31.75 fof(sos_04, axiom, ![A]: '>='(A, A)). 249.84/31.75 fof(sos_05, axiom, ![X0, X1, X2]: ('>='(X0, X2) <= ('>='(X1, X2) & '>='(X0, X1)))). 249.84/31.75 fof(sos_06, axiom, ![X3, X4]: (('>='(X4, X3) & '>='(X3, X4)) => X4=X3)). 249.84/31.75 fof(sos_07, axiom, ![X5, X6, X7]: ('>='(X6, '==>'(X5, X7)) <=> '>='('+'(X5, X6), X7))). 249.84/31.75 fof(sos_08, axiom, ![A]: '>='(A, '0')). 249.84/31.75 fof(sos_09, axiom, ![X8, X9, X10]: ('>='('+'(X8, X10), '+'(X9, X10)) <= '>='(X8, X9))). 249.84/31.75 fof(sos_10, axiom, ![X11, X12, X13]: ('>='('==>'(X12, X13), '==>'(X11, X13)) <= '>='(X11, X12))). 249.84/31.75 fof(sos_11, axiom, ![X14, X15, X16]: ('>='('==>'(X16, X14), '==>'(X16, X15)) <= '>='(X14, X15))). 249.84/31.75 fof(sos_12, axiom, ![A, B]: '+'(A, '==>'(A, B))='+'(B, '==>'(B, A))). 249.84/31.75 249.84/31.75 Now clausify the problem and encode Horn clauses using encoding 3 of 249.84/31.75 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 249.84/31.75 We repeatedly replace C & s=t => u=v by the two clauses: 249.84/31.75 fresh(y, y, x1...xn) = u 249.84/31.75 C => fresh(s, t, x1...xn) = v 249.84/31.75 where fresh is a fresh function symbol and x1..xn are the free 249.84/31.75 variables of u and v. 249.84/31.75 A predicate p(X) is encoded as p(X)=true (this is sound, because the 249.84/31.75 input problem has no model of domain size 1). 249.84/31.75 249.84/31.75 The encoding turns the above axioms into the following unit equations and goals: 249.84/31.75 249.84/31.75 Axiom 1 (sos_05): fresh7(X, X, Y, Z, W) = Y >= W. 249.84/31.75 Axiom 2 (sos_05): fresh8(X, X, Y, Z) = true. 249.84/31.75 Axiom 3 (sos_06): fresh9(X, X, Y, Z) = Y. 249.84/31.75 Axiom 4 (sos_06): fresh(X, X, Y, Z) = Z. 249.84/31.75 Axiom 5 (sos_07): fresh6(X, X, Y, Z, W) = true. 249.84/31.75 Axiom 6 (sos_07_1): fresh5(X, X, Y, Z, W) = true. 249.84/31.75 Axiom 7 (sos_09): fresh4(X, X, Y, Z, W) = true. 249.84/31.75 Axiom 8 (sos_10): fresh3(X, X, Y, Z, W) = true. 249.84/31.75 Axiom 9 (sos_11): fresh2(X, X, Y, Z, W) = true. 249.84/31.75 Axiom 10 (sos_01): (X + Y) + Z = X + (Y + Z). 249.84/31.75 Axiom 11 (sos_06): fresh(X >= Y, true, Y, X) = fresh9(Y >= X, true, Y, X). 249.84/31.75 Axiom 12 (sos_08): X >= 0 = true. 249.84/31.75 Axiom 13 (sos_12): X + (X ==> Y) = Y + (Y ==> X). 249.84/31.75 Axiom 14 (sos_09): fresh4(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z). 249.84/31.75 Axiom 15 (sos_03): X + 0 = X. 249.84/31.75 Axiom 16 (sos_05): fresh7(X >= Y, true, Z, X, Y) = fresh8(Z >= X, true, Z, Y). 249.84/31.75 Axiom 17 (sos_02): X + Y = Y + X. 249.84/31.75 Axiom 18 (sos_10): fresh3(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z). 249.84/31.75 Axiom 19 (sos_11): fresh2(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y). 249.84/31.75 Axiom 20 (sos_04): X >= X = true. 249.84/31.75 Axiom 21 (sos_07_1): fresh5((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z). 249.84/31.75 Axiom 22 (sos_07): fresh6(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z. 249.84/31.75 Axiom 23 (goals_13): sK2_goals_13_X19 = sK2_goals_13_X19 ==> sK3_goals_13_X18. 251.84/32.01 Axiom 24 (goals_13_1): sK1_goals_13_X17 >= (sK1_goals_13_X17 ==> sK3_goals_13_X18) = true. 251.84/32.01 251.84/32.01 Lemma 25: X + (Y + Z) = Y + (X + Z). 251.84/32.01 Proof: 251.84/32.01 X + (Y + Z) 251.84/32.01 = { by axiom 17 (sos_02) } 251.84/32.01 (Y + Z) + X 251.84/32.01 = { by axiom 10 (sos_01) } 251.84/32.01 Y + (Z + X) 251.84/32.01 = { by axiom 17 (sos_02) } 251.84/32.01 Y + (X + Z) 251.84/32.01 251.84/32.01 Lemma 26: 0 + X = X. 251.84/32.01 Proof: 251.84/32.01 0 + X 251.84/32.01 = { by axiom 17 (sos_02) } 251.84/32.01 X + 0 251.84/32.01 = { by axiom 15 (sos_03) } 251.84/32.01 X 251.84/32.01 251.84/32.01 Lemma 27: (X + Y) >= X = true. 251.84/32.01 Proof: 251.84/32.01 (X + Y) >= X 251.84/32.01 = { by axiom 17 (sos_02) } 251.84/32.01 (Y + X) >= X 251.84/32.01 = { by lemma 26 } 251.84/32.01 (Y + X) >= (0 + X) 251.84/32.01 = { by axiom 14 (sos_09) } 251.84/32.01 fresh4(Y >= 0, true, Y, 0, X) 251.84/32.01 = { by axiom 12 (sos_08) } 251.84/32.01 fresh4(true, true, Y, 0, X) 251.84/32.01 = { by axiom 7 (sos_09) } 251.84/32.01 true 251.84/32.01 251.84/32.01 Lemma 28: (Y + (Y ==> X)) >= X = true. 251.84/32.01 Proof: 251.84/32.01 (Y + (Y ==> X)) >= X 251.84/32.01 = { by axiom 13 (sos_12) } 251.84/32.01 (X + (X ==> Y)) >= X 251.84/32.01 = { by lemma 27 } 251.84/32.01 true 251.84/32.01 251.84/32.01 Lemma 29: (Z + (Y ==> (Z ==> X))) >= (Y ==> X) = true. 251.84/32.01 Proof: 251.84/32.01 (Z + (Y ==> (Z ==> X))) >= (Y ==> X) 251.84/32.01 = { by axiom 21 (sos_07_1) } 251.84/32.01 fresh5((Y + (Z + (Y ==> (Z ==> X)))) >= X, true, Y, Z + (Y ==> (Z ==> X)), X) 251.84/32.01 = { by lemma 25 } 251.84/32.01 fresh5((Z + (Y + (Y ==> (Z ==> X)))) >= X, true, Y, Z + (Y ==> (Z ==> X)), X) 251.84/32.01 = { by axiom 22 (sos_07) } 251.84/32.01 fresh5(fresh6((Y + (Y ==> (Z ==> X))) >= (Z ==> X), true, Z, Y + (Y ==> (Z ==> X)), X), true, Y, Z + (Y ==> (Z ==> X)), X) 251.84/32.01 = { by lemma 28 } 251.84/32.01 fresh5(fresh6(true, true, Z, Y + (Y ==> (Z ==> X)), X), true, Y, Z + (Y ==> (Z ==> X)), X) 251.84/32.01 = { by axiom 5 (sos_07) } 251.84/32.01 fresh5(true, true, Y, Z + (Y ==> (Z ==> X)), X) 251.84/32.01 = { by axiom 6 (sos_07_1) } 251.84/32.01 true 251.84/32.01 251.84/32.01 Lemma 30: (Z ==> (Y ==> X)) >= (Y ==> (Z ==> X)) = true. 251.84/32.01 Proof: 251.84/32.01 (Z ==> (Y ==> X)) >= (Y ==> (Z ==> X)) 251.84/32.01 = { by axiom 21 (sos_07_1) } 251.84/32.01 fresh5((Y + (Z ==> (Y ==> X))) >= (Z ==> X), true, Y, Z ==> (Y ==> X), Z ==> X) 251.84/32.01 = { by lemma 29 } 251.84/32.01 fresh5(true, true, Y, Z ==> (Y ==> X), Z ==> X) 251.84/32.01 = { by axiom 6 (sos_07_1) } 251.84/32.01 true 251.84/32.01 251.84/32.01 Lemma 31: Z ==> (Y ==> X) = Y ==> (Z ==> X). 251.84/32.01 Proof: 251.84/32.01 Z ==> (Y ==> X) 251.84/32.01 = { by axiom 4 (sos_06) } 251.84/32.01 fresh(true, true, Y ==> (Z ==> X), Z ==> (Y ==> X)) 251.84/32.01 = { by lemma 30 } 251.84/32.01 fresh((Z ==> (Y ==> X)) >= (Y ==> (Z ==> X)), true, Y ==> (Z ==> X), Z ==> (Y ==> X)) 251.84/32.01 = { by axiom 11 (sos_06) } 251.84/32.01 fresh9((Y ==> (Z ==> X)) >= (Z ==> (Y ==> X)), true, Y ==> (Z ==> X), Z ==> (Y ==> X)) 251.84/32.01 = { by lemma 30 } 251.84/32.01 fresh9(true, true, Y ==> (Z ==> X), Z ==> (Y ==> X)) 251.84/32.01 = { by axiom 3 (sos_06) } 251.84/32.01 Y ==> (Z ==> X) 251.84/32.01 251.84/32.01 Lemma 32: X ==> (X + (Y ==> (X ==> Z))) = X ==> (Y ==> Z). 251.84/32.01 Proof: 251.84/32.01 X ==> (X + (Y ==> (X ==> Z))) 251.84/32.01 = { by lemma 31 } 251.84/32.01 X ==> (X + (X ==> (Y ==> Z))) 251.84/32.01 = { by axiom 13 (sos_12) } 251.84/32.01 X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)) 251.84/32.01 = { by axiom 4 (sos_06) } 251.84/32.01 fresh(true, true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.01 = { by axiom 9 (sos_11) } 251.84/32.01 fresh(fresh2(true, true, (Y ==> Z) + ((Y ==> Z) ==> X), Y ==> Z, X), true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.01 = { by lemma 27 } 251.84/32.01 fresh(fresh2(((Y ==> Z) + ((Y ==> Z) ==> X)) >= (Y ==> Z), true, (Y ==> Z) + ((Y ==> Z) ==> X), Y ==> Z, X), true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.01 = { by axiom 19 (sos_11) } 251.84/32.01 fresh((X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) >= (X ==> (Y ==> Z)), true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.01 = { by axiom 11 (sos_06) } 251.84/32.01 fresh9((X ==> (Y ==> Z)) >= (X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))), true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.01 = { by axiom 13 (sos_12) } 251.84/32.01 fresh9((X ==> (Y ==> Z)) >= (X ==> (X + (X ==> (Y ==> Z)))), true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.01 = { by axiom 21 (sos_07_1) } 251.84/32.02 fresh9(fresh5((X + (X ==> (Y ==> Z))) >= (X + (X ==> (Y ==> Z))), true, X, X ==> (Y ==> Z), X + (X ==> (Y ==> Z))), true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.02 = { by axiom 20 (sos_04) } 251.84/32.02 fresh9(fresh5(true, true, X, X ==> (Y ==> Z), X + (X ==> (Y ==> Z))), true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.02 = { by axiom 6 (sos_07_1) } 251.84/32.02 fresh9(true, true, X ==> (Y ==> Z), X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) 251.84/32.02 = { by axiom 3 (sos_06) } 251.84/32.02 X ==> (Y ==> Z) 251.84/32.02 251.84/32.02 Lemma 33: fresh(0 >= X, true, X, 0) = X. 251.84/32.02 Proof: 251.84/32.02 fresh(0 >= X, true, X, 0) 251.84/32.02 = { by axiom 11 (sos_06) } 251.84/32.02 fresh9(X >= 0, true, X, 0) 251.84/32.02 = { by axiom 12 (sos_08) } 251.84/32.02 fresh9(true, true, X, 0) 251.84/32.02 = { by axiom 3 (sos_06) } 251.84/32.02 X 251.84/32.02 251.84/32.02 Lemma 34: (Y + X) >= X = true. 251.84/32.02 Proof: 251.84/32.02 (Y + X) >= X 251.84/32.02 = { by axiom 17 (sos_02) } 251.84/32.02 (X + Y) >= X 251.84/32.02 = { by lemma 27 } 251.84/32.02 true 251.84/32.02 251.84/32.02 Lemma 35: (X + Y) >= (Z ==> X) = true. 251.84/32.02 Proof: 251.84/32.02 (X + Y) >= (Z ==> X) 251.84/32.02 = { by axiom 21 (sos_07_1) } 251.84/32.02 fresh5((Z + (X + Y)) >= X, true, Z, X + Y, X) 251.84/32.02 = { by axiom 17 (sos_02) } 251.84/32.02 fresh5((Z + (Y + X)) >= X, true, Z, X + Y, X) 251.84/32.02 = { by lemma 25 } 251.84/32.02 fresh5((Y + (Z + X)) >= X, true, Z, X + Y, X) 251.84/32.02 = { by axiom 10 (sos_01) } 251.84/32.02 fresh5(((Y + Z) + X) >= X, true, Z, X + Y, X) 251.84/32.02 = { by lemma 34 } 251.84/32.02 fresh5(true, true, Z, X + Y, X) 251.84/32.02 = { by axiom 6 (sos_07_1) } 252.20/32.06 true 252.20/32.06 252.20/32.06 Lemma 36: sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18) = X ==> sK2_goals_13_X19. 252.20/32.06 Proof: 252.20/32.06 sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18) 252.20/32.06 = { by axiom 3 (sos_06) } 252.20/32.06 fresh9(true, true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 6 (sos_07_1) } 252.20/32.06 fresh9(fresh5(true, true, X, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by lemma 29 } 252.20/32.06 fresh9(fresh5((X + (sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18))) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, X, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 23 (goals_13) } 252.20/32.06 fresh9(fresh5((X + (sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18))) >= sK2_goals_13_X19, true, X, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), sK2_goals_13_X19), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 21 (sos_07_1) } 252.20/32.06 fresh9((sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18)) >= (X ==> sK2_goals_13_X19), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 11 (sos_06) } 252.20/32.06 fresh((X ==> sK2_goals_13_X19) >= (sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18)), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 21 (sos_07_1) } 252.20/32.06 fresh(fresh5((sK2_goals_13_X19 + (X ==> sK2_goals_13_X19)) >= (X ==> sK3_goals_13_X18), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 17 (sos_02) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> sK3_goals_13_X18), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 15 (sos_03) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK3_goals_13_X18 + 0)), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 4 (sos_06) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK3_goals_13_X18 + fresh(true, true, sK3_goals_13_X18 ==> sK2_goals_13_X19, 0))), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 6 (sos_07_1) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK3_goals_13_X18 + fresh(fresh5(true, true, sK3_goals_13_X18, 0, sK2_goals_13_X19), true, sK3_goals_13_X18 ==> sK2_goals_13_X19, 0))), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by lemma 35 } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK3_goals_13_X18 + fresh(fresh5((sK3_goals_13_X18 + 0) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, sK3_goals_13_X18, 0, sK2_goals_13_X19), true, sK3_goals_13_X18 ==> sK2_goals_13_X19, 0))), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 23 (goals_13) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK3_goals_13_X18 + fresh(fresh5((sK3_goals_13_X18 + 0) >= sK2_goals_13_X19, true, sK3_goals_13_X18, 0, sK2_goals_13_X19), true, sK3_goals_13_X18 ==> sK2_goals_13_X19, 0))), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 21 (sos_07_1) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK3_goals_13_X18 + fresh(0 >= (sK3_goals_13_X18 ==> sK2_goals_13_X19), true, sK3_goals_13_X18 ==> sK2_goals_13_X19, 0))), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by lemma 33 } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK3_goals_13_X18 + (sK3_goals_13_X18 ==> sK2_goals_13_X19))), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 13 (sos_12) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK3_goals_13_X18))), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 23 (goals_13) } 252.20/32.06 fresh(fresh5(((X ==> sK2_goals_13_X19) + sK2_goals_13_X19) >= (X ==> (sK2_goals_13_X19 + sK2_goals_13_X19)), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 21 (sos_07_1) } 252.20/32.06 fresh(fresh5(fresh5((X + ((X ==> sK2_goals_13_X19) + sK2_goals_13_X19)) >= (sK2_goals_13_X19 + sK2_goals_13_X19), true, X, (X ==> sK2_goals_13_X19) + sK2_goals_13_X19, sK2_goals_13_X19 + sK2_goals_13_X19), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.06 = { by axiom 10 (sos_01) } 252.20/32.06 fresh(fresh5(fresh5(((X + (X ==> sK2_goals_13_X19)) + sK2_goals_13_X19) >= (sK2_goals_13_X19 + sK2_goals_13_X19), true, X, (X ==> sK2_goals_13_X19) + sK2_goals_13_X19, sK2_goals_13_X19 + sK2_goals_13_X19), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.07 = { by axiom 14 (sos_09) } 252.20/32.07 fresh(fresh5(fresh5(fresh4((X + (X ==> sK2_goals_13_X19)) >= sK2_goals_13_X19, true, X + (X ==> sK2_goals_13_X19), sK2_goals_13_X19, sK2_goals_13_X19), true, X, (X ==> sK2_goals_13_X19) + sK2_goals_13_X19, sK2_goals_13_X19 + sK2_goals_13_X19), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.07 = { by lemma 28 } 252.20/32.07 fresh(fresh5(fresh5(fresh4(true, true, X + (X ==> sK2_goals_13_X19), sK2_goals_13_X19, sK2_goals_13_X19), true, X, (X ==> sK2_goals_13_X19) + sK2_goals_13_X19, sK2_goals_13_X19 + sK2_goals_13_X19), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.07 = { by axiom 7 (sos_09) } 252.20/32.07 fresh(fresh5(fresh5(true, true, X, (X ==> sK2_goals_13_X19) + sK2_goals_13_X19, sK2_goals_13_X19 + sK2_goals_13_X19), true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.07 = { by axiom 6 (sos_07_1) } 252.20/32.07 fresh(fresh5(true, true, sK2_goals_13_X19, X ==> sK2_goals_13_X19, X ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.07 = { by axiom 6 (sos_07_1) } 252.20/32.07 fresh(true, true, sK2_goals_13_X19 ==> (X ==> sK3_goals_13_X18), X ==> sK2_goals_13_X19) 252.20/32.07 = { by axiom 4 (sos_06) } 252.20/32.07 X ==> sK2_goals_13_X19 252.20/32.07 252.20/32.07 Lemma 37: (X + ((X + Y) ==> Z)) >= (Y ==> Z) = true. 252.20/32.07 Proof: 252.20/32.07 (X + ((X + Y) ==> Z)) >= (Y ==> Z) 252.20/32.07 = { by axiom 17 (sos_02) } 252.20/32.07 (X + ((Y + X) ==> Z)) >= (Y ==> Z) 252.20/32.07 = { by axiom 21 (sos_07_1) } 252.20/32.07 fresh5((Y + (X + ((Y + X) ==> Z))) >= Z, true, Y, X + ((Y + X) ==> Z), Z) 252.20/32.07 = { by axiom 10 (sos_01) } 252.20/32.07 fresh5(((Y + X) + ((Y + X) ==> Z)) >= Z, true, Y, X + ((Y + X) ==> Z), Z) 252.20/32.07 = { by lemma 28 } 252.20/32.07 fresh5(true, true, Y, X + ((Y + X) ==> Z), Z) 252.20/32.07 = { by axiom 6 (sos_07_1) } 252.20/32.07 true 252.20/32.07 252.20/32.07 Lemma 38: (X + Y) ==> X = 0. 252.20/32.07 Proof: 252.20/32.07 (X + Y) ==> X 252.20/32.07 = { by axiom 4 (sos_06) } 252.20/32.07 fresh(true, true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 12 (sos_08) } 252.20/32.07 fresh(((X + Y) ==> X) >= 0, true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 11 (sos_06) } 252.20/32.07 fresh9(0 >= ((X + Y) ==> X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 4 (sos_06) } 252.20/32.07 fresh9(fresh(true, true, X ==> X, 0) >= ((X + Y) ==> X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 6 (sos_07_1) } 252.20/32.07 fresh9(fresh(fresh5(true, true, X, 0, X), true, X ==> X, 0) >= ((X + Y) ==> X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by lemma 27 } 252.20/32.07 fresh9(fresh(fresh5((X + 0) >= X, true, X, 0, X), true, X ==> X, 0) >= ((X + Y) ==> X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 21 (sos_07_1) } 252.20/32.07 fresh9(fresh(0 >= (X ==> X), true, X ==> X, 0) >= ((X + Y) ==> X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by lemma 33 } 252.20/32.07 fresh9((X ==> X) >= ((X + Y) ==> X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 18 (sos_10) } 252.20/32.07 fresh9(fresh3((X + Y) >= X, true, X + Y, X, X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by lemma 27 } 252.20/32.07 fresh9(fresh3(true, true, X + Y, X, X), true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 8 (sos_10) } 252.20/32.07 fresh9(true, true, 0, (X + Y) ==> X) 252.20/32.07 = { by axiom 3 (sos_06) } 252.20/32.07 0 252.20/32.07 252.20/32.07 Lemma 39: fresh7(Z >= Y, true, X + Z, Z, Y) = true. 252.20/32.07 Proof: 252.20/32.07 fresh7(Z >= Y, true, X + Z, Z, Y) 252.20/32.07 = { by axiom 16 (sos_05) } 252.20/32.07 fresh8((X + Z) >= Z, true, X + Z, Y) 252.20/32.07 = { by lemma 34 } 252.20/32.07 fresh8(true, true, X + Z, Y) 252.20/32.07 = { by axiom 2 (sos_05) } 252.20/32.08 true 252.20/32.08 252.20/32.08 Lemma 40: Y ==> ((Y ==> X) ==> X) = 0. 252.20/32.08 Proof: 252.20/32.08 Y ==> ((Y ==> X) ==> X) 252.20/32.08 = { by lemma 33 } 252.20/32.08 fresh(0 >= (Y ==> ((Y ==> X) ==> X)), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by axiom 21 (sos_07_1) } 252.20/32.08 fresh(fresh5((Y + 0) >= ((Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by axiom 17 (sos_02) } 252.20/32.08 fresh(fresh5((0 + Y) >= ((Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by axiom 1 (sos_05) } 252.20/32.08 fresh(fresh5(fresh7(true, true, 0 + Y, Y, (Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by lemma 37 } 252.20/32.08 fresh(fresh5(fresh7((Y + ((Y + (Y ==> X)) ==> X)) >= ((Y ==> X) ==> X), true, 0 + Y, Y, (Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by axiom 13 (sos_12) } 252.20/32.08 fresh(fresh5(fresh7((Y + ((X + (X ==> Y)) ==> X)) >= ((Y ==> X) ==> X), true, 0 + Y, Y, (Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by lemma 38 } 252.20/32.08 fresh(fresh5(fresh7((Y + 0) >= ((Y ==> X) ==> X), true, 0 + Y, Y, (Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by axiom 15 (sos_03) } 252.20/32.08 fresh(fresh5(fresh7(Y >= ((Y ==> X) ==> X), true, 0 + Y, Y, (Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by lemma 39 } 252.20/32.08 fresh(fresh5(true, true, Y, 0, (Y ==> X) ==> X), true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by axiom 6 (sos_07_1) } 252.20/32.08 fresh(true, true, Y ==> ((Y ==> X) ==> X), 0) 252.20/32.08 = { by axiom 4 (sos_06) } 252.20/32.08 0 252.20/32.08 252.20/32.08 Lemma 41: Z + (X + (Z ==> Y)) = Y + ((Y ==> Z) + X). 252.20/32.08 Proof: 252.20/32.08 Z + (X + (Z ==> Y)) 252.20/32.08 = { by axiom 17 (sos_02) } 252.20/32.08 Z + ((Z ==> Y) + X) 252.20/32.08 = { by axiom 10 (sos_01) } 252.20/32.08 (Z + (Z ==> Y)) + X 252.20/32.08 = { by axiom 13 (sos_12) } 252.20/32.08 (Y + (Y ==> Z)) + X 252.20/32.08 = { by axiom 10 (sos_01) } 252.20/32.08 Y + ((Y ==> Z) + X) 252.20/32.08 252.20/32.08 Lemma 42: (Z + (Y + (Y ==> (Z ==> X)))) ==> X = 0. 252.20/32.08 Proof: 252.20/32.08 (Z + (Y + (Y ==> (Z ==> X)))) ==> X 252.20/32.08 = { by axiom 13 (sos_12) } 252.20/32.08 (Z + ((Z ==> X) + ((Z ==> X) ==> Y))) ==> X 252.20/32.08 = { by lemma 41 } 252.20/32.08 (X + (((Z ==> X) ==> Y) + (X ==> Z))) ==> X 252.20/32.08 = { by lemma 38 } 252.20/32.12 0 252.20/32.12 252.20/32.12 Lemma 43: (Y + Z) ==> X = Y ==> (Z ==> X). 252.20/32.12 Proof: 252.20/32.12 (Y + Z) ==> X 252.20/32.12 = { by axiom 17 (sos_02) } 252.20/32.12 (Z + Y) ==> X 252.20/32.12 = { by axiom 4 (sos_06) } 252.20/32.12 fresh(true, true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 6 (sos_07_1) } 252.20/32.12 fresh(fresh5(true, true, Z, (Z + Y) ==> X, Y ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 37 } 252.20/32.12 fresh(fresh5((Z + ((Z + Y) ==> X)) >= (Y ==> X), true, Z, (Z + Y) ==> X, Y ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 21 (sos_07_1) } 252.20/32.12 fresh(((Z + Y) ==> X) >= (Z ==> (Y ==> X)), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 11 (sos_06) } 252.20/32.12 fresh9((Z ==> (Y ==> X)) >= ((Z + Y) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 31 } 252.20/32.12 fresh9((Y ==> (Z ==> X)) >= ((Z + Y) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 15 (sos_03) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + 0) >= ((Z + Y) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 42 } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= ((Z + Y) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 17 (sos_02) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= ((Y + Z) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 15 (sos_03) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= ((Y + (Z + 0)) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 10 (sos_01) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + 0) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 42 } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Y + (Z + (Z ==> (Y ==> ((Z ==> (Y ==> X)) ==> X))))) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 17 (sos_02) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + (((Z + (Z ==> (Y ==> ((Z ==> (Y ==> X)) ==> X)))) + Y) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 10 (sos_01) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Z + ((Z ==> (Y ==> ((Z ==> (Y ==> X)) ==> X))) + Y)) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 17 (sos_02) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Z + (Y + (Z ==> (Y ==> ((Z ==> (Y ==> X)) ==> X))))) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 31 } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Z + (Y + (Z ==> ((Z ==> (Y ==> X)) ==> (Y ==> X))))) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 40 } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Z + (Y + 0)) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 15 (sos_03) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Z + Y) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 17 (sos_02) } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Y + Z) ==> ((Z ==> (Y ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 31 } 252.20/32.12 fresh9(((Y ==> (Z ==> X)) + (((Y ==> (Z ==> X)) + ((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)))) ==> X)) >= (((Y + Z) + ((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X))) ==> X), true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by lemma 37 } 252.20/32.12 fresh9(true, true, Z ==> (Y ==> X), (Z + Y) ==> X) 252.20/32.12 = { by axiom 3 (sos_06) } 252.20/32.12 Z ==> (Y ==> X) 252.20/32.12 = { by lemma 31 } 252.20/32.12 Y ==> (Z ==> X) 252.20/32.12 252.20/32.12 Lemma 44: Y >= (X ==> Y) = true. 252.20/32.12 Proof: 252.20/32.12 Y >= (X ==> Y) 252.20/32.12 = { by axiom 21 (sos_07_1) } 252.20/32.12 fresh5((X + Y) >= Y, true, X, Y, Y) 252.20/32.12 = { by lemma 34 } 252.20/32.12 fresh5(true, true, X, Y, Y) 252.20/32.12 = { by axiom 6 (sos_07_1) } 252.20/32.12 true 252.20/32.12 252.20/32.12 Lemma 45: 0 ==> X = X. 252.20/32.12 Proof: 252.20/32.12 0 ==> X 252.20/32.12 = { by axiom 3 (sos_06) } 252.20/32.12 fresh9(true, true, 0 ==> X, X) 252.20/32.12 = { by lemma 27 } 252.20/32.12 fresh9((X + (X ==> 0)) >= X, true, 0 ==> X, X) 252.20/32.12 = { by axiom 13 (sos_12) } 252.20/32.12 fresh9((0 + (0 ==> X)) >= X, true, 0 ==> X, X) 252.20/32.12 = { by lemma 26 } 252.20/32.12 fresh9((0 ==> X) >= X, true, 0 ==> X, X) 252.20/32.12 = { by axiom 11 (sos_06) } 252.20/32.12 fresh(X >= (0 ==> X), true, 0 ==> X, X) 252.20/32.12 = { by lemma 44 } 252.20/32.12 fresh(true, true, 0 ==> X, X) 252.20/32.12 = { by axiom 4 (sos_06) } 252.20/32.12 X 252.20/32.12 252.20/32.12 Lemma 46: Y ==> (X ==> Y) = 0. 252.20/32.12 Proof: 252.20/32.12 Y ==> (X ==> Y) 252.20/32.12 = { by lemma 33 } 252.20/32.12 fresh(0 >= (Y ==> (X ==> Y)), true, Y ==> (X ==> Y), 0) 252.20/32.12 = { by axiom 21 (sos_07_1) } 252.20/32.12 fresh(fresh5((Y + 0) >= (X ==> Y), true, Y, 0, X ==> Y), true, Y ==> (X ==> Y), 0) 252.20/32.12 = { by lemma 35 } 252.20/32.12 fresh(fresh5(true, true, Y, 0, X ==> Y), true, Y ==> (X ==> Y), 0) 252.20/32.12 = { by axiom 6 (sos_07_1) } 252.20/32.12 fresh(true, true, Y ==> (X ==> Y), 0) 252.20/32.12 = { by axiom 4 (sos_06) } 252.20/32.12 0 252.20/32.12 252.20/32.12 Lemma 47: fresh5(Y >= X, true, Y, 0, X) = 0 >= (Y ==> X). 252.20/32.12 Proof: 252.20/32.12 fresh5(Y >= X, true, Y, 0, X) 252.20/32.12 = { by axiom 15 (sos_03) } 252.20/32.12 fresh5((Y + 0) >= X, true, Y, 0, X) 252.20/32.12 = { by axiom 21 (sos_07_1) } 253.86/32.30 0 >= (Y ==> X) 253.86/32.30 253.86/32.30 Lemma 48: X ==> ((X ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) = (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19. 253.86/32.30 Proof: 253.86/32.30 X ==> ((X ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by lemma 43 } 253.86/32.30 (X + (X ==> sK2_goals_13_X19)) ==> sK3_goals_13_X18 253.86/32.30 = { by axiom 13 (sos_12) } 253.86/32.30 (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> X)) ==> sK3_goals_13_X18 253.86/32.30 = { by axiom 17 (sos_02) } 253.86/32.30 ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18 253.86/32.30 = { by axiom 4 (sos_06) } 253.86/32.30 fresh(true, true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 6 (sos_07_1) } 253.86/32.30 fresh(fresh5(true, true, sK2_goals_13_X19 ==> X, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18, sK2_goals_13_X19), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by lemma 37 } 253.86/32.30 fresh(fresh5(((sK2_goals_13_X19 ==> X) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18)) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, sK2_goals_13_X19 ==> X, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18, sK2_goals_13_X19), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 23 (goals_13) } 253.86/32.30 fresh(fresh5(((sK2_goals_13_X19 ==> X) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18)) >= sK2_goals_13_X19, true, sK2_goals_13_X19 ==> X, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18, sK2_goals_13_X19), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 21 (sos_07_1) } 253.86/32.30 fresh((((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) >= ((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 11 (sos_06) } 253.86/32.30 fresh9(((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 15 (sos_03) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + 0) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by lemma 38 } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + ((((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19) + ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> (sK2_goals_13_X19 ==> X))) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 17 (sos_02) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + ((((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> (sK2_goals_13_X19 ==> X)) + ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19)) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by lemma 25 } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + (((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> (sK2_goals_13_X19 ==> X)) + sK2_goals_13_X19)) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 10 (sos_01) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + ((((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> (sK2_goals_13_X19 ==> X))) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 13 (sos_12) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + ((((sK2_goals_13_X19 ==> X) + ((sK2_goals_13_X19 ==> X) ==> (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19))) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 10 (sos_01) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + (((sK2_goals_13_X19 ==> X) ==> (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19)) + sK2_goals_13_X19)) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 17 (sos_02) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + (sK2_goals_13_X19 + ((sK2_goals_13_X19 ==> X) ==> (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19)))) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by lemma 40 } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + (sK2_goals_13_X19 + 0)) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 15 (sos_03) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) + sK2_goals_13_X19))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 17 (sos_02) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> (sK2_goals_13_X19 + (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by lemma 36 } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> (sK2_goals_13_X19 + (sK2_goals_13_X19 ==> (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18))))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 13 (sos_12) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.30 = { by axiom 4 (sos_06) } 253.86/32.30 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh(true, true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 12 (sos_08) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh(((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19) >= 0, true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 11 (sos_06) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh9(0 >= ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19), true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by lemma 47 } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh9(fresh5((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) >= sK2_goals_13_X19, true, ((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18, 0, sK2_goals_13_X19), true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 23 (goals_13) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh9(fresh5((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) >= (sK2_goals_13_X19 ==> sK3_goals_13_X18), true, ((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18, 0, sK2_goals_13_X19), true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 18 (sos_10) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh9(fresh5(fresh3(sK2_goals_13_X19 >= ((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19), true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, sK3_goals_13_X18), true, ((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18, 0, sK2_goals_13_X19), true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by lemma 44 } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh9(fresh5(fresh3(true, true, sK2_goals_13_X19, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, sK3_goals_13_X18), true, ((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18, 0, sK2_goals_13_X19), true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 8 (sos_10) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh9(fresh5(true, true, ((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18, 0, sK2_goals_13_X19), true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 6 (sos_07_1) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + fresh9(true, true, 0, (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) ==> sK2_goals_13_X19)))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 3 (sos_06) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> ((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18) + 0))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 15 (sos_03) } 253.86/32.31 fresh9((((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) + (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> (((sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18))) >= (((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18), true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by lemma 29 } 253.86/32.31 fresh9(true, true, (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19, ((sK2_goals_13_X19 ==> X) + sK2_goals_13_X19) ==> sK3_goals_13_X18) 253.86/32.31 = { by axiom 3 (sos_06) } 264.34/33.57 (sK2_goals_13_X19 ==> X) ==> sK2_goals_13_X19 264.34/33.57 264.34/33.57 Goal 1 (goals_13_2): sK1_goals_13_X17 >= sK2_goals_13_X19 = true. 264.34/33.57 Proof: 264.34/33.57 sK1_goals_13_X17 >= sK2_goals_13_X19 264.34/33.57 = { by axiom 15 (sos_03) } 264.34/33.57 (sK1_goals_13_X17 + 0) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 4 (sos_06) } 264.34/33.57 (sK1_goals_13_X17 + fresh(true, true, sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 6 (sos_07_1) } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(true, true, sK1_goals_13_X17, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by lemma 39 } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7(sK1_goals_13_X17 >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 15 (sos_03) } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + 0) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 3 (sos_06) } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(true, true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 6 (sos_07_1) } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(true, true, sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 6 (sos_07_1) } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 5 (sos_07) } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(true, true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 5 (sos_07) } 264.34/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6(true, true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.34/33.57 = { by axiom 12 (sos_08) } 264.41/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= 0, true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.57 = { by axiom 3 (sos_06) } 264.41/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= fresh9(true, true, 0, sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.57 = { by axiom 6 (sos_07_1) } 264.41/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= fresh9(fresh5(true, true, sK1_goals_13_X17, 0, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, 0, sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.57 = { by axiom 24 (goals_13_1) } 264.41/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= fresh9(fresh5(sK1_goals_13_X17 >= (sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, 0, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, 0, sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.57 = { by lemma 47 } 264.41/33.57 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= fresh9(0 >= (sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, 0, sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.57 = { by axiom 11 (sos_06) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= fresh((sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)) >= 0, true, 0, sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 12 (sos_08) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= fresh(true, true, 0, sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 4 (sos_06) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(fresh6((sK1_goals_13_X17 ==> sK2_goals_13_X19) >= (sK1_goals_13_X17 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)), true, sK1_goals_13_X17, sK1_goals_13_X17 ==> sK2_goals_13_X19, sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 22 (sos_07) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6((sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)) >= (sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 17 (sos_02) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(fresh6(((sK1_goals_13_X17 ==> sK2_goals_13_X19) + sK1_goals_13_X17) >= (sK1_goals_13_X17 ==> sK3_goals_13_X18), true, sK1_goals_13_X17, (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 22 (sos_07) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5((sK1_goals_13_X17 + ((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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 25 } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(((sK1_goals_13_X17 ==> sK2_goals_13_X19) + (sK1_goals_13_X17 + 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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 17 (sos_02) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5(((sK1_goals_13_X17 + sK1_goals_13_X17) + (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 10 (sos_01) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5((sK1_goals_13_X17 + (sK1_goals_13_X17 + (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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 41 } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(fresh5((sK2_goals_13_X19 + ((sK2_goals_13_X19 ==> sK1_goals_13_X17) + 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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 17 (sos_02) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5(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 ==> sK1_goals_13_X17), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 21 (sos_07_1) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(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), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 23 (goals_13) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(fresh5((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), 0, sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 47 } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh9(0 >= ((sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19), true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 11 (sos_06) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh(((sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19) >= 0, true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 12 (sos_08) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + fresh(true, true, 0, (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 4 (sos_06) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7((sK1_goals_13_X17 + ((sK1_goals_13_X17 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> sK2_goals_13_X19)) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 37 } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5(fresh7(true, true, 0 + 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, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 1 (sos_05) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5((0 + sK1_goals_13_X17) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 17 (sos_02) } 264.41/33.58 (sK1_goals_13_X17 + fresh(fresh5((sK1_goals_13_X17 + 0) >= ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19), true, sK1_goals_13_X17, 0, (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 21 (sos_07_1) } 264.41/33.58 (sK1_goals_13_X17 + fresh(0 >= (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), 0)) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 33 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> sK2_goals_13_X19))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 31 } 264.41/33.58 (sK1_goals_13_X17 + ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> (sK1_goals_13_X17 ==> sK2_goals_13_X19))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 36 } 264.41/33.58 (sK1_goals_13_X17 + ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> (sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK3_goals_13_X18)))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 32 } 264.41/33.58 (sK1_goals_13_X17 + ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> (sK2_goals_13_X19 ==> (sK2_goals_13_X19 + (sK1_goals_13_X17 ==> (sK2_goals_13_X19 ==> sK3_goals_13_X18)))))) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 23 (goals_13) } 264.41/33.58 (sK1_goals_13_X17 + ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> (sK2_goals_13_X19 ==> (sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19))))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 31 } 264.41/33.58 (sK1_goals_13_X17 + (sK2_goals_13_X19 ==> ((sK2_goals_13_X19 ==> sK1_goals_13_X17) ==> (sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19))))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 43 } 264.41/33.58 (sK1_goals_13_X17 + ((sK2_goals_13_X19 + (sK2_goals_13_X19 ==> sK1_goals_13_X17)) ==> (sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)))) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 13 (sos_12) } 264.41/33.58 (sK1_goals_13_X17 + ((sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)) ==> (sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 43 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> (sK2_goals_13_X19 + (sK1_goals_13_X17 ==> sK2_goals_13_X19))))) >= sK2_goals_13_X19 264.41/33.58 = { by axiom 17 (sos_02) } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) + sK2_goals_13_X19)))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 45 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) + (0 ==> sK2_goals_13_X19))))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 46 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) + ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK2_goals_13_X19)) ==> sK2_goals_13_X19))))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 48 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((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 ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18)))))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 45 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) + (0 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> (((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18))))))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 32 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> (0 ==> (((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18))))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 45 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> (((sK1_goals_13_X17 ==> sK2_goals_13_X19) ==> sK2_goals_13_X19) ==> sK3_goals_13_X18)))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 48 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> ((sK2_goals_13_X19 ==> (sK1_goals_13_X17 ==> sK2_goals_13_X19)) ==> sK2_goals_13_X19))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 46 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> (0 ==> sK2_goals_13_X19))) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 45 } 264.41/33.58 (sK1_goals_13_X17 + (sK1_goals_13_X17 ==> sK2_goals_13_X19)) >= sK2_goals_13_X19 264.41/33.58 = { by lemma 28 } 264.41/33.58 true 264.41/33.58 % SZS output end Proof 264.41/33.58 264.41/33.58 RESULT: Theorem (the conjecture is true). 264.41/33.60 EOF