0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.10 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.10/0.31 % Computer : n003.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 960 0.10/0.31 % WCLimit : 120 0.10/0.31 % DateTime : Thu Jul 2 09:17:58 EDT 2020 0.10/0.31 % CPUTime : 421.23/53.54 % SZS status Theorem 421.23/53.54 421.23/53.54 % SZS output start Proof 421.23/53.54 Take the following subset of the input axioms: 426.24/54.21 fof(goals_14, conjecture, ![X17, X18, X19]: ('>='(X19, X17) <= ('>='('==>'(X17, X18), X17) & X19='==>'(X19, X18)))). 426.24/54.21 fof(sos_01, axiom, ![A, B, C]: '+'(A, '+'(B, C))='+'('+'(A, B), C)). 426.24/54.21 fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)). 426.24/54.21 fof(sos_03, axiom, ![A]: '+'(A, '0')=A). 426.24/54.21 fof(sos_05, axiom, ![A]: '>='(A, A)). 426.24/54.21 fof(sos_06, axiom, ![X0, X1, X2]: (('>='(X0, X1) & '>='(X1, X2)) => '>='(X0, X2))). 426.24/54.21 fof(sos_07, axiom, ![X3, X4]: (X4=X3 <= ('>='(X4, X3) & '>='(X3, X4)))). 426.24/54.21 fof(sos_08, axiom, ![X5, X6, X7]: ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))). 426.24/54.21 fof(sos_09, axiom, ![A]: '>='(A, '0')). 426.24/54.21 fof(sos_10, axiom, ![X8, X9, X10]: ('>='('+'(X8, X10), '+'(X9, X10)) <= '>='(X8, X9))). 426.24/54.21 fof(sos_11, axiom, ![X11, X12, X13]: ('>='(X11, X12) => '>='('==>'(X12, X13), '==>'(X11, X13)))). 426.24/54.21 fof(sos_12, axiom, ![X14, X15, X16]: ('>='('==>'(X16, X14), '==>'(X16, X15)) <= '>='(X14, X15))). 426.24/54.21 fof(sos_13, axiom, ![A, B]: '+'(B, '==>'(B, A))='+'(A, '==>'(A, B))). 426.24/54.21 426.24/54.21 Now clausify the problem and encode Horn clauses using encoding 3 of 426.24/54.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 426.24/54.21 We repeatedly replace C & s=t => u=v by the two clauses: 426.24/54.21 fresh(y, y, x1...xn) = u 426.24/54.21 C => fresh(s, t, x1...xn) = v 426.24/54.21 where fresh is a fresh function symbol and x1..xn are the free 426.24/54.21 variables of u and v. 426.24/54.21 A predicate p(X) is encoded as p(X)=true (this is sound, because the 426.24/54.21 input problem has no model of domain size 1). 426.24/54.21 426.24/54.21 The encoding turns the above axioms into the following unit equations and goals: 426.24/54.21 426.24/54.21 Axiom 1 (sos_06): fresh6(X, X, Y, Z, W) = Y >= W. 426.24/54.21 Axiom 2 (sos_06): fresh7(X, X, Y, Z) = true. 426.24/54.21 Axiom 3 (sos_07): fresh(X, X, Y, Z) = Y. 426.24/54.21 Axiom 4 (sos_07): fresh2(X, X, Y, Z) = Z. 426.24/54.21 Axiom 5 (sos_08): fresh8(X, X, Y, Z, W) = true. 426.24/54.21 Axiom 6 (sos_08_1): fresh9(X, X, Y, Z, W) = true. 426.24/54.21 Axiom 7 (sos_10): fresh5(X, X, Y, Z, W) = true. 426.24/54.21 Axiom 8 (sos_11): fresh4(X, X, Y, Z, W) = true. 426.24/54.21 Axiom 9 (sos_12): fresh3(X, X, Y, Z, W) = true. 426.24/54.21 Axiom 10 (sos_01): X + (Y + Z) = (X + Y) + Z. 426.24/54.21 Axiom 11 (sos_08_1): fresh9((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z). 426.24/54.21 Axiom 12 (sos_08): fresh8(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z. 426.24/54.21 Axiom 13 (sos_12): fresh3(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y). 426.24/54.21 Axiom 14 (sos_02): X + Y = Y + X. 426.24/54.21 Axiom 15 (sos_05): X >= X = true. 426.24/54.21 Axiom 16 (sos_06): fresh6(X >= Y, true, Z, X, Y) = fresh7(Z >= X, true, Z, Y). 426.24/54.21 Axiom 17 (sos_11): fresh4(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z). 426.24/54.21 Axiom 18 (sos_07): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X). 426.24/54.21 Axiom 19 (sos_09): X >= 0 = true. 426.24/54.21 Axiom 20 (sos_03): X + 0 = X. 426.24/54.21 Axiom 21 (sos_10): fresh5(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z). 426.24/54.21 Axiom 22 (sos_13): X + (X ==> Y) = Y + (Y ==> X). 426.24/54.21 Axiom 23 (goals_14): sK2_goals_14_X19 = sK2_goals_14_X19 ==> sK3_goals_14_X18. 428.15/54.43 Axiom 24 (goals_14_1): (sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17 = true. 428.15/54.43 428.15/54.43 Lemma 25: Z + (X + (Z ==> Y)) = Y + ((Y ==> Z) + X). 428.15/54.43 Proof: 428.15/54.43 Z + (X + (Z ==> Y)) 428.15/54.43 = { by axiom 14 (sos_02) } 428.15/54.43 Z + ((Z ==> Y) + X) 428.15/54.43 = { by axiom 10 (sos_01) } 428.15/54.43 (Z + (Z ==> Y)) + X 428.15/54.43 = { by axiom 22 (sos_13) } 428.15/54.43 (Y + (Y ==> Z)) + X 428.15/54.43 = { by axiom 10 (sos_01) } 428.15/54.43 Y + ((Y ==> Z) + X) 428.15/54.43 428.15/54.43 Lemma 26: 0 + X = X. 428.15/54.43 Proof: 428.15/54.43 0 + X 428.15/54.43 = { by axiom 14 (sos_02) } 428.15/54.43 X + 0 428.15/54.43 = { by axiom 20 (sos_03) } 428.15/54.43 X 428.15/54.43 428.15/54.43 Lemma 27: (X + Y) >= X = true. 428.15/54.43 Proof: 428.15/54.43 (X + Y) >= X 428.15/54.43 = { by axiom 14 (sos_02) } 428.15/54.43 (Y + X) >= X 428.15/54.43 = { by lemma 26 } 428.15/54.43 (Y + X) >= (0 + X) 428.15/54.43 = { by axiom 21 (sos_10) } 428.15/54.43 fresh5(Y >= 0, true, Y, 0, X) 428.15/54.43 = { by axiom 19 (sos_09) } 428.15/54.43 fresh5(true, true, Y, 0, X) 428.15/54.43 = { by axiom 7 (sos_10) } 428.15/54.43 true 428.15/54.43 428.15/54.43 Lemma 28: (Z ==> (Y ==> X)) >= (Y ==> (Z ==> X)) = true. 428.15/54.43 Proof: 428.15/54.43 (Z ==> (Y ==> X)) >= (Y ==> (Z ==> X)) 428.15/54.43 = { by axiom 11 (sos_08_1) } 428.15/54.43 fresh9((Y + (Z ==> (Y ==> X))) >= (Z ==> X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by axiom 11 (sos_08_1) } 428.15/54.43 fresh9(fresh9((Z + (Y + (Z ==> (Y ==> X)))) >= X, true, Z, Y + (Z ==> (Y ==> X)), X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by axiom 14 (sos_02) } 428.15/54.43 fresh9(fresh9((Z + ((Z ==> (Y ==> X)) + Y)) >= X, true, Z, Y + (Z ==> (Y ==> X)), X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by axiom 10 (sos_01) } 428.15/54.43 fresh9(fresh9(((Z + (Z ==> (Y ==> X))) + Y) >= X, true, Z, Y + (Z ==> (Y ==> X)), X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by axiom 14 (sos_02) } 428.15/54.43 fresh9(fresh9((Y + (Z + (Z ==> (Y ==> X)))) >= X, true, Z, Y + (Z ==> (Y ==> X)), X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by axiom 22 (sos_13) } 428.15/54.43 fresh9(fresh9((Y + ((Y ==> X) + ((Y ==> X) ==> Z))) >= X, true, Z, Y + (Z ==> (Y ==> X)), X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by lemma 25 } 428.15/54.43 fresh9(fresh9((X + (((Y ==> X) ==> Z) + (X ==> Y))) >= X, true, Z, Y + (Z ==> (Y ==> X)), X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by lemma 27 } 428.15/54.43 fresh9(fresh9(true, true, Z, Y + (Z ==> (Y ==> X)), X), true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by axiom 6 (sos_08_1) } 428.15/54.43 fresh9(true, true, Y, Z ==> (Y ==> X), Z ==> X) 428.15/54.43 = { by axiom 6 (sos_08_1) } 428.15/54.44 true 428.15/54.44 428.15/54.44 Lemma 29: Z ==> (Y ==> X) = Y ==> (Z ==> X). 428.15/54.44 Proof: 428.15/54.44 Z ==> (Y ==> X) 428.15/54.44 = { by axiom 3 (sos_07) } 428.15/54.44 fresh(true, true, Z ==> (Y ==> X), Y ==> (Z ==> X)) 428.15/54.44 = { by lemma 28 } 428.15/54.44 fresh((Z ==> (Y ==> X)) >= (Y ==> (Z ==> X)), true, Z ==> (Y ==> X), Y ==> (Z ==> X)) 428.15/54.44 = { by axiom 18 (sos_07) } 428.15/54.44 fresh2((Y ==> (Z ==> X)) >= (Z ==> (Y ==> X)), true, Z ==> (Y ==> X), Y ==> (Z ==> X)) 428.15/54.44 = { by lemma 28 } 428.15/54.44 fresh2(true, true, Z ==> (Y ==> X), Y ==> (Z ==> X)) 428.15/54.44 = { by axiom 4 (sos_07) } 428.15/54.44 Y ==> (Z ==> X) 428.15/54.44 428.15/54.44 Lemma 30: (Y + (Y ==> X)) >= X = true. 428.15/54.44 Proof: 428.15/54.44 (Y + (Y ==> X)) >= X 428.15/54.44 = { by axiom 22 (sos_13) } 428.15/54.44 (X + (X ==> Y)) >= X 428.15/54.44 = { by lemma 27 } 428.15/54.44 true 428.15/54.44 428.15/54.44 Lemma 31: (X + ((X + Y) ==> Z)) >= (Y ==> Z) = true. 428.15/54.44 Proof: 428.15/54.44 (X + ((X + Y) ==> Z)) >= (Y ==> Z) 428.15/54.44 = { by axiom 14 (sos_02) } 428.15/54.44 (X + ((Y + X) ==> Z)) >= (Y ==> Z) 428.15/54.44 = { by axiom 11 (sos_08_1) } 428.15/54.44 fresh9((Y + (X + ((Y + X) ==> Z))) >= Z, true, Y, X + ((Y + X) ==> Z), Z) 428.15/54.44 = { by axiom 10 (sos_01) } 428.15/54.44 fresh9(((Y + X) + ((Y + X) ==> Z)) >= Z, true, Y, X + ((Y + X) ==> Z), Z) 428.15/54.44 = { by lemma 30 } 428.15/54.44 fresh9(true, true, Y, X + ((Y + X) ==> Z), Z) 428.15/54.44 = { by axiom 6 (sos_08_1) } 428.15/54.44 true 428.15/54.44 428.15/54.44 Lemma 32: (Y + X) >= X = true. 428.15/54.44 Proof: 428.15/54.44 (Y + X) >= X 428.15/54.44 = { by axiom 14 (sos_02) } 428.15/54.44 (X + Y) >= X 428.15/54.44 = { by lemma 27 } 428.15/54.44 true 428.15/54.44 428.15/54.44 Lemma 33: Y >= (X ==> Y) = true. 428.15/54.44 Proof: 428.15/54.44 Y >= (X ==> Y) 428.15/54.44 = { by axiom 11 (sos_08_1) } 428.15/54.44 fresh9((X + Y) >= Y, true, X, Y, Y) 428.15/54.44 = { by lemma 32 } 428.15/54.44 fresh9(true, true, X, Y, Y) 428.15/54.44 = { by axiom 6 (sos_08_1) } 428.15/54.44 true 428.15/54.44 428.15/54.44 Lemma 34: 0 ==> X = X. 428.15/54.44 Proof: 428.15/54.44 0 ==> X 428.15/54.44 = { by axiom 4 (sos_07) } 428.15/54.44 fresh2(true, true, X, 0 ==> X) 428.15/54.44 = { by lemma 27 } 428.15/54.44 fresh2((X + (X ==> 0)) >= X, true, X, 0 ==> X) 428.15/54.44 = { by axiom 22 (sos_13) } 428.15/54.44 fresh2((0 + (0 ==> X)) >= X, true, X, 0 ==> X) 428.15/54.44 = { by lemma 26 } 428.15/54.44 fresh2((0 ==> X) >= X, true, X, 0 ==> X) 428.15/54.44 = { by axiom 18 (sos_07) } 428.15/54.44 fresh(X >= (0 ==> X), true, X, 0 ==> X) 428.15/54.44 = { by lemma 33 } 428.15/54.44 fresh(true, true, X, 0 ==> X) 428.15/54.44 = { by axiom 3 (sos_07) } 428.15/54.44 X 428.15/54.44 428.15/54.44 Lemma 35: fresh(0 >= X, true, 0, X) = X. 428.15/54.44 Proof: 428.15/54.44 fresh(0 >= X, true, 0, X) 428.15/54.44 = { by axiom 18 (sos_07) } 428.15/54.44 fresh2(X >= 0, true, 0, X) 428.15/54.44 = { by axiom 19 (sos_09) } 428.15/54.44 fresh2(true, true, 0, X) 428.15/54.44 = { by axiom 4 (sos_07) } 428.15/54.44 X 428.15/54.44 428.15/54.44 Lemma 36: (Z ==> (Y + X)) >= (Z ==> Y) = true. 428.15/54.44 Proof: 428.15/54.44 (Z ==> (Y + X)) >= (Z ==> Y) 428.15/54.44 = { by axiom 13 (sos_12) } 428.15/54.44 fresh3((Y + X) >= Y, true, Y + X, Y, Z) 428.15/54.44 = { by lemma 27 } 428.15/54.44 fresh3(true, true, Y + X, Y, Z) 428.15/54.44 = { by axiom 9 (sos_12) } 428.15/54.44 true 428.15/54.44 428.15/54.44 Lemma 37: (X + Y) ==> X = 0. 428.15/54.44 Proof: 428.15/54.44 (X + Y) ==> X 428.15/54.44 = { by axiom 3 (sos_07) } 428.15/54.44 fresh(true, true, (X + Y) ==> X, 0) 428.15/54.44 = { by axiom 19 (sos_09) } 428.15/54.44 fresh(((X + Y) ==> X) >= 0, true, (X + Y) ==> X, 0) 428.15/54.44 = { by axiom 18 (sos_07) } 428.15/54.44 fresh2(0 >= ((X + Y) ==> X), true, (X + Y) ==> X, 0) 428.15/54.44 = { by axiom 3 (sos_07) } 428.15/54.44 fresh2(fresh(true, true, 0, (X + Y) ==> (X + Y)) >= ((X + Y) ==> X), true, (X + Y) ==> X, 0) 428.15/54.44 = { by axiom 6 (sos_08_1) } 428.15/54.44 fresh2(fresh(fresh9(true, true, X + Y, 0, X + Y), true, 0, (X + Y) ==> (X + Y)) >= ((X + Y) ==> X), true, (X + Y) ==> X, 0) 428.15/54.44 = { by lemma 27 } 428.15/54.44 fresh2(fresh(fresh9(((X + Y) + 0) >= (X + Y), true, X + Y, 0, X + Y), true, 0, (X + Y) ==> (X + Y)) >= ((X + Y) ==> X), true, (X + Y) ==> X, 0) 428.15/54.44 = { by axiom 11 (sos_08_1) } 428.15/54.44 fresh2(fresh(0 >= ((X + Y) ==> (X + Y)), true, 0, (X + Y) ==> (X + Y)) >= ((X + Y) ==> X), true, (X + Y) ==> X, 0) 428.15/54.44 = { by lemma 35 } 428.15/54.44 fresh2(((X + Y) ==> (X + Y)) >= ((X + Y) ==> X), true, (X + Y) ==> X, 0) 428.15/54.44 = { by lemma 36 } 428.15/54.44 fresh2(true, true, (X + Y) ==> X, 0) 428.15/54.44 = { by axiom 4 (sos_07) } 428.15/54.44 0 428.15/54.44 428.15/54.44 Lemma 38: Y >= ((Y ==> X) ==> X) = true. 428.15/54.44 Proof: 428.15/54.44 Y >= ((Y ==> X) ==> X) 428.15/54.44 = { by axiom 20 (sos_03) } 428.15/54.44 (Y + 0) >= ((Y ==> X) ==> X) 428.15/54.44 = { by lemma 37 } 428.15/54.44 (Y + ((X + (X ==> Y)) ==> X)) >= ((Y ==> X) ==> X) 428.15/54.44 = { by axiom 22 (sos_13) } 428.15/54.44 (Y + ((Y + (Y ==> X)) ==> X)) >= ((Y ==> X) ==> X) 428.15/54.44 = { by lemma 31 } 428.15/54.44 true 428.15/54.44 428.15/54.44 Lemma 39: fresh6(Z >= Y, true, X + Z, Z, Y) = true. 428.15/54.44 Proof: 428.15/54.44 fresh6(Z >= Y, true, X + Z, Z, Y) 428.15/54.44 = { by axiom 16 (sos_06) } 428.15/54.44 fresh7((X + Z) >= Z, true, X + Z, Y) 428.15/54.44 = { by lemma 32 } 428.15/54.44 fresh7(true, true, X + Z, Y) 428.15/54.44 = { by axiom 2 (sos_06) } 428.15/54.45 true 428.15/54.45 428.15/54.45 Lemma 40: Y ==> ((Y ==> X) ==> X) = 0. 428.15/54.45 Proof: 428.15/54.45 Y ==> ((Y ==> X) ==> X) 428.15/54.45 = { by lemma 35 } 428.15/54.45 fresh(0 >= (Y ==> ((Y ==> X) ==> X)), true, 0, Y ==> ((Y ==> X) ==> X)) 428.15/54.45 = { by axiom 11 (sos_08_1) } 428.15/54.45 fresh(fresh9((Y + 0) >= ((Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, 0, Y ==> ((Y ==> X) ==> X)) 428.15/54.45 = { by axiom 14 (sos_02) } 428.15/54.45 fresh(fresh9((0 + Y) >= ((Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, 0, Y ==> ((Y ==> X) ==> X)) 428.15/54.45 = { by axiom 1 (sos_06) } 428.15/54.45 fresh(fresh9(fresh6(true, true, 0 + Y, Y, (Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, 0, Y ==> ((Y ==> X) ==> X)) 428.15/54.45 = { by lemma 38 } 428.15/54.45 fresh(fresh9(fresh6(Y >= ((Y ==> X) ==> X), true, 0 + Y, Y, (Y ==> X) ==> X), true, Y, 0, (Y ==> X) ==> X), true, 0, Y ==> ((Y ==> X) ==> X)) 428.15/54.45 = { by lemma 39 } 428.15/54.45 fresh(fresh9(true, true, Y, 0, (Y ==> X) ==> X), true, 0, Y ==> ((Y ==> X) ==> X)) 428.15/54.45 = { by axiom 6 (sos_08_1) } 428.15/54.45 fresh(true, true, 0, Y ==> ((Y ==> X) ==> X)) 428.15/54.45 = { by axiom 3 (sos_07) } 428.15/54.45 0 428.15/54.45 428.15/54.45 Lemma 41: (Z + (Y + (Y ==> (Z ==> X)))) ==> X = 0. 428.15/54.45 Proof: 428.15/54.45 (Z + (Y + (Y ==> (Z ==> X)))) ==> X 428.15/54.45 = { by axiom 22 (sos_13) } 428.15/54.45 (Z + ((Z ==> X) + ((Z ==> X) ==> Y))) ==> X 428.15/54.45 = { by lemma 25 } 428.15/54.45 (X + (((Z ==> X) ==> Y) + (X ==> Z))) ==> X 428.15/54.45 = { by lemma 37 } 428.15/54.45 0 428.15/54.45 428.15/54.45 Lemma 42: (Z + (Y + (Z ==> (Y ==> X)))) ==> X = 0. 428.15/54.45 Proof: 428.15/54.45 (Z + (Y + (Z ==> (Y ==> X)))) ==> X 428.15/54.45 = { by axiom 14 (sos_02) } 428.15/54.45 (Z + ((Z ==> (Y ==> X)) + Y)) ==> X 428.15/54.45 = { by axiom 10 (sos_01) } 428.15/54.45 ((Z + (Z ==> (Y ==> X))) + Y) ==> X 428.15/54.45 = { by axiom 14 (sos_02) } 428.15/54.45 (Y + (Z + (Z ==> (Y ==> X)))) ==> X 428.15/54.45 = { by lemma 41 } 428.15/54.47 0 428.15/54.47 428.15/54.47 Lemma 43: (Y + Z) ==> X = Y ==> (Z ==> X). 428.15/54.47 Proof: 428.15/54.47 (Y + Z) ==> X 428.15/54.47 = { by axiom 14 (sos_02) } 428.15/54.47 (Z + Y) ==> X 428.15/54.47 = { by axiom 3 (sos_07) } 428.15/54.47 fresh(true, true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.15/54.47 = { by axiom 6 (sos_08_1) } 428.15/54.47 fresh(fresh9(true, true, Y, (Y + Z) ==> X, Z ==> X), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.15/54.47 = { by lemma 31 } 428.15/54.47 fresh(fresh9((Y + ((Y + Z) ==> X)) >= (Z ==> X), true, Y, (Y + Z) ==> X, Z ==> X), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.15/54.47 = { by axiom 11 (sos_08_1) } 428.15/54.47 fresh(((Y + Z) ==> X) >= (Y ==> (Z ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.15/54.47 = { by axiom 14 (sos_02) } 428.15/54.47 fresh(((Z + Y) ==> X) >= (Y ==> (Z ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.15/54.47 = { by lemma 29 } 428.95/54.47 fresh(((Z + Y) ==> X) >= (Z ==> (Y ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by axiom 18 (sos_07) } 428.95/54.47 fresh2((Z ==> (Y ==> X)) >= ((Z + Y) ==> X), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 29 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Z + Y) ==> X), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by axiom 14 (sos_02) } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> X), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 34 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (0 ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 42 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (((Z + (Y + (Z ==> (Y ==> ((Z ==> (Y ==> X)) ==> X))))) ==> ((Z ==> (Y ==> X)) ==> X)) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 29 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (((Z + (Y + (Z ==> ((Z ==> (Y ==> X)) ==> (Y ==> X))))) ==> ((Z ==> (Y ==> X)) ==> X)) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 40 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (((Z + (Y + 0)) ==> ((Z ==> (Y ==> X)) ==> X)) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by axiom 20 (sos_03) } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (((Z + Y) ==> ((Z ==> (Y ==> X)) ==> X)) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by axiom 14 (sos_02) } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (((Y + Z) ==> ((Z ==> (Y ==> X)) ==> X)) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 29 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (((Y + Z) ==> ((Y ==> (Z ==> X)) ==> X)) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 29 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= ((Y + Z) ==> (((Y ==> (Z ==> X)) ==> ((Y + Z) ==> X)) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 29 } 428.95/54.47 fresh2((Y ==> (Z ==> X)) >= (((Y ==> (Z ==> X)) ==> ((Y + Z) ==> X)) ==> ((Y + Z) ==> X)), true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by lemma 38 } 428.95/54.47 fresh2(true, true, (Z + Y) ==> X, Z ==> (Y ==> X)) 428.95/54.47 = { by axiom 4 (sos_07) } 428.95/54.47 Z ==> (Y ==> X) 428.95/54.47 = { by lemma 29 } 428.95/54.47 Y ==> (Z ==> X) 428.95/54.47 428.95/54.47 Lemma 44: (X + ((X + sK2_goals_14_X19) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19 = true. 428.95/54.47 Proof: 428.95/54.47 (X + ((X + sK2_goals_14_X19) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19 428.95/54.47 = { by axiom 23 (goals_14) } 428.95/54.47 (X + ((X + sK2_goals_14_X19) ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18) 428.95/54.47 = { by lemma 31 } 428.95/54.47 true 428.95/54.47 428.95/54.47 Lemma 45: X + (Y + Z) = Y + (X + Z). 428.95/54.47 Proof: 428.95/54.47 X + (Y + Z) 428.95/54.47 = { by axiom 14 (sos_02) } 428.95/54.47 (Y + Z) + X 428.95/54.47 = { by axiom 10 (sos_01) } 428.95/54.47 Y + (Z + X) 428.95/54.47 = { by axiom 14 (sos_02) } 428.95/54.47 Y + (X + Z) 428.95/54.47 428.95/54.47 Lemma 46: (X + Y) >= (Z ==> X) = true. 428.95/54.47 Proof: 428.95/54.47 (X + Y) >= (Z ==> X) 428.95/54.47 = { by axiom 11 (sos_08_1) } 428.95/54.47 fresh9((Z + (X + Y)) >= X, true, Z, X + Y, X) 428.95/54.47 = { by axiom 14 (sos_02) } 428.95/54.47 fresh9((Z + (Y + X)) >= X, true, Z, X + Y, X) 428.95/54.47 = { by lemma 45 } 428.95/54.47 fresh9((Y + (Z + X)) >= X, true, Z, X + Y, X) 428.95/54.47 = { by axiom 10 (sos_01) } 428.95/54.47 fresh9(((Y + Z) + X) >= X, true, Z, X + Y, X) 428.95/54.47 = { by lemma 32 } 428.95/54.47 fresh9(true, true, Z, X + Y, X) 428.95/54.47 = { by axiom 6 (sos_08_1) } 428.95/54.47 true 428.95/54.47 428.95/54.47 Lemma 47: sK2_goals_14_X19 + sK2_goals_14_X19 = sK3_goals_14_X18. 428.95/54.47 Proof: 428.95/54.47 sK2_goals_14_X19 + sK2_goals_14_X19 428.95/54.47 = { by axiom 23 (goals_14) } 428.95/54.47 sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK3_goals_14_X18) 428.95/54.47 = { by axiom 22 (sos_13) } 428.95/54.47 sK3_goals_14_X18 + (sK3_goals_14_X18 ==> sK2_goals_14_X19) 428.95/54.47 = { by lemma 35 } 428.95/54.47 sK3_goals_14_X18 + fresh(0 >= (sK3_goals_14_X18 ==> sK2_goals_14_X19), true, 0, sK3_goals_14_X18 ==> sK2_goals_14_X19) 428.95/54.47 = { by axiom 11 (sos_08_1) } 428.95/54.47 sK3_goals_14_X18 + fresh(fresh9((sK3_goals_14_X18 + 0) >= sK2_goals_14_X19, true, sK3_goals_14_X18, 0, sK2_goals_14_X19), true, 0, sK3_goals_14_X18 ==> sK2_goals_14_X19) 428.95/54.47 = { by axiom 23 (goals_14) } 428.95/54.47 sK3_goals_14_X18 + fresh(fresh9((sK3_goals_14_X18 + 0) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true, sK3_goals_14_X18, 0, sK2_goals_14_X19), true, 0, sK3_goals_14_X18 ==> sK2_goals_14_X19) 428.95/54.47 = { by lemma 46 } 428.95/54.47 sK3_goals_14_X18 + fresh(fresh9(true, true, sK3_goals_14_X18, 0, sK2_goals_14_X19), true, 0, sK3_goals_14_X18 ==> sK2_goals_14_X19) 428.95/54.47 = { by axiom 6 (sos_08_1) } 428.95/54.47 sK3_goals_14_X18 + fresh(true, true, 0, sK3_goals_14_X18 ==> sK2_goals_14_X19) 428.95/54.47 = { by axiom 3 (sos_07) } 428.95/54.47 sK3_goals_14_X18 + 0 428.95/54.47 = { by axiom 20 (sos_03) } 428.95/54.49 sK3_goals_14_X18 428.95/54.49 428.95/54.49 Lemma 48: sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18) = X ==> sK2_goals_14_X19. 428.95/54.49 Proof: 428.95/54.49 sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18) 428.95/54.49 = { by axiom 4 (sos_07) } 428.95/54.49 fresh2(true, true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 6 (sos_08_1) } 428.95/54.49 fresh2(fresh9(true, true, X, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18), sK2_goals_14_X19), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by lemma 44 } 428.95/54.49 fresh2(fresh9(((X + (sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18))) + (((X + (sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18))) + sK2_goals_14_X19) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19, true, X, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18), sK2_goals_14_X19), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 14 (sos_02) } 428.95/54.49 fresh2(fresh9(((X + (sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18))) + ((sK2_goals_14_X19 + (X + (sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19, true, X, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18), sK2_goals_14_X19), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by lemma 42 } 428.95/54.49 fresh2(fresh9(((X + (sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18))) + 0) >= sK2_goals_14_X19, true, X, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18), sK2_goals_14_X19), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 10 (sos_01) } 428.95/54.49 fresh2(fresh9((X + ((sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) + 0)) >= sK2_goals_14_X19, true, X, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18), sK2_goals_14_X19), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 20 (sos_03) } 428.95/54.49 fresh2(fresh9((X + (sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18))) >= sK2_goals_14_X19, true, X, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18), sK2_goals_14_X19), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 11 (sos_08_1) } 428.95/54.49 fresh2((sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) >= (X ==> sK2_goals_14_X19), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 18 (sos_07) } 428.95/54.49 fresh((X ==> sK2_goals_14_X19) >= (sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 11 (sos_08_1) } 428.95/54.49 fresh(fresh9((sK2_goals_14_X19 + (X ==> sK2_goals_14_X19)) >= (X ==> sK3_goals_14_X18), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 14 (sos_02) } 428.95/54.49 fresh(fresh9(((X ==> sK2_goals_14_X19) + sK2_goals_14_X19) >= (X ==> sK3_goals_14_X18), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by lemma 47 } 428.95/54.49 fresh(fresh9(((X ==> sK2_goals_14_X19) + sK2_goals_14_X19) >= (X ==> (sK2_goals_14_X19 + sK2_goals_14_X19)), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 11 (sos_08_1) } 428.95/54.49 fresh(fresh9(fresh9((X + ((X ==> sK2_goals_14_X19) + sK2_goals_14_X19)) >= (sK2_goals_14_X19 + sK2_goals_14_X19), true, X, (X ==> sK2_goals_14_X19) + sK2_goals_14_X19, sK2_goals_14_X19 + sK2_goals_14_X19), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 10 (sos_01) } 428.95/54.49 fresh(fresh9(fresh9(((X + (X ==> sK2_goals_14_X19)) + sK2_goals_14_X19) >= (sK2_goals_14_X19 + sK2_goals_14_X19), true, X, (X ==> sK2_goals_14_X19) + sK2_goals_14_X19, sK2_goals_14_X19 + sK2_goals_14_X19), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 21 (sos_10) } 428.95/54.49 fresh(fresh9(fresh9(fresh5((X + (X ==> sK2_goals_14_X19)) >= sK2_goals_14_X19, true, X + (X ==> sK2_goals_14_X19), sK2_goals_14_X19, sK2_goals_14_X19), true, X, (X ==> sK2_goals_14_X19) + sK2_goals_14_X19, sK2_goals_14_X19 + sK2_goals_14_X19), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by lemma 30 } 428.95/54.49 fresh(fresh9(fresh9(fresh5(true, true, X + (X ==> sK2_goals_14_X19), sK2_goals_14_X19, sK2_goals_14_X19), true, X, (X ==> sK2_goals_14_X19) + sK2_goals_14_X19, sK2_goals_14_X19 + sK2_goals_14_X19), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 7 (sos_10) } 428.95/54.49 fresh(fresh9(fresh9(true, true, X, (X ==> sK2_goals_14_X19) + sK2_goals_14_X19, sK2_goals_14_X19 + sK2_goals_14_X19), true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 6 (sos_08_1) } 428.95/54.49 fresh(fresh9(true, true, sK2_goals_14_X19, X ==> sK2_goals_14_X19, X ==> sK3_goals_14_X18), true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 6 (sos_08_1) } 428.95/54.49 fresh(true, true, X ==> sK2_goals_14_X19, sK2_goals_14_X19 ==> (X ==> sK3_goals_14_X18)) 428.95/54.49 = { by axiom 3 (sos_07) } 428.95/54.49 X ==> sK2_goals_14_X19 428.95/54.49 428.95/54.49 Lemma 49: fresh9(Y >= X, true, Y, 0, X) = 0 >= (Y ==> X). 428.95/54.49 Proof: 428.95/54.49 fresh9(Y >= X, true, Y, 0, X) 428.95/54.49 = { by axiom 20 (sos_03) } 428.95/54.49 fresh9((Y + 0) >= X, true, Y, 0, X) 428.95/54.49 = { by axiom 11 (sos_08_1) } 428.95/54.49 0 >= (Y ==> X) 428.95/54.49 428.95/54.49 Lemma 50: ((Z ==> Y) ==> X) >= (Y ==> X) = true. 428.95/54.49 Proof: 428.95/54.49 ((Z ==> Y) ==> X) >= (Y ==> X) 428.95/54.49 = { by axiom 17 (sos_11) } 428.95/54.49 fresh4(Y >= (Z ==> Y), true, Y, Z ==> Y, X) 428.95/54.49 = { by lemma 33 } 428.95/54.49 fresh4(true, true, Y, Z ==> Y, X) 428.95/54.49 = { by axiom 8 (sos_11) } 430.22/54.69 true 430.22/54.69 430.22/54.69 Lemma 51: X ==> ((X ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) = (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19. 430.22/54.69 Proof: 430.22/54.69 X ==> ((X ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) 430.22/54.69 = { by lemma 43 } 430.22/54.69 (X + (X ==> sK2_goals_14_X19)) ==> sK3_goals_14_X18 430.22/54.69 = { by axiom 22 (sos_13) } 430.22/54.69 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> X)) ==> sK3_goals_14_X18 430.22/54.69 = { by axiom 14 (sos_02) } 430.22/54.69 ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18 430.22/54.69 = { by axiom 3 (sos_07) } 430.22/54.69 fresh(true, true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 6 (sos_08_1) } 430.22/54.69 fresh(fresh9(true, true, sK2_goals_14_X19 ==> X, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK2_goals_14_X19), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 44 } 430.22/54.69 fresh(fresh9(((sK2_goals_14_X19 ==> X) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19, true, sK2_goals_14_X19 ==> X, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK2_goals_14_X19), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 11 (sos_08_1) } 430.22/54.69 fresh((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= ((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 18 (sos_07) } 430.22/54.69 fresh2(((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) >= (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 20 (sos_03) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + 0) >= (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 41 } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 20 (sos_03) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= (((sK2_goals_14_X19 ==> X) + (sK2_goals_14_X19 + 0)) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 10 (sos_01) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + 0) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 37 } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + ((((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 ==> X))) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 14 (sos_02) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + ((((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 ==> X)) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19)) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 45 } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + (((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 ==> X)) + sK2_goals_14_X19)) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 10 (sos_01) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + ((((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 ==> X))) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 22 (sos_13) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) + ((sK2_goals_14_X19 ==> X) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19))) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 10 (sos_01) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + (((sK2_goals_14_X19 ==> X) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19)) + sK2_goals_14_X19)) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 14 (sos_02) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + (sK2_goals_14_X19 + ((sK2_goals_14_X19 ==> X) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19)))) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 40 } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + (sK2_goals_14_X19 + 0)) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 20 (sos_03) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) + sK2_goals_14_X19))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 14 (sos_02) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (sK2_goals_14_X19 + (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK2_goals_14_X19)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 48 } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18))))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 22 (sos_13) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 3 (sos_07) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + fresh(true, true, (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19, 0)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 19 (sos_09) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + fresh(((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) >= 0, true, (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19, 0)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 18 (sos_07) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + fresh2(0 >= ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19), true, (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19, 0)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 49 } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + fresh2(fresh9((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) >= sK2_goals_14_X19, true, ((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18, 0, sK2_goals_14_X19), true, (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19, 0)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 23 (goals_14) } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + fresh2(fresh9((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18, 0, sK2_goals_14_X19), true, (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19, 0)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by lemma 50 } 430.22/54.69 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + fresh2(fresh9(true, true, ((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18, 0, sK2_goals_14_X19), true, (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19, 0)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.69 = { by axiom 6 (sos_08_1) } 430.22/54.70 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + fresh2(true, true, (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK2_goals_14_X19, 0)))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.22/54.70 = { by axiom 4 (sos_07) } 430.78/54.70 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) + 0))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.78/54.70 = { by axiom 20 (sos_03) } 430.78/54.70 fresh2((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + ((((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) ==> sK3_goals_14_X18)) >= ((((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) + (((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> (((sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18))) ==> sK3_goals_14_X18), true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.78/54.70 = { by lemma 31 } 430.78/54.70 fresh2(true, true, ((sK2_goals_14_X19 ==> X) + sK2_goals_14_X19) ==> sK3_goals_14_X18, (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19) 430.78/54.70 = { by axiom 4 (sos_07) } 430.78/54.70 (sK2_goals_14_X19 ==> X) ==> sK2_goals_14_X19 430.78/54.70 430.78/54.70 Lemma 52: (Z ==> Y) + ((Z ==> Y) ==> X) = X + (Z ==> (X ==> Y)). 430.78/54.70 Proof: 430.78/54.70 (Z ==> Y) + ((Z ==> Y) ==> X) 430.78/54.70 = { by axiom 22 (sos_13) } 430.78/54.70 X + (X ==> (Z ==> Y)) 430.78/54.70 = { by lemma 29 } 430.78/54.70 X + (Z ==> (X ==> Y)) 430.78/54.70 430.78/54.70 Lemma 53: (sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17 = 0. 430.78/54.70 Proof: 430.78/54.70 (sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17 430.78/54.70 = { by axiom 3 (sos_07) } 430.78/54.70 fresh(true, true, (sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 19 (sos_09) } 430.78/54.70 fresh(((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17) >= 0, true, (sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 18 (sos_07) } 430.78/54.70 fresh2(0 >= ((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, 0) 430.78/54.70 = { by lemma 49 } 430.78/54.70 fresh2(fresh9((sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17, true, sK1_goals_14_X17 ==> sK3_goals_14_X18, 0, sK1_goals_14_X17), true, (sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 24 (goals_14_1) } 430.78/54.70 fresh2(fresh9(true, true, sK1_goals_14_X17 ==> sK3_goals_14_X18, 0, sK1_goals_14_X17), true, (sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 6 (sos_08_1) } 430.78/54.70 fresh2(true, true, (sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 4 (sos_07) } 430.78/54.70 0 430.78/54.70 430.78/54.70 Lemma 54: sK3_goals_14_X18 ==> sK1_goals_14_X17 = 0. 430.78/54.70 Proof: 430.78/54.70 sK3_goals_14_X18 ==> sK1_goals_14_X17 430.78/54.70 = { by axiom 3 (sos_07) } 430.78/54.70 fresh(true, true, sK3_goals_14_X18 ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 19 (sos_09) } 430.78/54.70 fresh((sK3_goals_14_X18 ==> sK1_goals_14_X17) >= 0, true, sK3_goals_14_X18 ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 18 (sos_07) } 430.78/54.70 fresh2(0 >= (sK3_goals_14_X18 ==> sK1_goals_14_X17), true, sK3_goals_14_X18 ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by lemma 53 } 430.78/54.70 fresh2(((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17) >= (sK3_goals_14_X18 ==> sK1_goals_14_X17), true, sK3_goals_14_X18 ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by lemma 50 } 430.78/54.70 fresh2(true, true, sK3_goals_14_X18 ==> sK1_goals_14_X17, 0) 430.78/54.70 = { by axiom 4 (sos_07) } 430.78/54.70 0 430.78/54.70 430.78/54.70 Lemma 55: Y ==> (X ==> Y) = 0. 430.78/54.70 Proof: 430.78/54.70 Y ==> (X ==> Y) 430.78/54.70 = { by lemma 35 } 430.78/54.70 fresh(0 >= (Y ==> (X ==> Y)), true, 0, Y ==> (X ==> Y)) 430.78/54.70 = { by axiom 11 (sos_08_1) } 430.78/54.70 fresh(fresh9((Y + 0) >= (X ==> Y), true, Y, 0, X ==> Y), true, 0, Y ==> (X ==> Y)) 430.78/54.70 = { by lemma 46 } 430.78/54.70 fresh(fresh9(true, true, Y, 0, X ==> Y), true, 0, Y ==> (X ==> Y)) 430.78/54.70 = { by axiom 6 (sos_08_1) } 430.78/54.70 fresh(true, true, 0, Y ==> (X ==> Y)) 430.78/54.70 = { by axiom 3 (sos_07) } 430.78/54.72 0 430.78/54.72 430.78/54.72 Lemma 56: X ==> (X + (Y ==> (X ==> Z))) = X ==> (Y ==> Z). 430.78/54.72 Proof: 430.78/54.72 X ==> (X + (Y ==> (X ==> Z))) 430.78/54.72 = { by lemma 52 } 430.78/54.72 X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)) 430.78/54.72 = { by axiom 3 (sos_07) } 430.78/54.72 fresh(true, true, X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)), X ==> (Y ==> Z)) 430.78/54.72 = { by lemma 36 } 430.78/54.72 fresh((X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))) >= (X ==> (Y ==> Z)), true, X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)), X ==> (Y ==> Z)) 430.78/54.72 = { by axiom 18 (sos_07) } 430.78/54.72 fresh2((X ==> (Y ==> Z)) >= (X ==> ((Y ==> Z) + ((Y ==> Z) ==> X))), true, X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)), X ==> (Y ==> Z)) 430.78/54.72 = { by axiom 22 (sos_13) } 430.78/54.72 fresh2((X ==> (Y ==> Z)) >= (X ==> (X + (X ==> (Y ==> Z)))), true, X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)), X ==> (Y ==> Z)) 430.78/54.72 = { by axiom 11 (sos_08_1) } 430.78/54.72 fresh2(fresh9((X + (X ==> (Y ==> Z))) >= (X + (X ==> (Y ==> Z))), true, X, X ==> (Y ==> Z), X + (X ==> (Y ==> Z))), true, X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)), X ==> (Y ==> Z)) 430.78/54.72 = { by axiom 15 (sos_05) } 430.78/54.72 fresh2(fresh9(true, true, X, X ==> (Y ==> Z), X + (X ==> (Y ==> Z))), true, X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)), X ==> (Y ==> Z)) 430.78/54.72 = { by axiom 6 (sos_08_1) } 430.78/54.72 fresh2(true, true, X ==> ((Y ==> Z) + ((Y ==> Z) ==> X)), X ==> (Y ==> Z)) 430.78/54.72 = { by axiom 4 (sos_07) } 430.78/54.72 X ==> (Y ==> Z) 430.78/54.72 430.78/54.72 Lemma 57: (X ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 + (X ==> sK2_goals_14_X19)) = sK2_goals_14_X19. 430.78/54.72 Proof: 430.78/54.72 (X ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 + (X ==> sK2_goals_14_X19)) 430.78/54.72 = { by axiom 14 (sos_02) } 430.78/54.72 (X ==> sK2_goals_14_X19) ==> ((X ==> sK2_goals_14_X19) + sK2_goals_14_X19) 430.78/54.72 = { by lemma 34 } 430.78/54.72 (X ==> sK2_goals_14_X19) ==> ((X ==> sK2_goals_14_X19) + (0 ==> sK2_goals_14_X19)) 430.78/54.72 = { by lemma 55 } 430.78/54.72 (X ==> sK2_goals_14_X19) ==> ((X ==> sK2_goals_14_X19) + ((sK2_goals_14_X19 ==> (X ==> sK2_goals_14_X19)) ==> sK2_goals_14_X19)) 430.78/54.72 = { by lemma 51 } 430.78/54.72 (X ==> sK2_goals_14_X19) ==> ((X ==> sK2_goals_14_X19) + ((X ==> sK2_goals_14_X19) ==> (((X ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18))) 430.78/54.72 = { by lemma 34 } 430.78/54.72 (X ==> sK2_goals_14_X19) ==> ((X ==> sK2_goals_14_X19) + (0 ==> ((X ==> sK2_goals_14_X19) ==> (((X ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)))) 430.78/54.72 = { by lemma 56 } 430.78/54.72 (X ==> sK2_goals_14_X19) ==> (0 ==> (((X ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)) 430.78/54.72 = { by lemma 34 } 430.78/54.72 (X ==> sK2_goals_14_X19) ==> (((X ==> sK2_goals_14_X19) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18) 430.78/54.72 = { by lemma 51 } 430.78/54.72 (sK2_goals_14_X19 ==> (X ==> sK2_goals_14_X19)) ==> sK2_goals_14_X19 430.78/54.72 = { by lemma 55 } 430.78/54.72 0 ==> sK2_goals_14_X19 430.78/54.72 = { by lemma 34 } 436.20/55.38 sK2_goals_14_X19 436.20/55.38 436.20/55.38 Goal 1 (goals_14_2): sK2_goals_14_X19 >= sK1_goals_14_X17 = true. 436.20/55.38 Proof: 436.20/55.38 sK2_goals_14_X19 >= sK1_goals_14_X17 436.20/55.38 = { by axiom 20 (sos_03) } 436.20/55.38 (sK2_goals_14_X19 + 0) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 54 } 436.20/55.38 (sK2_goals_14_X19 + (sK3_goals_14_X18 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 4 (sos_07) } 436.20/55.38 (sK2_goals_14_X19 + fresh2(true, true, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), sK3_goals_14_X18 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 6 (sos_08_1) } 436.20/55.38 (sK2_goals_14_X19 + fresh2(fresh9(true, true, sK2_goals_14_X19, sK3_goals_14_X18 ==> sK1_goals_14_X17, 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)) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 31 } 436.20/55.38 (sK2_goals_14_X19 + fresh2(fresh9((sK2_goals_14_X19 + ((sK2_goals_14_X19 + sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true, sK2_goals_14_X19, sK3_goals_14_X18 ==> sK1_goals_14_X17, 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)) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 47 } 436.20/55.38 (sK2_goals_14_X19 + fresh2(fresh9((sK2_goals_14_X19 + (sK3_goals_14_X18 ==> sK1_goals_14_X17)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true, sK2_goals_14_X19, sK3_goals_14_X18 ==> sK1_goals_14_X17, 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)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 11 (sos_08_1) } 436.20/55.38 (sK2_goals_14_X19 + fresh2((sK3_goals_14_X18 ==> sK1_goals_14_X17) >= (sK2_goals_14_X19 ==> (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)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 18 (sos_07) } 436.20/55.38 (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), true, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), sK3_goals_14_X18 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 11 (sos_08_1) } 436.20/55.38 (sK2_goals_14_X19 + fresh(fresh9((sK3_goals_14_X18 + (sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true, sK3_goals_14_X18, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), 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)) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 47 } 436.20/55.38 (sK2_goals_14_X19 + fresh(fresh9(((sK2_goals_14_X19 + sK2_goals_14_X19) + (sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true, sK3_goals_14_X18, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), 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)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 10 (sos_01) } 436.20/55.38 (sK2_goals_14_X19 + fresh(fresh9((sK2_goals_14_X19 + (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17)))) >= sK1_goals_14_X17, true, sK3_goals_14_X18, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), 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)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 12 (sos_08) } 436.20/55.38 (sK2_goals_14_X19 + fresh(fresh9(fresh8((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17))) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true, sK2_goals_14_X19, sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17)), sK1_goals_14_X17), true, sK3_goals_14_X18, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), 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)) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 30 } 436.20/55.38 (sK2_goals_14_X19 + fresh(fresh9(fresh8(true, true, sK2_goals_14_X19, sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17)), sK1_goals_14_X17), true, sK3_goals_14_X18, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), 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)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 5 (sos_08) } 436.20/55.38 (sK2_goals_14_X19 + fresh(fresh9(true, true, sK3_goals_14_X18, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), 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)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 6 (sos_08_1) } 436.20/55.38 (sK2_goals_14_X19 + fresh(true, true, sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17), sK3_goals_14_X18 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 3 (sos_07) } 436.20/55.38 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK2_goals_14_X19 ==> sK1_goals_14_X17))) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 22 (sos_13) } 436.20/55.38 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK2_goals_14_X19 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19)) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 51 } 436.20/55.38 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + (sK1_goals_14_X17 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK3_goals_14_X18))) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 29 } 436.20/55.38 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 20 (sos_03) } 436.20/55.38 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + 0))) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 3 (sos_07) } 436.20/55.38 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(true, true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 6 (sos_08_1) } 436.20/55.38 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(fresh9(true, true, sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19), 0, (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.38 = { by lemma 39 } 436.20/55.38 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(fresh9(fresh6((sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) >= ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0 + (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19), (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((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), 0, (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.38 = { by axiom 17 (sos_11) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(fresh9(fresh6(fresh4((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK1_goals_14_X17, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19), true, 0 + (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19), (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((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), 0, (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 27 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(fresh9(fresh6(fresh4(true, true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)), sK1_goals_14_X17, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19), true, 0 + (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19), (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((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), 0, (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 8 (sos_11) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(fresh9(fresh6(true, true, 0 + (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19), (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((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), 0, (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 1 (sos_06) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(fresh9((0 + (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19))) >= ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((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), 0, (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 14 (sos_02) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(fresh9(((sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) + 0) >= ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((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), 0, (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 11 (sos_08_1) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + fresh(0 >= ((sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19))), true, 0, (sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 35 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + ((sK1_goals_14_X17 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 51 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + ((sK1_goals_14_X17 ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18))) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 43 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 22 (sos_13) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (((sK3_goals_14_X18 + (sK3_goals_14_X18 ==> sK1_goals_14_X17)) ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 54 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (((sK3_goals_14_X18 + 0) ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 20 (sos_03) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + ((sK3_goals_14_X18 ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) ==> sK3_goals_14_X18)) ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 55 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 22 (sos_13) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK1_goals_14_X17)) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 53 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) + 0) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 20 (sos_03) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 29 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 48 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK3_goals_14_X18))))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 56 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> (sK2_goals_14_X19 ==> (sK2_goals_14_X19 + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> (sK2_goals_14_X19 ==> sK3_goals_14_X18))))))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 23 (goals_14) } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> (sK2_goals_14_X19 ==> (sK2_goals_14_X19 + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)))))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 29 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> (sK2_goals_14_X19 + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)))))))) >= sK1_goals_14_X17 436.20/55.39 = { by lemma 43 } 436.20/55.39 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> (sK2_goals_14_X19 + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19))))))) >= sK1_goals_14_X17 436.20/55.39 = { by axiom 22 (sos_13) } 436.20/55.40 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)) ==> (sK2_goals_14_X19 + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19))))))) >= sK1_goals_14_X17 436.20/55.40 = { by lemma 43 } 436.20/55.40 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> (((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)))))))) >= sK1_goals_14_X17 436.20/55.40 = { by lemma 57 } 436.20/55.40 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + (0 ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19))))) >= sK1_goals_14_X17 436.20/55.40 = { by lemma 34 } 436.20/55.40 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> ((sK1_goals_14_X17 ==> sK3_goals_14_X18) + ((sK1_goals_14_X17 ==> sK3_goals_14_X18) ==> sK2_goals_14_X19)))) >= sK1_goals_14_X17 436.20/55.40 = { by lemma 52 } 436.20/55.40 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> (sK2_goals_14_X19 ==> sK3_goals_14_X18))))) >= sK1_goals_14_X17 436.20/55.40 = { by axiom 23 (goals_14) } 436.20/55.40 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19)))) >= sK1_goals_14_X17 436.20/55.40 = { by lemma 57 } 436.20/55.40 ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + sK2_goals_14_X19) >= sK1_goals_14_X17 436.20/55.40 = { by axiom 14 (sos_02) } 436.20/55.40 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17 436.20/55.40 = { by lemma 30 } 436.20/55.40 true 436.20/55.40 % SZS output end Proof 436.20/55.40 436.20/55.40 RESULT: Theorem (the conjecture is true). 436.20/55.44 EOF