0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.13/0.33 % Computer : n005.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 180 0.13/0.33 % DateTime : Thu Aug 29 11:24:33 EDT 2019 0.13/0.33 % CPUTime : 0.20/0.48 % SZS status Theorem 0.20/0.48 0.20/0.48 % SZS output start Proof 0.20/0.48 Take the following subset of the input axioms: 0.20/0.53 fof(goals_14, conjecture, ![X17]: '==>'('==>'(X17, '1'), '1')=X17). 0.20/0.53 fof(sos_02, axiom, ![A, B]: '+'(A, B)='+'(B, A)). 0.20/0.53 fof(sos_03, axiom, ![A]: A='+'(A, '0')). 0.20/0.53 fof(sos_04, axiom, ![A]: '>='(A, A)). 0.20/0.53 fof(sos_06, axiom, ![X3, X4]: (X3=X4 <= ('>='(X3, X4) & '>='(X4, X3)))). 0.20/0.53 fof(sos_07, axiom, ![X5, X6, X7]: ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))). 0.20/0.53 fof(sos_08, axiom, ![A]: '>='(A, '0')). 0.20/0.53 fof(sos_09, axiom, ![X8, X9, X10]: ('>='('+'(X8, X10), '+'(X9, X10)) <= '>='(X8, X9))). 0.20/0.53 fof(sos_10, axiom, ![X11, X12, X13]: ('>='(X11, X12) => '>='('==>'(X12, X13), '==>'(X11, X13)))). 0.20/0.53 fof(sos_11, axiom, ![X14, X15, X16]: ('>='('==>'(X16, X14), '==>'(X16, X15)) <= '>='(X14, X15))). 0.20/0.53 fof(sos_12, axiom, ![A]: '1'='+'(A, '1')). 0.20/0.53 fof(sos_13, axiom, ![A]: '==>'('==>'('==>'(A, '1'), A), A)='0'). 0.20/0.53 0.20/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of 0.20/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 0.20/0.53 We repeatedly replace C & s=t => u=v by the two clauses: 0.20/0.53 fresh(y, y, x1...xn) = u 0.20/0.53 C => fresh(s, t, x1...xn) = v 0.20/0.53 where fresh is a fresh function symbol and x1..xn are the free 0.20/0.53 variables of u and v. 0.20/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the 0.20/0.53 input problem has no model of domain size 1). 0.20/0.53 0.20/0.53 The encoding turns the above axioms into the following unit equations and goals: 0.20/0.53 0.20/0.53 Axiom 1 (sos_06): fresh2(X, X, Y, Z) = Y. 0.20/0.53 Axiom 2 (sos_06): fresh(X, X, Y, Z) = Z. 0.20/0.53 Axiom 3 (sos_07): fresh5(X, X, Y, Z, W) = true. 0.20/0.53 Axiom 4 (sos_07_1): fresh8(X, X, Y, Z, W) = true. 0.20/0.53 Axiom 5 (sos_09): fresh9(X, X, Y, Z, W) = true. 0.20/0.53 Axiom 6 (sos_10): fresh4(X, X, Y, Z, W) = true. 0.20/0.53 Axiom 7 (sos_11): fresh3(X, X, Y, Z, W) = true. 0.20/0.53 Axiom 8 (sos_09): fresh9(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z). 0.20/0.53 Axiom 9 (sos_07_1): fresh8((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z). 0.20/0.53 Axiom 10 (sos_07): fresh5(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z. 0.20/0.53 Axiom 11 (sos_02): X + Y = Y + X. 0.20/0.53 Axiom 12 (sos_08): X >= 0 = true. 0.20/0.53 Axiom 13 (sos_06): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X). 0.20/0.53 Axiom 14 (sos_11): fresh3(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y). 0.20/0.53 Axiom 15 (sos_03): X = X + 0. 0.20/0.53 Axiom 16 (sos_10): fresh4(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z). 0.20/0.53 Axiom 17 (sos_12): 1 = X + 1. 0.20/0.53 Axiom 18 (sos_13): ((X ==> 1) ==> X) ==> X = 0. 0.20/0.53 Axiom 19 (sos_04): X >= X = true. 0.20/0.53 0.20/0.53 Lemma 20: 0 + X = X. 0.20/0.53 Proof: 0.20/0.53 0 + X 0.20/0.53 = { by axiom 11 (sos_02) } 0.20/0.53 X + 0 0.20/0.53 = { by axiom 15 (sos_03) } 0.20/0.53 X 0.20/0.53 0.20/0.53 Lemma 21: (X + Y) >= X = true. 0.20/0.53 Proof: 0.20/0.53 (X + Y) >= X 0.20/0.53 = { by axiom 11 (sos_02) } 0.20/0.53 (Y + X) >= X 0.20/0.53 = { by lemma 20 } 0.20/0.53 (Y + X) >= (0 + X) 0.20/0.53 = { by axiom 8 (sos_09) } 0.20/0.53 fresh9(Y >= 0, true, Y, 0, X) 0.20/0.53 = { by axiom 12 (sos_08) } 0.20/0.53 fresh9(true, true, Y, 0, X) 0.20/0.53 = { by axiom 5 (sos_09) } 0.20/0.53 true 0.20/0.53 0.20/0.53 Lemma 22: 1 >= X = true. 0.20/0.53 Proof: 0.20/0.53 1 >= X 0.20/0.53 = { by axiom 17 (sos_12) } 0.20/0.53 (X + 1) >= X 0.20/0.53 = { by lemma 21 } 0.20/0.53 true 0.20/0.53 0.20/0.53 Lemma 23: (X + (X ==> Y)) >= Y = true. 0.20/0.53 Proof: 0.20/0.53 (X + (X ==> Y)) >= Y 0.20/0.53 = { by axiom 10 (sos_07) } 0.20/0.53 fresh5((X ==> Y) >= (X ==> Y), true, X, X ==> Y, Y) 0.20/0.53 = { by axiom 19 (sos_04) } 0.20/0.53 fresh5(true, true, X, X ==> Y, Y) 0.20/0.53 = { by axiom 3 (sos_07) } 0.43/0.58 true 0.43/0.58 0.43/0.58 Goal 1 (goals_14): (sK1_goals_14_X17 ==> 1) ==> 1 = sK1_goals_14_X17. 0.43/0.58 Proof: 0.43/0.58 (sK1_goals_14_X17 ==> 1) ==> 1 0.43/0.58 = { by axiom 17 (sos_12) } 0.43/0.58 (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1) 0.43/0.58 = { by axiom 2 (sos_06) } 0.43/0.58 fresh(true, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 4 (sos_07_1) } 0.43/0.58 fresh(fresh8(true, true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by lemma 22 } 0.43/0.58 fresh(fresh8(1 >= (sK1_goals_14_X17 + 1), true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 2 (sos_06) } 0.43/0.58 fresh(fresh8(fresh(true, true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by lemma 23 } 0.43/0.58 fresh(fresh8(fresh((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1)) >= 1, true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 13 (sos_06) } 0.43/0.58 fresh(fresh8(fresh2(1 >= (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1)), true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by lemma 22 } 0.43/0.58 fresh(fresh8(fresh2(true, true, sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1), 1) >= (sK1_goals_14_X17 + 1), true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 1 (sos_06) } 0.43/0.58 fresh(fresh8((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 1)) >= (sK1_goals_14_X17 + 1), true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 11 (sos_02) } 0.43/0.58 fresh(fresh8(((sK1_goals_14_X17 ==> 1) + sK1_goals_14_X17) >= (sK1_goals_14_X17 + 1), true, sK1_goals_14_X17 ==> 1, sK1_goals_14_X17, sK1_goals_14_X17 + 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 9 (sos_07_1) } 0.43/0.58 fresh(sK1_goals_14_X17 >= ((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 13 (sos_06) } 0.43/0.58 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= sK1_goals_14_X17, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 1 (sos_06) } 0.43/0.58 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh2(true, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by lemma 23 } 0.43/0.58 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh2((((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) + (((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 18 (sos_13) } 0.43/0.58 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh2((((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) + 0) >= sK1_goals_14_X17, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 15 (sos_03) } 0.43/0.58 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh2(((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17) >= sK1_goals_14_X17, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 13 (sos_06) } 0.43/0.58 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(sK1_goals_14_X17 >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.58 = { by axiom 1 (sos_06) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh2(true, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by lemma 23 } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh2((0 + (0 ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by lemma 20 } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh2((0 ==> sK1_goals_14_X17) >= sK1_goals_14_X17, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 13 (sos_06) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh(sK1_goals_14_X17 >= (0 ==> sK1_goals_14_X17), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 15 (sos_03) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh(sK1_goals_14_X17 >= (0 ==> (sK1_goals_14_X17 + 0)), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 11 (sos_02) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh(sK1_goals_14_X17 >= (0 ==> (0 + sK1_goals_14_X17)), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 9 (sos_07_1) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh(fresh8((0 + sK1_goals_14_X17) >= (0 + sK1_goals_14_X17), true, 0, sK1_goals_14_X17, 0 + sK1_goals_14_X17), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 19 (sos_04) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh(fresh8(true, true, 0, sK1_goals_14_X17, 0 + sK1_goals_14_X17), true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 4 (sos_07_1) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh(true, true, sK1_goals_14_X17, 0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 2 (sos_06) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh((0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 16 (sos_10) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh4((sK1_goals_14_X17 ==> 1) >= 0, true, sK1_goals_14_X17 ==> 1, 0, sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 12 (sos_08) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(fresh4(true, true, sK1_goals_14_X17 ==> 1, 0, sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 6 (sos_10) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= fresh(true, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 2 (sos_06) } 0.43/0.59 fresh2(((sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) >= ((sK1_goals_14_X17 ==> 1) ==> sK1_goals_14_X17), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 14 (sos_11) } 0.43/0.59 fresh2(fresh3((sK1_goals_14_X17 + 1) >= sK1_goals_14_X17, true, sK1_goals_14_X17 + 1, sK1_goals_14_X17, sK1_goals_14_X17 ==> 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by lemma 21 } 0.43/0.59 fresh2(fresh3(true, true, sK1_goals_14_X17 + 1, sK1_goals_14_X17, sK1_goals_14_X17 ==> 1), true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 7 (sos_11) } 0.43/0.59 fresh2(true, true, sK1_goals_14_X17, (sK1_goals_14_X17 ==> 1) ==> (sK1_goals_14_X17 + 1)) 0.43/0.59 = { by axiom 1 (sos_06) } 0.43/0.59 sK1_goals_14_X17 0.43/0.59 % SZS output end Proof 0.43/0.59 0.43/0.59 RESULT: Theorem (the conjecture is true). 0.43/0.59 EOF