TSTP Solution File: LCL903+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:21:07 EDT 2023
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 05:02:42 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.56
% 0.19/0.56 % SZS status Theorem
% 0.19/0.56
% 0.19/0.58 % SZS output start Proof
% 0.19/0.58 Take the following subset of the input axioms:
% 0.19/0.58 fof(goals_14, conjecture, ![X17]: '+'(X17, X17)=X17).
% 0.19/0.58 fof(sos_01, axiom, ![A, B, C]: '+'('+'(A, B), C)='+'(A, '+'(B, C))).
% 0.19/0.58 fof(sos_02, axiom, ![A2, B2]: '+'(A2, B2)='+'(B2, A2)).
% 0.19/0.58 fof(sos_03, axiom, ![A2]: '+'(A2, '0')=A2).
% 0.19/0.58 fof(sos_04, axiom, ![A2]: '>='(A2, A2)).
% 0.19/0.58 fof(sos_05, axiom, ![X0, X1, X2]: (('>='(X0, X1) & '>='(X1, X2)) => '>='(X0, X2))).
% 0.19/0.58 fof(sos_06, axiom, ![X3, X4]: (('>='(X3, X4) & '>='(X4, X3)) => X3=X4)).
% 0.19/0.58 fof(sos_07, axiom, ![X5, X6, X7]: ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))).
% 0.19/0.58 fof(sos_08, axiom, ![A2]: '>='(A2, '0')).
% 0.19/0.58 fof(sos_09, axiom, ![X8, X9, X10]: ('>='(X8, X9) => '>='('+'(X8, X10), '+'(X9, X10)))).
% 0.19/0.58 fof(sos_11, axiom, ![X14, X15, X16]: ('>='(X14, X15) => '>='('==>'(X16, X14), '==>'(X16, X15)))).
% 0.19/0.58 fof(sos_12, axiom, ![A2]: '+'(A2, '1')='1').
% 0.19/0.58 fof(sos_13, axiom, ![A2]: '==>'('==>'('==>'(A2, '1'), A2), A2)='0').
% 0.19/0.58
% 0.19/0.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.58 fresh(y, y, x1...xn) = u
% 0.19/0.58 C => fresh(s, t, x1...xn) = v
% 0.19/0.58 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.58 variables of u and v.
% 0.19/0.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.58 input problem has no model of domain size 1).
% 0.19/0.58
% 0.19/0.58 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.58
% 0.19/0.58 Axiom 1 (sos_02): X + Y = Y + X.
% 0.19/0.58 Axiom 2 (sos_03): X + 0 = X.
% 0.19/0.58 Axiom 3 (sos_12): X + 1 = 1.
% 0.19/0.58 Axiom 4 (sos_04): X >= X = true.
% 0.19/0.58 Axiom 5 (sos_08): X >= 0 = true.
% 0.19/0.58 Axiom 6 (sos_06): fresh(X, X, Y, Z) = Z.
% 0.19/0.58 Axiom 7 (sos_05): fresh9(X, X, Y, Z) = true.
% 0.19/0.58 Axiom 8 (sos_06): fresh2(X, X, Y, Z) = Y.
% 0.19/0.58 Axiom 9 (sos_01): (X + Y) + Z = X + (Y + Z).
% 0.19/0.58 Axiom 10 (sos_05): fresh8(X, X, Y, Z, W) = Y >= W.
% 0.19/0.58 Axiom 11 (sos_07): fresh7(X, X, Y, Z, W) = true.
% 0.19/0.58 Axiom 12 (sos_07_1): fresh6(X, X, Y, Z, W) = true.
% 0.19/0.58 Axiom 13 (sos_09): fresh5(X, X, Y, Z, W) = true.
% 0.19/0.58 Axiom 14 (sos_11): fresh3(X, X, Y, Z, W) = true.
% 0.19/0.58 Axiom 15 (sos_06): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X).
% 0.19/0.58 Axiom 16 (sos_13): ((X ==> 1) ==> X) ==> X = 0.
% 0.19/0.58 Axiom 17 (sos_05): fresh8(X >= Y, true, Z, X, Y) = fresh9(Z >= X, true, Z, Y).
% 0.19/0.58 Axiom 18 (sos_09): fresh5(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z).
% 0.19/0.58 Axiom 19 (sos_11): fresh3(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y).
% 0.19/0.58 Axiom 20 (sos_07): fresh7(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z.
% 0.19/0.58 Axiom 21 (sos_07_1): fresh6((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z).
% 0.19/0.58
% 0.19/0.58 Lemma 22: 0 + X = X.
% 0.19/0.58 Proof:
% 0.19/0.58 0 + X
% 0.19/0.58 = { by axiom 1 (sos_02) R->L }
% 0.19/0.58 X + 0
% 0.19/0.58 = { by axiom 2 (sos_03) }
% 0.19/0.58 X
% 0.19/0.58
% 0.19/0.58 Lemma 23: (X + Y) >= X = true.
% 0.19/0.58 Proof:
% 0.19/0.58 (X + Y) >= X
% 0.19/0.58 = { by axiom 1 (sos_02) R->L }
% 0.19/0.58 (Y + X) >= X
% 0.19/0.59 = { by lemma 22 R->L }
% 0.19/0.59 (Y + X) >= (0 + X)
% 0.19/0.59 = { by axiom 18 (sos_09) R->L }
% 0.19/0.59 fresh5(Y >= 0, true, Y, 0, X)
% 0.19/0.59 = { by axiom 5 (sos_08) }
% 0.19/0.59 fresh5(true, true, Y, 0, X)
% 0.19/0.59 = { by axiom 13 (sos_09) }
% 0.19/0.59 true
% 0.19/0.59
% 0.19/0.59 Lemma 24: 1 >= X = true.
% 0.19/0.59 Proof:
% 0.19/0.59 1 >= X
% 0.19/0.59 = { by axiom 3 (sos_12) R->L }
% 0.19/0.59 (X + 1) >= X
% 0.19/0.59 = { by lemma 23 }
% 0.19/0.59 true
% 0.19/0.59
% 0.19/0.59 Lemma 25: X >= (Y ==> X) = true.
% 0.19/0.59 Proof:
% 0.19/0.59 X >= (Y ==> X)
% 0.19/0.59 = { by axiom 21 (sos_07_1) R->L }
% 0.19/0.59 fresh6((Y + X) >= X, true, Y, X, X)
% 0.19/0.59 = { by axiom 1 (sos_02) R->L }
% 0.19/0.59 fresh6((X + Y) >= X, true, Y, X, X)
% 0.19/0.59 = { by lemma 23 }
% 0.19/0.59 fresh6(true, true, Y, X, X)
% 0.19/0.59 = { by axiom 12 (sos_07_1) }
% 0.19/0.59 true
% 0.19/0.59
% 0.19/0.59 Lemma 26: (X + (X ==> Y)) >= Y = true.
% 0.19/0.59 Proof:
% 0.19/0.59 (X + (X ==> Y)) >= Y
% 0.19/0.59 = { by axiom 20 (sos_07) R->L }
% 0.19/0.59 fresh7((X ==> Y) >= (X ==> Y), true, X, X ==> Y, Y)
% 0.19/0.59 = { by axiom 4 (sos_04) }
% 0.19/0.59 fresh7(true, true, X, X ==> Y, Y)
% 0.19/0.59 = { by axiom 11 (sos_07) }
% 0.19/0.59 true
% 0.19/0.59
% 0.19/0.59 Lemma 27: X + (X ==> 1) = 1.
% 0.19/0.59 Proof:
% 0.19/0.59 X + (X ==> 1)
% 0.19/0.59 = { by axiom 8 (sos_06) R->L }
% 0.19/0.59 fresh2(true, true, X + (X ==> 1), 1)
% 0.19/0.59 = { by lemma 24 R->L }
% 0.19/0.59 fresh2(1 >= (X + (X ==> 1)), true, X + (X ==> 1), 1)
% 0.19/0.59 = { by axiom 15 (sos_06) }
% 0.19/0.59 fresh((X + (X ==> 1)) >= 1, true, X + (X ==> 1), 1)
% 0.19/0.59 = { by lemma 26 }
% 0.19/0.59 fresh(true, true, X + (X ==> 1), 1)
% 0.19/0.59 = { by axiom 6 (sos_06) }
% 0.19/0.59 1
% 0.19/0.59
% 0.19/0.59 Lemma 28: (X ==> 1) ==> X = X.
% 0.19/0.59 Proof:
% 0.19/0.59 (X ==> 1) ==> X
% 0.19/0.59 = { by axiom 6 (sos_06) R->L }
% 0.19/0.59 fresh(true, true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by lemma 25 R->L }
% 0.19/0.59 fresh(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by axiom 15 (sos_06) R->L }
% 0.19/0.59 fresh2(((X ==> 1) ==> X) >= X, true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by lemma 22 R->L }
% 0.19/0.59 fresh2((0 + ((X ==> 1) ==> X)) >= X, true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by axiom 1 (sos_02) R->L }
% 0.19/0.59 fresh2((((X ==> 1) ==> X) + 0) >= X, true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by axiom 20 (sos_07) R->L }
% 0.19/0.59 fresh2(fresh7(0 >= (((X ==> 1) ==> X) ==> X), true, (X ==> 1) ==> X, 0, X), true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by axiom 16 (sos_13) }
% 0.19/0.59 fresh2(fresh7(0 >= 0, true, (X ==> 1) ==> X, 0, X), true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by axiom 5 (sos_08) }
% 0.19/0.59 fresh2(fresh7(true, true, (X ==> 1) ==> X, 0, X), true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by axiom 11 (sos_07) }
% 0.19/0.59 fresh2(true, true, X, (X ==> 1) ==> X)
% 0.19/0.59 = { by axiom 8 (sos_06) }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 29: X >= (Y ==> (X + Y)) = true.
% 0.19/0.59 Proof:
% 0.19/0.59 X >= (Y ==> (X + Y))
% 0.19/0.59 = { by axiom 1 (sos_02) R->L }
% 0.19/0.59 X >= (Y ==> (Y + X))
% 0.19/0.59 = { by axiom 21 (sos_07_1) R->L }
% 0.19/0.59 fresh6((Y + X) >= (Y + X), true, Y, X, Y + X)
% 0.19/0.59 = { by axiom 4 (sos_04) }
% 0.19/0.59 fresh6(true, true, Y, X, Y + X)
% 0.19/0.59 = { by axiom 12 (sos_07_1) }
% 0.19/0.59 true
% 0.19/0.59
% 0.19/0.59 Lemma 30: (X ==> 1) ==> 1 = X.
% 0.19/0.59 Proof:
% 0.19/0.59 (X ==> 1) ==> 1
% 0.19/0.59 = { by axiom 8 (sos_06) R->L }
% 0.19/0.59 fresh2(true, true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by lemma 29 R->L }
% 0.19/0.59 fresh2(X >= ((X ==> 1) ==> (X + (X ==> 1))), true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by lemma 27 }
% 0.19/0.59 fresh2(X >= ((X ==> 1) ==> 1), true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by axiom 15 (sos_06) }
% 0.19/0.59 fresh(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by lemma 28 R->L }
% 0.19/0.59 fresh(((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by axiom 19 (sos_11) R->L }
% 0.19/0.59 fresh(fresh3(1 >= X, true, 1, X, X ==> 1), true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by lemma 24 }
% 0.19/0.59 fresh(fresh3(true, true, 1, X, X ==> 1), true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by axiom 14 (sos_11) }
% 0.19/0.59 fresh(true, true, (X ==> 1) ==> 1, X)
% 0.19/0.59 = { by axiom 6 (sos_06) }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Lemma 31: X ==> (Y ==> (Y + X)) = 0.
% 0.19/0.59 Proof:
% 0.19/0.59 X ==> (Y ==> (Y + X))
% 0.19/0.59 = { by axiom 1 (sos_02) R->L }
% 0.19/0.59 X ==> (Y ==> (X + Y))
% 0.19/0.59 = { by axiom 6 (sos_06) R->L }
% 0.19/0.59 fresh(true, true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 12 (sos_07_1) R->L }
% 0.19/0.59 fresh(fresh6(true, true, X, 0, Y ==> (X + Y)), true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 7 (sos_05) R->L }
% 0.19/0.59 fresh(fresh6(fresh9(true, true, X + 0, Y ==> (X + Y)), true, X, 0, Y ==> (X + Y)), true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by lemma 23 R->L }
% 0.19/0.59 fresh(fresh6(fresh9((X + 0) >= X, true, X + 0, Y ==> (X + Y)), true, X, 0, Y ==> (X + Y)), true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 17 (sos_05) R->L }
% 0.19/0.59 fresh(fresh6(fresh8(X >= (Y ==> (X + Y)), true, X + 0, X, Y ==> (X + Y)), true, X, 0, Y ==> (X + Y)), true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by lemma 29 }
% 0.19/0.59 fresh(fresh6(fresh8(true, true, X + 0, X, Y ==> (X + Y)), true, X, 0, Y ==> (X + Y)), true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 10 (sos_05) }
% 0.19/0.59 fresh(fresh6((X + 0) >= (Y ==> (X + Y)), true, X, 0, Y ==> (X + Y)), true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 21 (sos_07_1) }
% 0.19/0.59 fresh(0 >= (X ==> (Y ==> (X + Y))), true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 15 (sos_06) R->L }
% 0.19/0.59 fresh2((X ==> (Y ==> (X + Y))) >= 0, true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 5 (sos_08) }
% 0.19/0.59 fresh2(true, true, 0, X ==> (Y ==> (X + Y)))
% 0.19/0.59 = { by axiom 8 (sos_06) }
% 0.19/0.59 0
% 0.19/0.59
% 0.19/0.59 Lemma 32: (X ==> 1) ==> (Y + (Y ==> X)) = X.
% 0.19/0.59 Proof:
% 0.19/0.59 (X ==> 1) ==> (Y + (Y ==> X))
% 0.19/0.59 = { by axiom 6 (sos_06) R->L }
% 0.19/0.59 fresh(true, true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by axiom 14 (sos_11) R->L }
% 0.19/0.59 fresh(fresh3(true, true, 1, Y + (Y ==> X), X ==> 1), true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by lemma 24 R->L }
% 0.19/0.59 fresh(fresh3(1 >= (Y + (Y ==> X)), true, 1, Y + (Y ==> X), X ==> 1), true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by axiom 19 (sos_11) }
% 0.19/0.59 fresh(((X ==> 1) ==> 1) >= ((X ==> 1) ==> (Y + (Y ==> X))), true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by lemma 30 }
% 0.19/0.59 fresh(X >= ((X ==> 1) ==> (Y + (Y ==> X))), true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by axiom 15 (sos_06) R->L }
% 0.19/0.59 fresh2(((X ==> 1) ==> (Y + (Y ==> X))) >= X, true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by lemma 28 R->L }
% 0.19/0.59 fresh2(((X ==> 1) ==> (Y + (Y ==> X))) >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by axiom 19 (sos_11) R->L }
% 0.19/0.59 fresh2(fresh3((Y + (Y ==> X)) >= X, true, Y + (Y ==> X), X, X ==> 1), true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by lemma 26 }
% 0.19/0.59 fresh2(fresh3(true, true, Y + (Y ==> X), X, X ==> 1), true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by axiom 14 (sos_11) }
% 0.19/0.59 fresh2(true, true, X, (X ==> 1) ==> (Y + (Y ==> X)))
% 0.19/0.59 = { by axiom 8 (sos_06) }
% 0.19/0.59 X
% 0.19/0.59
% 0.19/0.59 Goal 1 (goals_14): x17 + x17 = x17.
% 0.19/0.59 Proof:
% 0.19/0.59 x17 + x17
% 0.19/0.60 = { by axiom 8 (sos_06) R->L }
% 0.19/0.60 fresh2(true, true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 26 R->L }
% 0.19/0.60 fresh2((x17 + (x17 ==> (x17 + x17))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 30 R->L }
% 0.19/0.60 fresh2((x17 + (x17 ==> (((x17 + x17) ==> 1) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 2 (sos_03) R->L }
% 0.19/0.60 fresh2((x17 + (x17 ==> ((((x17 + x17) ==> 1) + 0) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 30 R->L }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + 0) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 31 R->L }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> (x17 + ((x17 + x17) ==> 1))))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 2 (sos_03) R->L }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> (x17 + (((x17 + x17) ==> 1) + 0))))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 9 (sos_01) R->L }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + 0)))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 30 R->L }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (((x17 ==> 1) ==> 1) ==> ((x17 + ((x17 + x17) ==> 1)) + 0)))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 31 R->L }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (((x17 ==> 1) ==> 1) ==> ((x17 + ((x17 + x17) ==> 1)) + ((x17 + ((x17 + x17) ==> 1)) ==> (x17 ==> (x17 + (x17 + ((x17 + x17) ==> 1))))))))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 9 (sos_01) R->L }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (((x17 ==> 1) ==> 1) ==> ((x17 + ((x17 + x17) ==> 1)) + ((x17 + ((x17 + x17) ==> 1)) ==> (x17 ==> ((x17 + x17) + ((x17 + x17) ==> 1)))))))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 27 }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (((x17 ==> 1) ==> 1) ==> ((x17 + ((x17 + x17) ==> 1)) + ((x17 + ((x17 + x17) ==> 1)) ==> (x17 ==> 1)))))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 32 }
% 0.19/0.60 fresh2((x17 + (((x17 ==> 1) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 32 R->L }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> 1))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 8 (sos_06) R->L }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> fresh2(true, true, 1, (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 13 (sos_09) R->L }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> fresh2(fresh5(true, true, ((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)), ((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))), (((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1), true, 1, (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 25 R->L }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> fresh2(fresh5((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) >= (((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))), true, ((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)), ((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))), (((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1), true, 1, (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 18 (sos_09) }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> fresh2(((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1)) >= ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1)), true, 1, (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 27 }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> fresh2(((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1)) >= 1, true, 1, (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 15 (sos_06) }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> fresh(1 >= ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1)), true, 1, (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 24 }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> fresh(true, true, 1, (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 6 (sos_06) }
% 0.19/0.60 fresh2((x17 + (((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) ==> ((((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1))) + ((((x17 ==> 1) ==> 1) ==> (((x17 + x17) ==> 1) + (((x17 + x17) ==> 1) ==> (x17 ==> 1)))) ==> 1))))) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 31 }
% 0.19/0.60 fresh2((x17 + 0) >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 2 (sos_03) }
% 0.19/0.60 fresh2(x17 >= (x17 + x17), true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 15 (sos_06) }
% 0.19/0.60 fresh((x17 + x17) >= x17, true, x17 + x17, x17)
% 0.19/0.60 = { by lemma 23 }
% 0.19/0.60 fresh(true, true, x17 + x17, x17)
% 0.19/0.60 = { by axiom 6 (sos_06) }
% 0.19/0.60 x17
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60
% 0.19/0.60 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------