TSTP Solution File: LCL889+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL889+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 : n003.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 08:21:04 EDT 2023
% Result : Theorem 241.03s 31.30s
% Output : Proof 241.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL889+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
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 18:22:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 241.03/31.30 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 241.03/31.30
% 241.03/31.30 % SZS status Theorem
% 241.03/31.30
% 241.82/31.34 % SZS output start Proof
% 241.82/31.34 Take the following subset of the input axioms:
% 241.82/31.34 fof(goals_13, conjecture, ![X17, X18, X19]: (('>='(X17, '==>'(X17, X18)) & X19='==>'(X19, X18)) => '>='(X17, X19))).
% 241.82/31.34 fof(sos_01, axiom, ![A, B, C]: '+'('+'(A, B), C)='+'(A, '+'(B, C))).
% 241.82/31.34 fof(sos_02, axiom, ![A2, B2]: '+'(A2, B2)='+'(B2, A2)).
% 241.82/31.34 fof(sos_03, axiom, ![A2]: '+'(A2, '0')=A2).
% 241.82/31.34 fof(sos_06, axiom, ![X3, X4]: (('>='(X3, X4) & '>='(X4, X3)) => X3=X4)).
% 241.82/31.34 fof(sos_07, axiom, ![X5, X6, X7]: ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))).
% 241.82/31.34 fof(sos_08, axiom, ![A2]: '>='(A2, '0')).
% 241.82/31.34 fof(sos_09, axiom, ![X8, X9, X10]: ('>='(X8, X9) => '>='('+'(X8, X10), '+'(X9, X10)))).
% 241.82/31.34 fof(sos_10, axiom, ![X11, X12, X13]: ('>='(X11, X12) => '>='('==>'(X12, X13), '==>'(X11, X13)))).
% 241.82/31.34 fof(sos_11, axiom, ![X14, X15, X16]: ('>='(X14, X15) => '>='('==>'(X16, X14), '==>'(X16, X15)))).
% 241.82/31.34 fof(sos_12, axiom, ![A2, B2]: '+'(A2, '==>'(A2, B2))='+'(B2, '==>'(B2, A2))).
% 241.82/31.34
% 241.82/31.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 241.82/31.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 241.82/31.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 241.82/31.34 fresh(y, y, x1...xn) = u
% 241.82/31.34 C => fresh(s, t, x1...xn) = v
% 241.82/31.34 where fresh is a fresh function symbol and x1..xn are the free
% 241.82/31.34 variables of u and v.
% 241.82/31.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 241.82/31.34 input problem has no model of domain size 1).
% 241.82/31.34
% 241.82/31.34 The encoding turns the above axioms into the following unit equations and goals:
% 241.82/31.34
% 241.82/31.34 Axiom 1 (sos_08): X >= 0 = true.
% 241.82/31.34 Axiom 2 (sos_02): X + Y = Y + X.
% 241.82/31.34 Axiom 3 (sos_03): X + 0 = X.
% 241.82/31.34 Axiom 4 (goals_13): x19 = x19 ==> x18.
% 241.82/31.34 Axiom 5 (goals_13_1): x17 >= (x17 ==> x18) = true.
% 241.82/31.35 Axiom 6 (sos_12): X + (X ==> Y) = Y + (Y ==> X).
% 241.82/31.35 Axiom 7 (sos_01): (X + Y) + Z = X + (Y + Z).
% 241.82/31.35 Axiom 8 (sos_06): fresh(X, X, Y, Z) = Z.
% 241.82/31.35 Axiom 9 (sos_06): fresh2(X, X, Y, Z) = Y.
% 241.82/31.35 Axiom 10 (sos_07_1): fresh6(X, X, Y, Z, W) = true.
% 241.82/31.35 Axiom 11 (sos_09): fresh5(X, X, Y, Z, W) = true.
% 241.82/31.35 Axiom 12 (sos_10): fresh4(X, X, Y, Z, W) = true.
% 241.82/31.35 Axiom 13 (sos_11): fresh3(X, X, Y, Z, W) = true.
% 241.82/31.35 Axiom 14 (sos_06): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X).
% 241.82/31.35 Axiom 15 (sos_09): fresh5(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z).
% 241.82/31.35 Axiom 16 (sos_10): fresh4(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z).
% 241.82/31.35 Axiom 17 (sos_11): fresh3(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y).
% 241.82/31.35 Axiom 18 (sos_07_1): fresh6((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z).
% 241.82/31.35
% 241.82/31.35 Lemma 19: 0 + X = X.
% 241.82/31.35 Proof:
% 241.82/31.35 0 + X
% 241.82/31.35 = { by axiom 2 (sos_02) R->L }
% 241.82/31.35 X + 0
% 241.82/31.35 = { by axiom 3 (sos_03) }
% 241.82/31.35 X
% 241.82/31.35
% 241.82/31.35 Lemma 20: fresh(0 >= X, true, 0, X) = 0.
% 241.82/31.35 Proof:
% 241.82/31.35 fresh(0 >= X, true, 0, X)
% 241.82/31.35 = { by axiom 14 (sos_06) R->L }
% 241.82/31.35 fresh2(X >= 0, true, 0, X)
% 241.82/31.35 = { by axiom 1 (sos_08) }
% 241.82/31.35 fresh2(true, true, 0, X)
% 241.82/31.35 = { by axiom 9 (sos_06) }
% 241.82/31.35 0
% 241.82/31.35
% 241.82/31.35 Lemma 21: 0 ==> X = X.
% 241.82/31.35 Proof:
% 241.82/31.35 0 ==> X
% 241.82/31.35 = { by lemma 19 R->L }
% 241.82/31.35 0 + (0 ==> X)
% 241.82/31.35 = { by axiom 6 (sos_12) R->L }
% 241.82/31.35 X + (X ==> 0)
% 241.82/31.35 = { by axiom 8 (sos_06) R->L }
% 241.82/31.35 X + fresh(true, true, 0, X ==> 0)
% 241.82/31.35 = { by axiom 10 (sos_07_1) R->L }
% 241.82/31.35 X + fresh(fresh6(true, true, X, 0, 0), true, 0, X ==> 0)
% 241.82/31.35 = { by axiom 1 (sos_08) R->L }
% 241.82/31.35 X + fresh(fresh6((X + 0) >= 0, true, X, 0, 0), true, 0, X ==> 0)
% 241.82/31.35 = { by axiom 18 (sos_07_1) }
% 241.82/31.35 X + fresh(0 >= (X ==> 0), true, 0, X ==> 0)
% 241.82/31.35 = { by lemma 20 }
% 241.82/31.35 X + 0
% 241.82/31.35 = { by axiom 3 (sos_03) }
% 241.82/31.35 X
% 241.82/31.35
% 241.82/31.35 Lemma 22: (X + Y) >= X = true.
% 241.82/31.35 Proof:
% 241.82/31.35 (X + Y) >= X
% 241.82/31.35 = { by axiom 2 (sos_02) R->L }
% 241.82/31.35 (Y + X) >= X
% 241.82/31.35 = { by lemma 19 R->L }
% 241.82/31.35 (Y + X) >= (0 + X)
% 241.82/31.35 = { by axiom 15 (sos_09) R->L }
% 241.82/31.35 fresh5(Y >= 0, true, Y, 0, X)
% 241.82/31.35 = { by axiom 1 (sos_08) }
% 241.82/31.35 fresh5(true, true, Y, 0, X)
% 241.82/31.35 = { by axiom 11 (sos_09) }
% 241.82/31.35 true
% 241.82/31.35
% 241.82/31.35 Lemma 23: Y + (X + Z) = X + (Y + Z).
% 241.82/31.35 Proof:
% 241.82/31.35 Y + (X + Z)
% 241.82/31.35 = { by axiom 2 (sos_02) R->L }
% 241.82/31.35 (X + Z) + Y
% 241.82/31.35 = { by axiom 7 (sos_01) }
% 241.82/31.35 X + (Z + Y)
% 241.82/31.35 = { by axiom 2 (sos_02) }
% 241.82/31.35 X + (Y + Z)
% 241.82/31.35
% 241.82/31.35 Lemma 24: (0 ==> X) >= (Y ==> X) = true.
% 241.82/31.35 Proof:
% 241.82/31.35 (0 ==> X) >= (Y ==> X)
% 241.82/31.35 = { by axiom 16 (sos_10) R->L }
% 241.82/31.35 fresh4(Y >= 0, true, Y, 0, X)
% 241.82/31.35 = { by axiom 1 (sos_08) }
% 241.82/31.35 fresh4(true, true, Y, 0, X)
% 241.82/31.35 = { by axiom 12 (sos_10) }
% 241.82/31.35 true
% 241.82/31.35
% 241.82/31.35 Lemma 25: (X + (X ==> Y)) >= Y = true.
% 241.82/31.35 Proof:
% 241.82/31.35 (X + (X ==> Y)) >= Y
% 241.82/31.35 = { by axiom 6 (sos_12) R->L }
% 241.82/31.35 (Y + (Y ==> X)) >= Y
% 241.82/31.35 = { by lemma 22 }
% 241.82/31.35 true
% 241.82/31.35
% 241.82/31.35 Lemma 26: fresh6((X + (X ==> Y)) >= Z, true, Y, Y ==> X, Z) = (Y ==> X) >= (Y ==> Z).
% 241.82/31.35 Proof:
% 241.82/31.35 fresh6((X + (X ==> Y)) >= Z, true, Y, Y ==> X, Z)
% 241.82/31.35 = { by axiom 6 (sos_12) R->L }
% 241.82/31.35 fresh6((Y + (Y ==> X)) >= Z, true, Y, Y ==> X, Z)
% 241.82/31.35 = { by axiom 18 (sos_07_1) }
% 241.82/31.36 (Y ==> X) >= (Y ==> Z)
% 241.82/31.36
% 241.82/31.36 Goal 1 (goals_13_2): x17 >= x19 = true.
% 241.82/31.36 Proof:
% 241.82/31.36 x17 >= x19
% 241.82/31.36 = { by axiom 3 (sos_03) R->L }
% 241.82/31.36 (x17 + 0) >= x19
% 241.82/31.36 = { by axiom 8 (sos_06) R->L }
% 241.82/31.36 (x17 + fresh(true, true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 1 (sos_08) R->L }
% 241.82/31.36 (x17 + fresh((x17 ==> ((x19 + (x19 ==> x17)) ==> x18)) >= 0, true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 14 (sos_06) R->L }
% 241.82/31.36 (x17 + fresh2(0 >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by lemma 20 R->L }
% 241.82/31.36 (x17 + fresh2(fresh(0 >= (x17 ==> (0 + (x17 ==> x18))), true, 0, x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 2 (sos_02) R->L }
% 241.82/31.36 (x17 + fresh2(fresh(0 >= (x17 ==> ((x17 ==> x18) + 0)), true, 0, x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 18 (sos_07_1) R->L }
% 241.82/31.36 (x17 + fresh2(fresh(fresh6((x17 + 0) >= ((x17 ==> x18) + 0), true, x17, 0, (x17 ==> x18) + 0), true, 0, x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 15 (sos_09) R->L }
% 241.82/31.36 (x17 + fresh2(fresh(fresh6(fresh5(x17 >= (x17 ==> x18), true, x17, x17 ==> x18, 0), true, x17, 0, (x17 ==> x18) + 0), true, 0, x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 5 (goals_13_1) }
% 241.82/31.36 (x17 + fresh2(fresh(fresh6(fresh5(true, true, x17, x17 ==> x18, 0), true, x17, 0, (x17 ==> x18) + 0), true, 0, x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 11 (sos_09) }
% 241.82/31.36 (x17 + fresh2(fresh(fresh6(true, true, x17, 0, (x17 ==> x18) + 0), true, 0, x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 10 (sos_07_1) }
% 241.82/31.36 (x17 + fresh2(fresh(true, true, 0, x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 8 (sos_06) }
% 241.82/31.36 (x17 + fresh2((x17 ==> (0 + (x17 ==> x18))) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by lemma 19 }
% 241.82/31.36 (x17 + fresh2((x17 ==> (x17 ==> x18)) >= (x17 ==> ((x19 + (x19 ==> x17)) ==> x18)), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 17 (sos_11) R->L }
% 241.82/31.36 (x17 + fresh2(fresh3((x17 ==> x18) >= ((x19 + (x19 ==> x17)) ==> x18), true, x17 ==> x18, (x19 + (x19 ==> x17)) ==> x18, x17), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 16 (sos_10) R->L }
% 241.82/31.36 (x17 + fresh2(fresh3(fresh4((x19 + (x19 ==> x17)) >= x17, true, x19 + (x19 ==> x17), x17, x18), true, x17 ==> x18, (x19 + (x19 ==> x17)) ==> x18, x17), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by lemma 25 }
% 241.82/31.36 (x17 + fresh2(fresh3(fresh4(true, true, x19 + (x19 ==> x17), x17, x18), true, x17 ==> x18, (x19 + (x19 ==> x17)) ==> x18, x17), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 12 (sos_10) }
% 241.82/31.36 (x17 + fresh2(fresh3(true, true, x17 ==> x18, (x19 + (x19 ==> x17)) ==> x18, x17), true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 13 (sos_11) }
% 241.82/31.36 (x17 + fresh2(true, true, x17 ==> ((x19 + (x19 ==> x17)) ==> x18), 0)) >= x19
% 241.82/31.36 = { by axiom 9 (sos_06) }
% 241.82/31.36 (x17 + (x17 ==> ((x19 + (x19 ==> x17)) ==> x18))) >= x19
% 241.82/31.36 = { by axiom 2 (sos_02) R->L }
% 241.82/31.36 (x17 + (x17 ==> (((x19 ==> x17) + x19) ==> x18))) >= x19
% 241.82/31.36 = { by axiom 9 (sos_06) R->L }
% 241.82/31.36 (x17 + (x17 ==> fresh2(true, true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by axiom 10 (sos_07_1) R->L }
% 241.82/31.36 (x17 + (x17 ==> fresh2(fresh6(true, true, (x19 ==> x17) + x19, (x19 ==> x17) ==> x19, x19 + x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by axiom 11 (sos_09) R->L }
% 241.82/31.36 (x17 + (x17 ==> fresh2(fresh6(fresh5(true, true, (x19 ==> x17) + ((x19 ==> x17) ==> x19), x19, x19), true, (x19 ==> x17) + x19, (x19 ==> x17) ==> x19, x19 + x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by lemma 25 R->L }
% 241.82/31.36 (x17 + (x17 ==> fresh2(fresh6(fresh5(((x19 ==> x17) + ((x19 ==> x17) ==> x19)) >= x19, true, (x19 ==> x17) + ((x19 ==> x17) ==> x19), x19, x19), true, (x19 ==> x17) + x19, (x19 ==> x17) ==> x19, x19 + x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by axiom 15 (sos_09) }
% 241.82/31.36 (x17 + (x17 ==> fresh2(fresh6((((x19 ==> x17) + ((x19 ==> x17) ==> x19)) + x19) >= (x19 + x19), true, (x19 ==> x17) + x19, (x19 ==> x17) ==> x19, x19 + x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by axiom 7 (sos_01) }
% 241.82/31.36 (x17 + (x17 ==> fresh2(fresh6(((x19 ==> x17) + (((x19 ==> x17) ==> x19) + x19)) >= (x19 + x19), true, (x19 ==> x17) + x19, (x19 ==> x17) ==> x19, x19 + x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by axiom 2 (sos_02) R->L }
% 241.82/31.36 (x17 + (x17 ==> fresh2(fresh6(((x19 ==> x17) + (x19 + ((x19 ==> x17) ==> x19))) >= (x19 + x19), true, (x19 ==> x17) + x19, (x19 ==> x17) ==> x19, x19 + x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by axiom 7 (sos_01) R->L }
% 241.82/31.36 (x17 + (x17 ==> fresh2(fresh6((((x19 ==> x17) + x19) + ((x19 ==> x17) ==> x19)) >= (x19 + x19), true, (x19 ==> x17) + x19, (x19 ==> x17) ==> x19, x19 + x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by axiom 18 (sos_07_1) }
% 241.82/31.36 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x19 + x19)), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by lemma 19 R->L }
% 241.82/31.36 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (0 + (x19 + x19))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.36 = { by lemma 23 }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x19 + (0 + x19))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 2 (sos_02) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x19 + (x19 + 0))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 4 (goals_13) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x19 + ((x19 ==> x18) + 0))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 7 (sos_01) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> ((x19 + (x19 ==> x18)) + 0)), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 6 (sos_12) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> ((x18 + (x18 ==> x19)) + 0)), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 7 (sos_01) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + ((x18 ==> x19) + 0))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 2 (sos_02) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + (x18 ==> x19)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 4 (goals_13) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + (x18 ==> (x19 ==> x18))))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 9 (sos_06) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh2(true, true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 10 (sos_07_1) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh2(fresh6(true, true, 0 ==> x18, 0, x19 ==> x18), true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 24 R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh2(fresh6((0 ==> x18) >= (x19 ==> x18), true, 0 ==> x18, 0, x19 ==> x18), true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 3 (sos_03) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh2(fresh6(((0 ==> x18) + 0) >= (x19 ==> x18), true, 0 ==> x18, 0, x19 ==> x18), true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 18 (sos_07_1) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh2(0 >= ((0 ==> x18) ==> (x19 ==> x18)), true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 21 }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh2(0 >= (x18 ==> (x19 ==> x18)), true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 14 (sos_06) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh((x18 ==> (x19 ==> x18)) >= 0, true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 1 (sos_08) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + fresh(true, true, x18 ==> (x19 ==> x18), 0)))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 8 (sos_06) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + (0 + 0))), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 3 (sos_03) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (x18 + 0)), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 2 (sos_02) }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> (0 + x18)), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 19 }
% 241.82/31.37 (x17 + (x17 ==> fresh2(((x19 ==> x17) ==> x19) >= (((x19 ==> x17) + x19) ==> x18), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 14 (sos_06) }
% 241.82/31.37 (x17 + (x17 ==> fresh((((x19 ==> x17) + x19) ==> x18) >= ((x19 ==> x17) ==> x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 18 (sos_07_1) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(((x19 ==> x17) + (((x19 ==> x17) + x19) ==> x18)) >= x19, true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 4 (goals_13) }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(((x19 ==> x17) + (((x19 ==> x17) + x19) ==> x18)) >= (x19 ==> x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 2 (sos_02) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(((x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18)) >= (x19 ==> x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 18 (sos_07_1) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(fresh6((x19 + ((x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18))) >= x18, true, x19, (x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18), x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 2 (sos_02) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(fresh6((x19 + ((x19 ==> x17) + (((x19 ==> x17) + x19) ==> x18))) >= x18, true, x19, (x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18), x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 23 }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(fresh6(((x19 ==> x17) + (x19 + (((x19 ==> x17) + x19) ==> x18))) >= x18, true, x19, (x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18), x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 7 (sos_01) R->L }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(fresh6((((x19 ==> x17) + x19) + (((x19 ==> x17) + x19) ==> x18)) >= x18, true, x19, (x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18), x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 6 (sos_12) }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(fresh6((x18 + (x18 ==> ((x19 ==> x17) + x19))) >= x18, true, x19, (x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18), x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 22 }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(fresh6(true, true, x19, (x19 ==> x17) + ((x19 + (x19 ==> x17)) ==> x18), x18), true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 10 (sos_07_1) }
% 241.82/31.37 (x17 + (x17 ==> fresh(fresh6(true, true, x19 ==> x17, ((x19 ==> x17) + x19) ==> x18, x19), true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 10 (sos_07_1) }
% 241.82/31.37 (x17 + (x17 ==> fresh(true, true, ((x19 ==> x17) + x19) ==> x18, (x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 8 (sos_06) }
% 241.82/31.37 (x17 + (x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 8 (sos_06) R->L }
% 241.82/31.37 (x17 + fresh(true, true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 13 (sos_11) R->L }
% 241.82/31.37 (x17 + fresh(fresh3(true, true, 0 ==> x19, (x19 ==> x17) ==> x19, x17), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 24 R->L }
% 241.82/31.37 (x17 + fresh(fresh3((0 ==> x19) >= ((x19 ==> x17) ==> x19), true, 0 ==> x19, (x19 ==> x17) ==> x19, x17), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 17 (sos_11) }
% 241.82/31.37 (x17 + fresh((x17 ==> (0 ==> x19)) >= (x17 ==> ((x19 ==> x17) ==> x19)), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 21 }
% 241.82/31.37 (x17 + fresh((x17 ==> x19) >= (x17 ==> ((x19 ==> x17) ==> x19)), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 14 (sos_06) R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= (x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 8 (sos_06) R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh(true, true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 13 (sos_11) R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh(fresh3(true, true, x19 + (x19 ==> (x19 ==> x17)), x19, x17), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 22 R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh(fresh3((x19 + (x19 ==> (x19 ==> x17))) >= x19, true, x19 + (x19 ==> (x19 ==> x17)), x19, x17), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 17 (sos_11) }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh((x17 ==> (x19 + (x19 ==> (x19 ==> x17)))) >= (x17 ==> x19), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 14 (sos_06) R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2((x17 ==> x19) >= (x17 ==> (x19 + (x19 ==> (x19 ==> x17)))), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 6 (sos_12) R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2((x17 ==> x19) >= (x17 ==> ((x19 ==> x17) + ((x19 ==> x17) ==> x19))), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 2 (sos_02) R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2((x17 ==> x19) >= (x17 ==> (((x19 ==> x17) ==> x19) + (x19 ==> x17))), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 26 R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2(fresh6((x19 + (x19 ==> x17)) >= (((x19 ==> x17) ==> x19) + (x19 ==> x17)), true, x17, x17 ==> x19, ((x19 ==> x17) ==> x19) + (x19 ==> x17)), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 21 R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2(fresh6(((0 ==> x19) + (x19 ==> x17)) >= (((x19 ==> x17) ==> x19) + (x19 ==> x17)), true, x17, x17 ==> x19, ((x19 ==> x17) ==> x19) + (x19 ==> x17)), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 15 (sos_09) R->L }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2(fresh6(fresh5((0 ==> x19) >= ((x19 ==> x17) ==> x19), true, 0 ==> x19, (x19 ==> x17) ==> x19, x19 ==> x17), true, x17, x17 ==> x19, ((x19 ==> x17) ==> x19) + (x19 ==> x17)), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 24 }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2(fresh6(fresh5(true, true, 0 ==> x19, (x19 ==> x17) ==> x19, x19 ==> x17), true, x17, x17 ==> x19, ((x19 ==> x17) ==> x19) + (x19 ==> x17)), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 11 (sos_09) }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2(fresh6(true, true, x17, x17 ==> x19, ((x19 ==> x17) ==> x19) + (x19 ==> x17)), true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 10 (sos_07_1) }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= fresh2(true, true, x17 ==> (x19 + (x19 ==> (x19 ==> x17))), x17 ==> x19), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 9 (sos_06) }
% 241.82/31.37 (x17 + fresh2((x17 ==> ((x19 ==> x17) ==> x19)) >= (x17 ==> (x19 + (x19 ==> (x19 ==> x17)))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by lemma 26 R->L }
% 241.82/31.37 (x17 + fresh2(fresh6((((x19 ==> x17) ==> x19) + (((x19 ==> x17) ==> x19) ==> x17)) >= (x19 + (x19 ==> (x19 ==> x17))), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 2 (sos_02) R->L }
% 241.82/31.37 (x17 + fresh2(fresh6(((((x19 ==> x17) ==> x19) ==> x17) + ((x19 ==> x17) ==> x19)) >= (x19 + (x19 ==> (x19 ==> x17))), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 6 (sos_12) R->L }
% 241.82/31.37 (x17 + fresh2(fresh6(((((x19 ==> x17) ==> x19) ==> x17) + ((x19 ==> x17) ==> x19)) >= ((x19 ==> x17) + ((x19 ==> x17) ==> x19)), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.37 = { by axiom 15 (sos_09) R->L }
% 241.82/31.38 (x17 + fresh2(fresh6(fresh5((((x19 ==> x17) ==> x19) ==> x17) >= (x19 ==> x17), true, ((x19 ==> x17) ==> x19) ==> x17, x19 ==> x17, (x19 ==> x17) ==> x19), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.38 = { by lemma 21 R->L }
% 241.82/31.38 (x17 + fresh2(fresh6(fresh5((((x19 ==> x17) ==> x19) ==> x17) >= ((0 ==> x19) ==> x17), true, ((x19 ==> x17) ==> x19) ==> x17, x19 ==> x17, (x19 ==> x17) ==> x19), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.38 = { by axiom 16 (sos_10) R->L }
% 241.82/31.38 (x17 + fresh2(fresh6(fresh5(fresh4((0 ==> x19) >= ((x19 ==> x17) ==> x19), true, 0 ==> x19, (x19 ==> x17) ==> x19, x17), true, ((x19 ==> x17) ==> x19) ==> x17, x19 ==> x17, (x19 ==> x17) ==> x19), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.38 = { by lemma 24 }
% 241.82/31.38 (x17 + fresh2(fresh6(fresh5(fresh4(true, true, 0 ==> x19, (x19 ==> x17) ==> x19, x17), true, ((x19 ==> x17) ==> x19) ==> x17, x19 ==> x17, (x19 ==> x17) ==> x19), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.38 = { by axiom 12 (sos_10) }
% 241.82/31.38 (x17 + fresh2(fresh6(fresh5(true, true, ((x19 ==> x17) ==> x19) ==> x17, x19 ==> x17, (x19 ==> x17) ==> x19), true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.38 = { by axiom 11 (sos_09) }
% 241.82/31.38 (x17 + fresh2(fresh6(true, true, x17, x17 ==> ((x19 ==> x17) ==> x19), x19 + (x19 ==> (x19 ==> x17))), true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.38 = { by axiom 10 (sos_07_1) }
% 241.82/31.38 (x17 + fresh2(true, true, x17 ==> x19, x17 ==> ((x19 ==> x17) ==> x19))) >= x19
% 241.82/31.39 = { by axiom 9 (sos_06) }
% 241.82/31.39 (x17 + (x17 ==> x19)) >= x19
% 241.82/31.39 = { by lemma 25 }
% 241.82/31.39 true
% 241.82/31.39 % SZS output end Proof
% 241.82/31.39
% 241.82/31.39 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------