TSTP Solution File: LCL891+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL891+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 : n020.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 08:21:05 EDT 2023
% Result : Theorem 230.23s 29.89s
% Output : Proof 230.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL891+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
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 20:09:45 EDT 2023
% 0.14/0.33 % CPUTime :
% 230.23/29.89 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 230.23/29.89
% 230.23/29.89 % SZS status Theorem
% 230.23/29.89
% 230.67/29.92 % SZS output start Proof
% 230.67/29.92 Take the following subset of the input axioms:
% 230.67/29.92 fof(goals_13, conjecture, ![X17, X18, X19]: (('>='('==>'(X17, X18), X17) & X19='==>'(X19, X18)) => '>='(X19, X17))).
% 230.67/29.92 fof(sos_01, axiom, ![A, B, C]: '+'('+'(A, B), C)='+'(A, '+'(B, C))).
% 230.67/29.92 fof(sos_02, axiom, ![A2, B2]: '+'(A2, B2)='+'(B2, A2)).
% 230.67/29.92 fof(sos_03, axiom, ![A2]: '+'(A2, '0')=A2).
% 230.67/29.92 fof(sos_05, axiom, ![X0, X1, X2]: (('>='(X0, X1) & '>='(X1, X2)) => '>='(X0, X2))).
% 230.67/29.92 fof(sos_06, axiom, ![X3, X4]: (('>='(X3, X4) & '>='(X4, X3)) => X3=X4)).
% 230.67/29.92 fof(sos_07, axiom, ![X5, X6, X7]: ('>='('+'(X5, X6), X7) <=> '>='(X6, '==>'(X5, X7)))).
% 230.67/29.92 fof(sos_08, axiom, ![A2]: '>='(A2, '0')).
% 230.67/29.92 fof(sos_09, axiom, ![X8, X9, X10]: ('>='(X8, X9) => '>='('+'(X8, X10), '+'(X9, X10)))).
% 230.67/29.92 fof(sos_10, axiom, ![X11, X12, X13]: ('>='(X11, X12) => '>='('==>'(X12, X13), '==>'(X11, X13)))).
% 230.67/29.92 fof(sos_11, axiom, ![X14, X15, X16]: ('>='(X14, X15) => '>='('==>'(X16, X14), '==>'(X16, X15)))).
% 230.67/29.92 fof(sos_12, axiom, ![A2, B2]: '+'(A2, '==>'(A2, B2))='+'(B2, '==>'(B2, A2))).
% 230.67/29.92
% 230.67/29.92 Now clausify the problem and encode Horn clauses using encoding 3 of
% 230.67/29.92 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 230.67/29.92 We repeatedly replace C & s=t => u=v by the two clauses:
% 230.67/29.92 fresh(y, y, x1...xn) = u
% 230.67/29.92 C => fresh(s, t, x1...xn) = v
% 230.67/29.92 where fresh is a fresh function symbol and x1..xn are the free
% 230.67/29.92 variables of u and v.
% 230.67/29.92 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 230.67/29.92 input problem has no model of domain size 1).
% 230.67/29.92
% 230.67/29.92 The encoding turns the above axioms into the following unit equations and goals:
% 230.67/29.92
% 230.67/29.92 Axiom 1 (sos_08): X >= 0 = true.
% 230.67/29.92 Axiom 2 (sos_02): X + Y = Y + X.
% 230.67/29.92 Axiom 3 (sos_03): X + 0 = X.
% 230.67/29.92 Axiom 4 (goals_13): x19 = x19 ==> x18.
% 230.67/29.92 Axiom 5 (goals_13_1): (x17 ==> x18) >= x17 = true.
% 230.67/29.92 Axiom 6 (sos_12): X + (X ==> Y) = Y + (Y ==> X).
% 230.67/29.92 Axiom 7 (sos_01): (X + Y) + Z = X + (Y + Z).
% 230.67/29.92 Axiom 8 (sos_06): fresh(X, X, Y, Z) = Z.
% 230.67/29.92 Axiom 9 (sos_05): fresh9(X, X, Y, Z) = true.
% 230.67/29.92 Axiom 10 (sos_06): fresh2(X, X, Y, Z) = Y.
% 230.67/29.92 Axiom 11 (sos_05): fresh8(X, X, Y, Z, W) = Y >= W.
% 230.67/29.92 Axiom 12 (sos_07): fresh7(X, X, Y, Z, W) = true.
% 230.67/29.92 Axiom 13 (sos_07_1): fresh6(X, X, Y, Z, W) = true.
% 230.67/29.92 Axiom 14 (sos_09): fresh5(X, X, Y, Z, W) = true.
% 230.67/29.92 Axiom 15 (sos_10): fresh4(X, X, Y, Z, W) = true.
% 230.67/29.92 Axiom 16 (sos_11): fresh3(X, X, Y, Z, W) = true.
% 230.67/29.92 Axiom 17 (sos_06): fresh2(X >= Y, true, Y, X) = fresh(Y >= X, true, Y, X).
% 230.67/29.92 Axiom 18 (sos_05): fresh8(X >= Y, true, Z, X, Y) = fresh9(Z >= X, true, Z, Y).
% 230.67/29.92 Axiom 19 (sos_09): fresh5(X >= Y, true, X, Y, Z) = (X + Z) >= (Y + Z).
% 230.67/29.92 Axiom 20 (sos_10): fresh4(X >= Y, true, X, Y, Z) = (Y ==> Z) >= (X ==> Z).
% 230.67/29.92 Axiom 21 (sos_11): fresh3(X >= Y, true, X, Y, Z) = (Z ==> X) >= (Z ==> Y).
% 230.67/29.92 Axiom 22 (sos_07): fresh7(X >= (Y ==> Z), true, Y, X, Z) = (Y + X) >= Z.
% 230.67/29.92 Axiom 23 (sos_07_1): fresh6((X + Y) >= Z, true, X, Y, Z) = Y >= (X ==> Z).
% 230.67/29.92
% 230.67/29.92 Lemma 24: 0 + X = X.
% 230.67/29.92 Proof:
% 230.67/29.92 0 + X
% 230.67/29.92 = { by axiom 2 (sos_02) R->L }
% 230.67/29.92 X + 0
% 230.67/29.92 = { by axiom 3 (sos_03) }
% 230.67/29.92 X
% 230.67/29.92
% 230.67/29.92 Lemma 25: 0 ==> X = X.
% 230.67/29.92 Proof:
% 230.67/29.92 0 ==> X
% 230.67/29.92 = { by lemma 24 R->L }
% 230.67/29.92 0 + (0 ==> X)
% 230.67/29.92 = { by axiom 6 (sos_12) R->L }
% 230.67/29.92 X + (X ==> 0)
% 230.67/29.92 = { by axiom 8 (sos_06) R->L }
% 230.67/29.92 X + fresh(true, true, 0, X ==> 0)
% 230.67/29.92 = { by axiom 13 (sos_07_1) R->L }
% 230.67/29.92 X + fresh(fresh6(true, true, X, 0, 0), true, 0, X ==> 0)
% 230.67/29.92 = { by axiom 1 (sos_08) R->L }
% 230.67/29.92 X + fresh(fresh6((X + 0) >= 0, true, X, 0, 0), true, 0, X ==> 0)
% 230.67/29.92 = { by axiom 23 (sos_07_1) }
% 230.67/29.92 X + fresh(0 >= (X ==> 0), true, 0, X ==> 0)
% 230.67/29.92 = { by axiom 17 (sos_06) R->L }
% 230.67/29.92 X + fresh2((X ==> 0) >= 0, true, 0, X ==> 0)
% 230.67/29.92 = { by axiom 1 (sos_08) }
% 230.67/29.92 X + fresh2(true, true, 0, X ==> 0)
% 230.67/29.92 = { by axiom 10 (sos_06) }
% 230.67/29.92 X + 0
% 230.67/29.92 = { by axiom 3 (sos_03) }
% 230.67/29.92 X
% 230.67/29.92
% 230.67/29.92 Lemma 26: (X + Y) >= X = true.
% 230.67/29.92 Proof:
% 230.67/29.92 (X + Y) >= X
% 230.67/29.92 = { by axiom 2 (sos_02) R->L }
% 230.67/29.92 (Y + X) >= X
% 230.67/29.92 = { by lemma 24 R->L }
% 230.67/29.92 (Y + X) >= (0 + X)
% 230.67/29.92 = { by axiom 19 (sos_09) R->L }
% 230.67/29.92 fresh5(Y >= 0, true, Y, 0, X)
% 230.67/29.92 = { by axiom 1 (sos_08) }
% 230.67/29.92 fresh5(true, true, Y, 0, X)
% 230.67/29.92 = { by axiom 14 (sos_09) }
% 230.67/29.92 true
% 230.67/29.92
% 230.67/29.92 Lemma 27: (0 ==> X) >= (Y ==> X) = true.
% 230.67/29.92 Proof:
% 230.67/29.92 (0 ==> X) >= (Y ==> X)
% 230.67/29.92 = { by axiom 20 (sos_10) R->L }
% 230.67/29.92 fresh4(Y >= 0, true, Y, 0, X)
% 230.67/29.92 = { by axiom 1 (sos_08) }
% 230.67/29.92 fresh4(true, true, Y, 0, X)
% 230.67/29.92 = { by axiom 15 (sos_10) }
% 230.67/29.92 true
% 230.67/29.92
% 230.67/29.92 Lemma 28: fresh6((X + (X ==> Y)) >= Z, true, Y, Y ==> X, Z) = (Y ==> X) >= (Y ==> Z).
% 230.67/29.92 Proof:
% 230.67/29.92 fresh6((X + (X ==> Y)) >= Z, true, Y, Y ==> X, Z)
% 230.67/29.92 = { by axiom 6 (sos_12) R->L }
% 230.67/29.92 fresh6((Y + (Y ==> X)) >= Z, true, Y, Y ==> X, Z)
% 230.67/29.92 = { by axiom 23 (sos_07_1) }
% 230.67/29.92 (Y ==> X) >= (Y ==> Z)
% 230.67/29.92
% 230.67/29.92 Goal 1 (goals_13_2): x19 >= x17 = true.
% 230.67/29.92 Proof:
% 230.67/29.92 x19 >= x17
% 230.67/29.92 = { by axiom 3 (sos_03) R->L }
% 230.67/29.92 (x19 + 0) >= x17
% 230.67/29.92 = { by axiom 22 (sos_07) R->L }
% 230.67/29.92 fresh7(0 >= (x19 ==> x17), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 10 (sos_06) R->L }
% 230.67/29.92 fresh7(0 >= fresh2(true, true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 13 (sos_07_1) R->L }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(true, true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 14 (sos_09) R->L }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(fresh5(true, true, ((x17 ==> x19) ==> x17) ==> x19, x17 ==> x19, (x17 ==> x19) ==> x17), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 15 (sos_10) R->L }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(fresh5(fresh4(true, true, 0 ==> x17, (x17 ==> x19) ==> x17, x19), true, ((x17 ==> x19) ==> x17) ==> x19, x17 ==> x19, (x17 ==> x19) ==> x17), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by lemma 27 R->L }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(fresh5(fresh4((0 ==> x17) >= ((x17 ==> x19) ==> x17), true, 0 ==> x17, (x17 ==> x19) ==> x17, x19), true, ((x17 ==> x19) ==> x17) ==> x19, x17 ==> x19, (x17 ==> x19) ==> x17), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 20 (sos_10) }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(fresh5((((x17 ==> x19) ==> x17) ==> x19) >= ((0 ==> x17) ==> x19), true, ((x17 ==> x19) ==> x17) ==> x19, x17 ==> x19, (x17 ==> x19) ==> x17), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by lemma 25 }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(fresh5((((x17 ==> x19) ==> x17) ==> x19) >= (x17 ==> x19), true, ((x17 ==> x19) ==> x17) ==> x19, x17 ==> x19, (x17 ==> x19) ==> x17), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 19 (sos_09) }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(((((x17 ==> x19) ==> x17) ==> x19) + ((x17 ==> x19) ==> x17)) >= ((x17 ==> x19) + ((x17 ==> x19) ==> x17)), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 6 (sos_12) }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6(((((x17 ==> x19) ==> x17) ==> x19) + ((x17 ==> x19) ==> x17)) >= (x17 + (x17 ==> (x17 ==> x19))), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 2 (sos_02) }
% 230.67/29.92 fresh7(0 >= fresh2(fresh6((((x17 ==> x19) ==> x17) + (((x17 ==> x19) ==> x17) ==> x19)) >= (x17 + (x17 ==> (x17 ==> x19))), true, x19, x19 ==> ((x17 ==> x19) ==> x17), x17 + (x17 ==> (x17 ==> x19))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by lemma 28 }
% 230.67/29.92 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= (x19 ==> (x17 + (x17 ==> (x17 ==> x19)))), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 10 (sos_06) R->L }
% 230.67/29.92 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2(true, true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 13 (sos_07_1) R->L }
% 230.67/29.92 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2(fresh6(true, true, x19, x19 ==> x17, ((x17 ==> x19) ==> x17) + (x17 ==> x19)), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 14 (sos_09) R->L }
% 230.67/29.92 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2(fresh6(fresh5(true, true, 0 ==> x17, (x17 ==> x19) ==> x17, x17 ==> x19), true, x19, x19 ==> x17, ((x17 ==> x19) ==> x17) + (x17 ==> x19)), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by lemma 27 R->L }
% 230.67/29.92 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2(fresh6(fresh5((0 ==> x17) >= ((x17 ==> x19) ==> x17), true, 0 ==> x17, (x17 ==> x19) ==> x17, x17 ==> x19), true, x19, x19 ==> x17, ((x17 ==> x19) ==> x17) + (x17 ==> x19)), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.92 = { by axiom 19 (sos_09) }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2(fresh6(((0 ==> x17) + (x17 ==> x19)) >= (((x17 ==> x19) ==> x17) + (x17 ==> x19)), true, x19, x19 ==> x17, ((x17 ==> x19) ==> x17) + (x17 ==> x19)), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by lemma 25 }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2(fresh6((x17 + (x17 ==> x19)) >= (((x17 ==> x19) ==> x17) + (x17 ==> x19)), true, x19, x19 ==> x17, ((x17 ==> x19) ==> x17) + (x17 ==> x19)), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by lemma 28 }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2((x19 ==> x17) >= (x19 ==> (((x17 ==> x19) ==> x17) + (x17 ==> x19))), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 2 (sos_02) }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2((x19 ==> x17) >= (x19 ==> ((x17 ==> x19) + ((x17 ==> x19) ==> x17))), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 6 (sos_12) }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh2((x19 ==> x17) >= (x19 ==> (x17 + (x17 ==> (x17 ==> x19)))), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 17 (sos_06) }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh((x19 ==> (x17 + (x17 ==> (x17 ==> x19)))) >= (x19 ==> x17), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 21 (sos_11) R->L }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh(fresh3((x17 + (x17 ==> (x17 ==> x19))) >= x17, true, x17 + (x17 ==> (x17 ==> x19)), x17, x19), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by lemma 26 }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh(fresh3(true, true, x17 + (x17 ==> (x17 ==> x19)), x17, x19), true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 16 (sos_11) }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= fresh(true, true, x19 ==> (x17 + (x17 ==> (x17 ==> x19))), x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 8 (sos_06) }
% 230.67/29.93 fresh7(0 >= fresh2((x19 ==> ((x17 ==> x19) ==> x17)) >= (x19 ==> x17), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 17 (sos_06) }
% 230.67/29.93 fresh7(0 >= fresh((x19 ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by lemma 25 R->L }
% 230.67/29.93 fresh7(0 >= fresh((x19 ==> (0 ==> x17)) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 21 (sos_11) R->L }
% 230.67/29.93 fresh7(0 >= fresh(fresh3((0 ==> x17) >= ((x17 ==> x19) ==> x17), true, 0 ==> x17, (x17 ==> x19) ==> x17, x19), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by lemma 27 }
% 230.67/29.93 fresh7(0 >= fresh(fresh3(true, true, 0 ==> x17, (x17 ==> x19) ==> x17, x19), true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 16 (sos_11) }
% 230.67/29.93 fresh7(0 >= fresh(true, true, x19 ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 8 (sos_06) }
% 230.67/29.93 fresh7(0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 23 (sos_07_1) R->L }
% 230.67/29.93 fresh7(fresh6((x19 + 0) >= ((x17 ==> x19) ==> x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 3 (sos_03) }
% 230.67/29.93 fresh7(fresh6(x19 >= ((x17 ==> x19) ==> x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 23 (sos_07_1) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(((x17 ==> x19) + x19) >= x17, true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 2 (sos_02) }
% 230.67/29.93 fresh7(fresh6(fresh6((x19 + (x17 ==> x19)) >= x17, true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 11 (sos_05) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh8(true, true, x19 + (x17 ==> x19), x17 ==> x18, x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 5 (goals_13_1) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh8((x17 ==> x18) >= x17, true, x19 + (x17 ==> x19), x17 ==> x18, x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 18 (sos_05) }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9((x19 + (x17 ==> x19)) >= (x17 ==> x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 23 (sos_07_1) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6((x17 + (x19 + (x17 ==> x19))) >= x18, true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 2 (sos_02) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6((x17 + ((x17 ==> x19) + x19)) >= x18, true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 7 (sos_01) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6(((x17 + (x17 ==> x19)) + x19) >= x18, true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 2 (sos_02) }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6((x19 + (x17 + (x17 ==> x19))) >= x18, true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 6 (sos_12) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6((x19 + (x19 + (x19 ==> x17))) >= x18, true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 22 (sos_07) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6(fresh7((x19 + (x19 ==> x17)) >= (x19 ==> x18), true, x19, x19 + (x19 ==> x17), x18), true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 4 (goals_13) R->L }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6(fresh7((x19 + (x19 ==> x17)) >= x19, true, x19, x19 + (x19 ==> x17), x18), true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by lemma 26 }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6(fresh7(true, true, x19, x19 + (x19 ==> x17), x18), true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 12 (sos_07) }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(fresh6(true, true, x17, x19 + (x17 ==> x19), x18), true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 13 (sos_07_1) }
% 230.67/29.93 fresh7(fresh6(fresh6(fresh9(true, true, x19 + (x17 ==> x19), x17), true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 9 (sos_05) }
% 230.67/29.93 fresh7(fresh6(fresh6(true, true, x17 ==> x19, x19, x17), true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 13 (sos_07_1) }
% 230.67/29.93 fresh7(fresh6(true, true, x19, 0, (x17 ==> x19) ==> x17), true, x19, 0, x17)
% 230.67/29.93 = { by axiom 13 (sos_07_1) }
% 230.67/29.93 fresh7(true, true, x19, 0, x17)
% 230.67/29.93 = { by axiom 12 (sos_07) }
% 230.67/29.93 true
% 230.67/29.93 % SZS output end Proof
% 230.67/29.93
% 230.67/29.93 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------