TSTP Solution File: LCL890-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL890-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n007.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 : Unsatisfiable 58.55s 7.83s
% Output : Proof 58.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL890-10 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.13 % 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 : n007.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 : Thu Aug 24 17:03:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 58.55/7.83 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 58.55/7.83
% 58.55/7.83 % SZS status Unsatisfiable
% 58.55/7.83
% 58.55/7.86 % SZS output start Proof
% 58.55/7.86 Axiom 1 (sos_05): X >= X = true.
% 58.55/7.86 Axiom 2 (sos_09): X >= 0 = true.
% 58.55/7.86 Axiom 3 (sos_02): X + Y = Y + X.
% 58.55/7.86 Axiom 4 (sos_03): X + 0 = X.
% 58.55/7.86 Axiom 5 (goals_14): sK2_goals_14_X19 = sK2_goals_14_X19 ==> sK3_goals_14_X18.
% 58.55/7.86 Axiom 6 (goals_14_1): (sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17 = true.
% 58.55/7.86 Axiom 7 (sos_13): X + (X ==> Y) = Y + (Y ==> X).
% 58.55/7.86 Axiom 8 (sos_01): (X + Y) + Z = X + (Y + Z).
% 58.55/7.86 Axiom 9 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 58.55/7.86 Axiom 10 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 58.55/7.86 Axiom 11 (sos_10): ifeq(X >= Y, true, (X + Z) >= (Y + Z), true) = true.
% 58.55/7.86 Axiom 12 (sos_11): ifeq(X >= Y, true, (Y ==> Z) >= (X ==> Z), true) = true.
% 58.55/7.86 Axiom 13 (sos_12): ifeq(X >= Y, true, (Z ==> X) >= (Z ==> Y), true) = true.
% 58.55/7.86 Axiom 14 (sos_08): ifeq(X >= (Y ==> Z), true, (Y + X) >= Z, true) = true.
% 58.55/7.86 Axiom 15 (sos_08_1): ifeq((X + Y) >= Z, true, Y >= (X ==> Z), true) = true.
% 58.55/7.86 Axiom 16 (sos_07): ifeq2(X >= Y, true, ifeq2(Y >= X, true, Y, X), X) = X.
% 58.55/7.86
% 58.55/7.86 Lemma 17: 0 + X = X.
% 58.55/7.86 Proof:
% 58.55/7.86 0 + X
% 58.55/7.86 = { by axiom 3 (sos_02) R->L }
% 58.55/7.86 X + 0
% 58.55/7.86 = { by axiom 4 (sos_03) }
% 58.55/7.86 X
% 58.55/7.86
% 58.55/7.86 Lemma 18: X + (Y + Z) = Y + (X + Z).
% 58.55/7.86 Proof:
% 58.55/7.86 X + (Y + Z)
% 58.55/7.86 = { by axiom 3 (sos_02) R->L }
% 58.55/7.86 (Y + Z) + X
% 58.55/7.86 = { by axiom 8 (sos_01) }
% 58.55/7.86 Y + (Z + X)
% 58.55/7.86 = { by axiom 3 (sos_02) }
% 58.55/7.86 Y + (X + Z)
% 58.55/7.86
% 58.55/7.86 Lemma 19: (X + (X ==> Y)) >= X = true.
% 58.55/7.86 Proof:
% 58.55/7.86 (X + (X ==> Y)) >= X
% 58.55/7.86 = { by axiom 7 (sos_13) R->L }
% 58.55/7.86 (Y + (Y ==> X)) >= X
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.86 ifeq(true, true, (Y + (Y ==> X)) >= X, true)
% 58.55/7.86 = { by axiom 1 (sos_05) R->L }
% 58.55/7.86 ifeq((Y ==> X) >= (Y ==> X), true, (Y + (Y ==> X)) >= X, true)
% 58.55/7.86 = { by axiom 14 (sos_08) }
% 58.55/7.86 true
% 58.55/7.86
% 58.55/7.86 Lemma 20: (X + (Y + ((X + Y) ==> Z))) >= Z = true.
% 58.55/7.86 Proof:
% 58.55/7.86 (X + (Y + ((X + Y) ==> Z))) >= Z
% 58.55/7.86 = { by axiom 8 (sos_01) R->L }
% 58.55/7.86 ((X + Y) + ((X + Y) ==> Z)) >= Z
% 58.55/7.86 = { by axiom 7 (sos_13) }
% 58.55/7.86 (Z + (Z ==> (X + Y))) >= Z
% 58.55/7.86 = { by lemma 19 }
% 58.55/7.86 true
% 58.55/7.86
% 58.55/7.86 Lemma 21: ifeq((X + (Y + Z)) >= W, true, Z >= ((X + Y) ==> W), true) = true.
% 58.55/7.86 Proof:
% 58.55/7.86 ifeq((X + (Y + Z)) >= W, true, Z >= ((X + Y) ==> W), true)
% 58.55/7.86 = { by axiom 8 (sos_01) R->L }
% 58.55/7.86 ifeq(((X + Y) + Z) >= W, true, Z >= ((X + Y) ==> W), true)
% 58.55/7.86 = { by axiom 15 (sos_08_1) }
% 58.55/7.86 true
% 58.55/7.86
% 58.55/7.86 Lemma 22: (X + Y) ==> Z = X ==> (Y ==> Z).
% 58.55/7.86 Proof:
% 58.55/7.86 (X + Y) ==> Z
% 58.55/7.86 = { by axiom 10 (ifeq_axiom) R->L }
% 58.55/7.86 ifeq2(true, true, (X + Y) ==> Z, X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 15 (sos_08_1) R->L }
% 58.55/7.86 ifeq2(ifeq((X + ((X + Y) ==> Z)) >= (Y ==> Z), true, ((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true), true, (X + Y) ==> Z, X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 3 (sos_02) R->L }
% 58.55/7.86 ifeq2(ifeq((X + ((Y + X) ==> Z)) >= (Y ==> Z), true, ((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true), true, (X + Y) ==> Z, X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.86 ifeq2(ifeq(ifeq(true, true, (X + ((Y + X) ==> Z)) >= (Y ==> Z), true), true, ((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true), true, (X + Y) ==> Z, X ==> (Y ==> Z))
% 58.55/7.86 = { by lemma 20 R->L }
% 58.55/7.86 ifeq2(ifeq(ifeq((Y + (X + ((Y + X) ==> Z))) >= Z, true, (X + ((Y + X) ==> Z)) >= (Y ==> Z), true), true, ((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true), true, (X + Y) ==> Z, X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 15 (sos_08_1) }
% 58.55/7.86 ifeq2(ifeq(true, true, ((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true), true, (X + Y) ==> Z, X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.86 ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 10 (ifeq_axiom) R->L }
% 58.55/7.86 ifeq2(true, true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by lemma 21 R->L }
% 58.55/7.86 ifeq2(ifeq((X + (Y + (X ==> (Y ==> Z)))) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by lemma 18 R->L }
% 58.55/7.86 ifeq2(ifeq((Y + (X + (X ==> (Y ==> Z)))) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 7 (sos_13) }
% 58.55/7.86 ifeq2(ifeq((Y + ((Y ==> Z) + ((Y ==> Z) ==> X))) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 8 (sos_01) R->L }
% 58.55/7.86 ifeq2(ifeq(((Y + (Y ==> Z)) + ((Y ==> Z) ==> X)) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 7 (sos_13) R->L }
% 58.55/7.86 ifeq2(ifeq(((Z + (Z ==> Y)) + ((Y ==> Z) ==> X)) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 8 (sos_01) }
% 58.55/7.86 ifeq2(ifeq((Z + ((Z ==> Y) + ((Y ==> Z) ==> X))) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 3 (sos_02) }
% 58.55/7.86 ifeq2(ifeq((Z + (((Y ==> Z) ==> X) + (Z ==> Y))) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 3 (sos_02) R->L }
% 58.55/7.86 ifeq2(ifeq(((((Y ==> Z) ==> X) + (Z ==> Y)) + Z) >= Z, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by lemma 17 R->L }
% 58.55/7.86 ifeq2(ifeq(((((Y ==> Z) ==> X) + (Z ==> Y)) + Z) >= (0 + Z), true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.86 ifeq2(ifeq(ifeq(true, true, ((((Y ==> Z) ==> X) + (Z ==> Y)) + Z) >= (0 + Z), true), true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 2 (sos_09) R->L }
% 58.55/7.86 ifeq2(ifeq(ifeq((((Y ==> Z) ==> X) + (Z ==> Y)) >= 0, true, ((((Y ==> Z) ==> X) + (Z ==> Y)) + Z) >= (0 + Z), true), true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 11 (sos_10) }
% 58.55/7.86 ifeq2(ifeq(true, true, (X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.86 ifeq2((X ==> (Y ==> Z)) >= ((X + Y) ==> Z), true, ifeq2(((X + Y) ==> Z) >= (X ==> (Y ==> Z)), true, (X + Y) ==> Z, X ==> (Y ==> Z)), X ==> (Y ==> Z))
% 58.55/7.86 = { by axiom 16 (sos_07) }
% 58.55/7.86 X ==> (Y ==> Z)
% 58.55/7.86
% 58.55/7.86 Goal 1 (goals_14_2): sK2_goals_14_X19 >= sK1_goals_14_X17 = true.
% 58.55/7.86 Proof:
% 58.55/7.86 sK2_goals_14_X19 >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 4 (sos_03) R->L }
% 58.55/7.86 (sK2_goals_14_X19 + 0) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 16 (sos_07) R->L }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(ifeq(true, true, 0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 14 (sos_08) R->L }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(ifeq(ifeq((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (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, true), true, 0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(ifeq(true, true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true), true, 0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 6 (goals_14_1) R->L }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(ifeq((sK1_goals_14_X17 ==> sK3_goals_14_X18) >= sK1_goals_14_X17, true, (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true), true, 0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 13 (sos_12) }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(ifeq(ifeq(true, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true), true, 0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(ifeq((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) >= sK1_goals_14_X17, true, 0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 4 (sos_03) R->L }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(ifeq(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) + 0) >= sK1_goals_14_X17, true, 0 >= ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17), true), true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 15 (sos_08_1) }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(true, true, ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0), 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 10 (ifeq_axiom) }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17) >= 0, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 2 (sos_09) }
% 58.55/7.86 (sK2_goals_14_X19 + ifeq2(true, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17, 0)) >= sK1_goals_14_X17
% 58.55/7.86 = { by axiom 10 (ifeq_axiom) }
% 58.55/7.86 (sK2_goals_14_X19 + ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18))) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17
% 58.55/7.86 = { by lemma 22 }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK2_goals_14_X19 ==> (sK1_goals_14_X17 ==> sK3_goals_14_X18)) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by lemma 22 R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (((sK2_goals_14_X19 + sK1_goals_14_X17) ==> sK3_goals_14_X18) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 3 (sos_02) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 10 (ifeq_axiom) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(true, true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 15 (sos_08_1) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK1_goals_14_X17 + ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19, true, ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 3 (sos_02) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK1_goals_14_X17 + ((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) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(true, true, (sK1_goals_14_X17 + ((sK2_goals_14_X19 + sK1_goals_14_X17) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19, true), true, ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by lemma 20 R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK2_goals_14_X19 + (sK1_goals_14_X17 + ((sK2_goals_14_X19 + sK1_goals_14_X17) ==> sK3_goals_14_X18))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + ((sK2_goals_14_X19 + sK1_goals_14_X17) ==> sK3_goals_14_X18)) >= sK2_goals_14_X19, true), true, ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 5 (goals_14) }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK2_goals_14_X19 + (sK1_goals_14_X17 + ((sK2_goals_14_X19 + sK1_goals_14_X17) ==> sK3_goals_14_X18))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 + ((sK2_goals_14_X19 + sK1_goals_14_X17) ==> sK3_goals_14_X18)) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true), true, ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 15 (sos_08_1) }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(true, true, ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 10 (ifeq_axiom) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(true, true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by lemma 21 R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK1_goals_14_X17 + (sK2_goals_14_X19 + (sK1_goals_14_X17 ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by lemma 18 R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK2_goals_14_X19 + (sK1_goals_14_X17 + (sK1_goals_14_X17 ==> sK2_goals_14_X19))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 7 (sos_13) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK2_goals_14_X19 + (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17))) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 3 (sos_02) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq((sK2_goals_14_X19 + ((sK2_goals_14_X19 ==> sK1_goals_14_X17) + sK2_goals_14_X19)) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 8 (sos_01) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq(true, true, ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by lemma 19 R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) >= sK2_goals_14_X19, true, ((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) + sK2_goals_14_X19) >= sK3_goals_14_X18, true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 3 (sos_02) R->L }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) >= sK2_goals_14_X19, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17))) >= sK3_goals_14_X18, true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 5 (goals_14) }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(ifeq((sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17)) >= (sK2_goals_14_X19 ==> sK3_goals_14_X18), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> sK1_goals_14_X17))) >= sK3_goals_14_X18, true), true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 14 (sos_08) }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2(ifeq(true, true, (sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> (ifeq2((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18), true, ifeq2(((sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, (sK1_goals_14_X17 + sK2_goals_14_X19) ==> sK3_goals_14_X18, sK1_goals_14_X17 ==> sK2_goals_14_X19), sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 16 (sos_07) }
% 58.55/7.87 (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.87 ifeq(true, true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 12 (sos_11) R->L }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= (sK1_goals_14_X17 ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 4 (sos_03) R->L }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + 0) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 10 (ifeq_axiom) R->L }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(true, true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 15 (sos_08_1) R->L }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(ifeq((sK1_goals_14_X17 + 0) >= 0, true, 0 >= (sK1_goals_14_X17 ==> 0), true), true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 2 (sos_09) }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(ifeq(true, true, 0 >= (sK1_goals_14_X17 ==> 0), true), true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(0 >= (sK1_goals_14_X17 ==> 0), true, 0, sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 10 (ifeq_axiom) R->L }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2(true, true, ifeq2(0 >= (sK1_goals_14_X17 ==> 0), true, 0, sK1_goals_14_X17 ==> 0), sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 2 (sos_09) R->L }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + ifeq2((sK1_goals_14_X17 ==> 0) >= 0, true, ifeq2(0 >= (sK1_goals_14_X17 ==> 0), true, 0, sK1_goals_14_X17 ==> 0), sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 16 (sos_07) }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((sK1_goals_14_X17 + (sK1_goals_14_X17 ==> 0)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 7 (sos_13) }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 + (0 ==> sK1_goals_14_X17)) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by lemma 17 }
% 58.55/7.87 ifeq(ifeq((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) R->L }
% 58.55/7.87 ifeq(ifeq(ifeq(true, true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 12 (sos_11) R->L }
% 58.55/7.87 ifeq(ifeq(ifeq(ifeq((sK1_goals_14_X17 ==> sK2_goals_14_X19) >= 0, true, (0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 2 (sos_09) }
% 58.55/7.87 ifeq(ifeq(ifeq(ifeq(true, true, (0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.87 ifeq(ifeq(ifeq((0 ==> sK1_goals_14_X17) >= ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) >= ((0 ==> sK1_goals_14_X17) ==> sK2_goals_14_X19), true), true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 12 (sos_11) }
% 58.55/7.87 ifeq(ifeq(true, true, ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true), true, (sK2_goals_14_X19 + (sK2_goals_14_X19 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 9 (ifeq_axiom_001) }
% 58.55/7.87 ifeq(((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> 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 ==> ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17))) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 7 (sos_13) R->L }
% 58.55/7.87 ifeq(((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) + (((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19)) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 3 (sos_02) R->L }
% 58.55/7.87 ifeq(((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) >= ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) ==> sK1_goals_14_X17), true, ((((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17) ==> sK2_goals_14_X19) + ((sK1_goals_14_X17 ==> sK2_goals_14_X19) ==> sK1_goals_14_X17)) >= sK1_goals_14_X17, true)
% 58.55/7.87 = { by axiom 14 (sos_08) }
% 58.55/7.87 true
% 58.55/7.87 % SZS output end Proof
% 58.55/7.87
% 58.55/7.87 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------