%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL892+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:50:44 AM UTC 2026
% Result : Theorem 94.30s 12.32s
% Output : Proof 94.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL892+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 17:05:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.30/12.32 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 94.30/12.32
% 94.30/12.32 % SZS status Theorem
% 94.30/12.32
% 94.30/12.36 % SZS output start Proof
% 94.30/12.36 Axiom 1 (sos_04): X >= X = true.
% 94.30/12.36 Axiom 2 (sos_08): X >= 0 = true.
% 94.30/12.36 Axiom 3 (sos_02): X + Y = Y + X.
% 94.30/12.36 Axiom 4 (sos_03): X + 0 = X.
% 94.30/12.36 Axiom 5 (goals_14): x19 = x19 ==> x18.
% 94.30/12.36 Axiom 6 (goals_14_1): (x17 ==> x18) >= x17 = true.
% 94.30/12.36 Axiom 7 (sos_12): X + (X ==> Y) = Y + (Y ==> X).
% 94.30/12.36 Axiom 8 (sos_01): (X + Y) + Z = X + (Y + Z).
% 94.30/12.36 Axiom 9 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 94.30/12.36 Axiom 10 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 94.30/12.36 Axiom 11 (sos_09): ifeq(X >= Y, true, (X + Z) >= (Y + Z), true) = true.
% 94.30/12.36 Axiom 12 (sos_10): ifeq(X >= Y, true, (Y ==> Z) >= (X ==> Z), true) = true.
% 94.30/12.36 Axiom 13 (sos_07): ifeq(X >= (Y ==> Z), true, (Y + X) >= Z, true) = true.
% 94.30/12.36 Axiom 14 (sos_07_1): ifeq((X + Y) >= Z, true, Y >= (X ==> Z), true) = true.
% 94.30/12.36 Axiom 15 (sos_06): ifeq2(X >= Y, true, ifeq2(Y >= X, true, Y, X), X) = X.
% 94.30/12.36 Axiom 16 (sos_05): ifeq(X >= Y, true, ifeq(Z >= X, true, Z >= Y, true), true) = true.
% 94.30/12.36
% 94.30/12.36 Lemma 17: 0 + X = X.
% 94.30/12.36 Proof:
% 94.30/12.36 0 + X
% 94.30/12.36 = { by axiom 3 (sos_02) R->L }
% 94.30/12.36 X + 0
% 94.30/12.36 = { by axiom 4 (sos_03) }
% 94.30/12.36 X
% 94.30/12.36
% 94.30/12.36 Lemma 18: X + (Y + Z) = Y + (X + Z).
% 94.30/12.36 Proof:
% 94.30/12.36 X + (Y + Z)
% 94.30/12.36 = { by axiom 3 (sos_02) R->L }
% 94.30/12.36 (Y + Z) + X
% 94.30/12.36 = { by axiom 8 (sos_01) }
% 94.30/12.36 Y + (Z + X)
% 94.30/12.36 = { by axiom 3 (sos_02) }
% 94.30/12.36 Y + (X + Z)
% 94.30/12.36
% 94.30/12.36 Goal 1 (goals_14_2): x19 >= x17 = true.
% 94.30/12.36 Proof:
% 94.30/12.36 x19 >= x17
% 94.30/12.36 = { by axiom 4 (sos_03) R->L }
% 94.30/12.36 (x19 + 0) >= x17
% 94.30/12.36 = { by axiom 15 (sos_06) R->L }
% 94.30/12.36 (x19 + ifeq2(0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.36 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.36 (x19 + ifeq2(ifeq(true, true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.36 = { by axiom 16 (sos_05) R->L }
% 94.30/12.36 (x19 + ifeq2(ifeq(ifeq((x17 ==> x18) >= x17, true, ifeq((x19 + (x17 ==> x19)) >= (x17 ==> x18), true, (x19 + (x17 ==> x19)) >= x17, true), true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.36 = { by axiom 6 (goals_14_1) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(true, true, ifeq((x19 + (x17 ==> x19)) >= (x17 ==> x18), true, (x19 + (x17 ==> x19)) >= x17, true), true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq((x19 + (x17 ==> x19)) >= (x17 ==> x18), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(true, true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 13 (sos_07) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(ifeq((x19 + (x19 ==> x17)) >= (x19 ==> x18), true, (x19 + (x19 + (x19 ==> x17))) >= x18, true), true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 5 (goals_14) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(ifeq((x19 + (x19 ==> x17)) >= x19, true, (x19 + (x19 + (x19 ==> x17))) >= x18, true), true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 3 (sos_02) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(ifeq((x19 + (x19 ==> x17)) >= x19, true, ((x19 + (x19 ==> x17)) + x19) >= x18, true), true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 7 (sos_12) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(ifeq((x17 + (x17 ==> x19)) >= x19, true, ((x19 + (x19 ==> x17)) + x19) >= x18, true), true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, (x17 + (x17 ==> x19)) >= x19, true), true, ((x19 + (x19 ==> x17)) + x19) >= x18, true), true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 1 (sos_04) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(ifeq(ifeq((x17 ==> x19) >= (x17 ==> x19), true, (x17 + (x17 ==> x19)) >= x19, true), true, ((x19 + (x19 ==> x17)) + x19) >= x18, true), true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 13 (sos_07) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, ((x19 + (x19 ==> x17)) + x19) >= x18, true), true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq(((x19 + (x19 ==> x17)) + x19) >= x18, true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 8 (sos_01) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq((x19 + ((x19 ==> x17) + x19)) >= x18, true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 3 (sos_02) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq((x19 + (x19 + (x19 ==> x17))) >= x18, true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 7 (sos_12) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq((x19 + (x17 + (x17 ==> x19))) >= x18, true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by lemma 18 }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(ifeq((x17 + (x19 + (x17 ==> x19))) >= x18, true, (x19 + (x17 ==> x19)) >= (x17 ==> x18), true), true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 14 (sos_07_1) }
% 94.30/12.37 (x19 + ifeq2(ifeq(ifeq(true, true, (x19 + (x17 ==> x19)) >= x17, true), true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.37 (x19 + ifeq2(ifeq((x19 + (x17 ==> x19)) >= x17, true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 3 (sos_02) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 15 (sos_06) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(true, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 11 (sos_09) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(ifeq(((((x17 ==> x19) ==> x17) ==> x19) + (x17 ==> (x17 ==> x19))) >= 0, true, (((((x17 ==> x19) ==> x17) ==> x19) + (x17 ==> (x17 ==> x19))) + x17) >= (0 + x17), true), true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 2 (sos_08) }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(ifeq(true, true, (((((x17 ==> x19) ==> x17) ==> x19) + (x17 ==> (x17 ==> x19))) + x17) >= (0 + x17), true), true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((((((x17 ==> x19) ==> x17) ==> x19) + (x17 ==> (x17 ==> x19))) + x17) >= (0 + x17), true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by lemma 17 }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((((((x17 ==> x19) ==> x17) ==> x19) + (x17 ==> (x17 ==> x19))) + x17) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 3 (sos_02) }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((x17 + ((((x17 ==> x19) ==> x17) ==> x19) + (x17 ==> (x17 ==> x19)))) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 3 (sos_02) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((x17 + ((x17 ==> (x17 ==> x19)) + (((x17 ==> x19) ==> x17) ==> x19))) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.37 = { by axiom 8 (sos_01) R->L }
% 94.30/12.37 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(((x17 + (x17 ==> (x17 ==> x19))) + (((x17 ==> x19) ==> x17) ==> x19)) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 7 (sos_12) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((((x17 ==> x19) + ((x17 ==> x19) ==> x17)) + (((x17 ==> x19) ==> x17) ==> x19)) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 8 (sos_01) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(((x17 ==> x19) + (((x17 ==> x19) ==> x17) + (((x17 ==> x19) ==> x17) ==> x19))) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 7 (sos_12) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(((x17 ==> x19) + (x19 + (x19 ==> ((x17 ==> x19) ==> x17)))) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by lemma 18 R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((x19 + ((x17 ==> x19) + (x19 ==> ((x17 ==> x19) ==> x17)))) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 8 (sos_01) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(((x19 + (x17 ==> x19)) + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true, (x19 ==> ((x17 ==> x19) ==> x17)) >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 14 (sos_07_1) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(true, true, ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 10 (ifeq_axiom) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(true, true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 14 (sos_07_1) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(ifeq(((x17 ==> x19) + (x19 + (((x17 ==> x19) + x19) ==> x17))) >= x17, true, (x19 + (((x17 ==> x19) + x19) ==> x17)) >= ((x17 ==> x19) ==> x17), true), true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 8 (sos_01) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(ifeq((((x17 ==> x19) + x19) + (((x17 ==> x19) + x19) ==> x17)) >= x17, true, (x19 + (((x17 ==> x19) + x19) ==> x17)) >= ((x17 ==> x19) ==> x17), true), true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(ifeq(ifeq(true, true, (((x17 ==> x19) + x19) + (((x17 ==> x19) + x19) ==> x17)) >= x17, true), true, (x19 + (((x17 ==> x19) + x19) ==> x17)) >= ((x17 ==> x19) ==> x17), true), true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 1 (sos_04) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(ifeq(ifeq((((x17 ==> x19) + x19) ==> x17) >= (((x17 ==> x19) + x19) ==> x17), true, (((x17 ==> x19) + x19) + (((x17 ==> x19) + x19) ==> x17)) >= x17, true), true, (x19 + (((x17 ==> x19) + x19) ==> x17)) >= ((x17 ==> x19) ==> x17), true), true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 13 (sos_07) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq(ifeq(true, true, (x19 + (((x17 ==> x19) + x19) ==> x17)) >= ((x17 ==> x19) ==> x17), true), true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((x19 + (((x17 ==> x19) + x19) ==> x17)) >= ((x17 ==> x19) ==> x17), true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 3 (sos_02) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(ifeq((x19 + ((x19 + (x17 ==> x19)) ==> x17)) >= ((x17 ==> x19) ==> x17), true, ((x19 + (x17 ==> x19)) ==> x17) >= (x19 ==> ((x17 ==> x19) ==> x17)), true), true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 14 (sos_07_1) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ifeq2(true, true, (x19 + (x17 ==> x19)) ==> x17, x19 ==> ((x17 ==> x19) ==> x17)), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 10 (ifeq_axiom) }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + x19) >= x17, true, 0 >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 4 (sos_03) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x17 ==> x19) + (x19 + 0)) >= x17, true, 0 >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by lemma 18 R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq((x19 + ((x17 ==> x19) + 0)) >= x17, true, 0 >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 8 (sos_01) R->L }
% 94.30/12.38 (x19 + ifeq2(ifeq(((x19 + (x17 ==> x19)) + 0) >= x17, true, 0 >= ((x19 + (x17 ==> x19)) ==> x17), true), true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 14 (sos_07_1) }
% 94.30/12.38 (x19 + ifeq2(true, true, ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0), 0)) >= x17
% 94.30/12.38 = { by axiom 10 (ifeq_axiom) }
% 94.30/12.38 (x19 + ifeq2((x19 ==> ((x17 ==> x19) ==> x17)) >= 0, true, x19 ==> ((x17 ==> x19) ==> x17), 0)) >= x17
% 94.30/12.38 = { by axiom 2 (sos_08) }
% 94.30/12.38 (x19 + ifeq2(true, true, x19 ==> ((x17 ==> x19) ==> x17), 0)) >= x17
% 94.30/12.38 = { by axiom 10 (ifeq_axiom) }
% 94.30/12.38 (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17
% 94.30/12.38 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.38 ifeq(true, true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.38 = { by axiom 12 (sos_10) R->L }
% 94.30/12.38 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= (x17 ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.38 = { by axiom 4 (sos_03) R->L }
% 94.30/12.38 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + 0) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.38 = { by axiom 10 (ifeq_axiom) R->L }
% 94.30/12.38 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + ifeq2(true, true, 0, x17 ==> 0)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.38 = { by axiom 14 (sos_07_1) R->L }
% 94.30/12.38 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + ifeq2(ifeq((x17 + 0) >= 0, true, 0 >= (x17 ==> 0), true), true, 0, x17 ==> 0)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.38 = { by axiom 2 (sos_08) }
% 94.30/12.38 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + ifeq2(ifeq(true, true, 0 >= (x17 ==> 0), true), true, 0, x17 ==> 0)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.38 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.39 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + ifeq2(0 >= (x17 ==> 0), true, 0, x17 ==> 0)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 10 (ifeq_axiom) R->L }
% 94.30/12.39 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + ifeq2(true, true, ifeq2(0 >= (x17 ==> 0), true, 0, x17 ==> 0), x17 ==> 0)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 2 (sos_08) R->L }
% 94.30/12.39 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + ifeq2((x17 ==> 0) >= 0, true, ifeq2(0 >= (x17 ==> 0), true, 0, x17 ==> 0), x17 ==> 0)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 15 (sos_06) }
% 94.30/12.39 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((x17 + (x17 ==> 0)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 7 (sos_12) }
% 94.30/12.39 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((0 + (0 ==> x17)) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by lemma 17 }
% 94.30/12.39 ifeq(ifeq((((x17 ==> x19) ==> x17) ==> x19) >= ((0 ==> x17) ==> x19), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 9 (ifeq_axiom) R->L }
% 94.30/12.39 ifeq(ifeq(ifeq(true, true, (((x17 ==> x19) ==> x17) ==> x19) >= ((0 ==> x17) ==> x19), true), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 12 (sos_10) R->L }
% 94.30/12.39 ifeq(ifeq(ifeq(ifeq((x17 ==> x19) >= 0, true, (0 ==> x17) >= ((x17 ==> x19) ==> x17), true), true, (((x17 ==> x19) ==> x17) ==> x19) >= ((0 ==> x17) ==> x19), true), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 2 (sos_08) }
% 94.30/12.39 ifeq(ifeq(ifeq(ifeq(true, true, (0 ==> x17) >= ((x17 ==> x19) ==> x17), true), true, (((x17 ==> x19) ==> x17) ==> x19) >= ((0 ==> x17) ==> x19), true), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.39 ifeq(ifeq(ifeq((0 ==> x17) >= ((x17 ==> x19) ==> x17), true, (((x17 ==> x19) ==> x17) ==> x19) >= ((0 ==> x17) ==> x19), true), true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 12 (sos_10) }
% 94.30/12.39 ifeq(ifeq(true, true, ((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 9 (ifeq_axiom) }
% 94.30/12.39 ifeq(((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true, (x19 + (x19 ==> ((x17 ==> x19) ==> x17))) >= x17, true)
% 94.30/12.39 = { by axiom 7 (sos_12) R->L }
% 94.30/12.39 ifeq(((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true, (((x17 ==> x19) ==> x17) + (((x17 ==> x19) ==> x17) ==> x19)) >= x17, true)
% 94.30/12.39 = { by axiom 3 (sos_02) R->L }
% 94.30/12.39 ifeq(((x17 ==> x19) ==> x17) >= ((((x17 ==> x19) ==> x17) ==> x19) ==> x17), true, ((((x17 ==> x19) ==> x17) ==> x19) + ((x17 ==> x19) ==> x17)) >= x17, true)
% 94.30/12.39 = { by axiom 13 (sos_07) }
% 94.30/12.39 true
% 94.30/12.39 % SZS output end Proof
% 94.30/12.39
% 94.30/12.39 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------