%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 11:50:46 AM UTC 2026
% Result : Theorem 2.28s 0.72s
% Output : Proof 2.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.35 % Computer : n016.cluster.edu
% 0.06/0.35 % Model : x86_64 x86_64
% 0.06/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.35 % Memory : 8046.5625MB
% 0.06/0.35 % OS : Linux 6.8.0-71-generic
% 0.06/0.35 % CPULimit : 300
% 0.06/0.35 % WCLimit : 300
% 0.06/0.35 % DateTime : Sun Sep 27 17:10:17 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.28/0.72 Command-line arguments: --flatten --complete-subsets
% 2.28/0.72
% 2.28/0.72 % SZS status Theorem
% 2.28/0.72
% 2.28/0.75 % SZS output start Proof
% 2.28/0.75 Axiom 1 (sos_02): X + Y = Y + X.
% 2.28/0.75 Axiom 2 (sos_03): X + 0 = X.
% 2.28/0.75 Axiom 3 (sos_12): X + 1 = 1.
% 2.28/0.75 Axiom 4 (sos_04): X >= X = true.
% 2.28/0.75 Axiom 5 (sos_08): X >= 0 = true.
% 2.28/0.75 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 2.28/0.75 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.28/0.75 Axiom 8 (sos_01): (X + Y) + Z = X + (Y + Z).
% 2.28/0.75 Axiom 9 (sos_13): ((X ==> 1) ==> X) ==> X = 0.
% 2.28/0.75 Axiom 10 (sos_06): ifeq2(X >= Y, true, ifeq2(Y >= X, true, Y, X), X) = X.
% 2.28/0.75 Axiom 11 (sos_11): ifeq(X >= Y, true, (Z ==> X) >= (Z ==> Y), true) = true.
% 2.28/0.75 Axiom 12 (sos_09): ifeq(X >= Y, true, (X + Z) >= (Y + Z), true) = true.
% 2.28/0.75 Axiom 13 (sos_07): ifeq(X >= (Y ==> Z), true, (Y + X) >= Z, true) = true.
% 2.28/0.75 Axiom 14 (sos_07_1): ifeq((X + Y) >= Z, true, Y >= (X ==> Z), true) = true.
% 2.28/0.75
% 2.28/0.75 Lemma 15: 0 + X = X.
% 2.28/0.75 Proof:
% 2.28/0.75 0 + X
% 2.28/0.75 = { by axiom 1 (sos_02) R->L }
% 2.28/0.75 X + 0
% 2.28/0.75 = { by axiom 2 (sos_03) }
% 2.28/0.75 X
% 2.28/0.75
% 2.28/0.75 Lemma 16: X + (X ==> 1) = 1.
% 2.28/0.75 Proof:
% 2.28/0.75 X + (X ==> 1)
% 2.28/0.75 = { by axiom 10 (sos_06) R->L }
% 2.28/0.75 ifeq2((X + (X ==> 1)) >= 1, true, ifeq2(1 >= (X + (X ==> 1)), true, 1, X + (X ==> 1)), X + (X ==> 1))
% 2.28/0.75 = { by axiom 3 (sos_12) R->L }
% 2.28/0.75 ifeq2((X + (X ==> 1)) >= 1, true, ifeq2(((X + (X ==> 1)) + 1) >= (X + (X ==> 1)), true, 1, X + (X ==> 1)), X + (X ==> 1))
% 2.28/0.75 = { by axiom 1 (sos_02) R->L }
% 2.28/0.75 ifeq2((X + (X ==> 1)) >= 1, true, ifeq2((1 + (X + (X ==> 1))) >= (X + (X ==> 1)), true, 1, X + (X ==> 1)), X + (X ==> 1))
% 2.28/0.75 = { by axiom 7 (ifeq_axiom) R->L }
% 2.28/0.75 ifeq2((X + (X ==> 1)) >= 1, true, ifeq2(ifeq(true, true, (1 + (X + (X ==> 1))) >= (X + (X ==> 1)), true), true, 1, X + (X ==> 1)), X + (X ==> 1))
% 2.28/0.75 = { by axiom 5 (sos_08) R->L }
% 2.28/0.75 ifeq2((X + (X ==> 1)) >= 1, true, ifeq2(ifeq(1 >= 0, true, (1 + (X + (X ==> 1))) >= (X + (X ==> 1)), true), true, 1, X + (X ==> 1)), X + (X ==> 1))
% 2.28/0.75 = { by lemma 15 R->L }
% 2.28/0.75 ifeq2((X + (X ==> 1)) >= 1, true, ifeq2(ifeq(1 >= 0, true, (1 + (X + (X ==> 1))) >= (0 + (X + (X ==> 1))), true), true, 1, X + (X ==> 1)), X + (X ==> 1))
% 2.28/0.75 = { by axiom 12 (sos_09) }
% 2.28/0.75 ifeq2((X + (X ==> 1)) >= 1, true, ifeq2(true, true, 1, X + (X ==> 1)), X + (X ==> 1))
% 2.28/0.76 = { by axiom 6 (ifeq_axiom) }
% 2.28/0.76 ifeq2((X + (X ==> 1)) >= 1, true, 1, X + (X ==> 1))
% 2.28/0.76 = { by axiom 7 (ifeq_axiom) R->L }
% 2.28/0.76 ifeq2(ifeq(true, true, (X + (X ==> 1)) >= 1, true), true, 1, X + (X ==> 1))
% 2.28/0.76 = { by axiom 4 (sos_04) R->L }
% 2.28/0.76 ifeq2(ifeq((X ==> 1) >= (X ==> 1), true, (X + (X ==> 1)) >= 1, true), true, 1, X + (X ==> 1))
% 2.28/0.76 = { by axiom 13 (sos_07) }
% 2.28/0.76 ifeq2(true, true, 1, X + (X ==> 1))
% 2.28/0.76 = { by axiom 6 (ifeq_axiom) }
% 2.28/0.76 1
% 2.28/0.76
% 2.28/0.76 Lemma 17: Y + (X + Z) = X + (Y + Z).
% 2.28/0.76 Proof:
% 2.28/0.76 Y + (X + Z)
% 2.28/0.76 = { by axiom 1 (sos_02) R->L }
% 2.28/0.76 (X + Z) + Y
% 2.28/0.76 = { by axiom 8 (sos_01) }
% 2.28/0.76 X + (Z + Y)
% 2.28/0.76 = { by axiom 1 (sos_02) }
% 2.28/0.76 X + (Y + Z)
% 2.28/0.76
% 2.28/0.76 Lemma 18: (X ==> 1) ==> X = X.
% 2.28/0.76 Proof:
% 2.28/0.76 (X ==> 1) ==> X
% 2.28/0.76 = { by axiom 10 (sos_06) R->L }
% 2.28/0.76 ifeq2(((X ==> 1) ==> X) >= X, true, ifeq2(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X), (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 2 (sos_03) R->L }
% 2.28/0.76 ifeq2((((X ==> 1) ==> X) + 0) >= X, true, ifeq2(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X), (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 9 (sos_13) R->L }
% 2.28/0.76 ifeq2((((X ==> 1) ==> X) + (((X ==> 1) ==> X) ==> X)) >= X, true, ifeq2(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X), (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 7 (ifeq_axiom) R->L }
% 2.28/0.76 ifeq2(ifeq(true, true, (((X ==> 1) ==> X) + (((X ==> 1) ==> X) ==> X)) >= X, true), true, ifeq2(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X), (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 4 (sos_04) R->L }
% 2.28/0.76 ifeq2(ifeq((((X ==> 1) ==> X) ==> X) >= (((X ==> 1) ==> X) ==> X), true, (((X ==> 1) ==> X) + (((X ==> 1) ==> X) ==> X)) >= X, true), true, ifeq2(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X), (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 13 (sos_07) }
% 2.28/0.76 ifeq2(true, true, ifeq2(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X), (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 6 (ifeq_axiom) }
% 2.28/0.76 ifeq2(X >= ((X ==> 1) ==> X), true, X, (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 7 (ifeq_axiom) R->L }
% 2.28/0.76 ifeq2(ifeq(true, true, X >= ((X ==> 1) ==> X), true), true, X, (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 12 (sos_09) R->L }
% 2.28/0.76 ifeq2(ifeq(ifeq((X ==> 1) >= 0, true, ((X ==> 1) + X) >= (0 + X), true), true, X >= ((X ==> 1) ==> X), true), true, X, (X ==> 1) ==> X)
% 2.28/0.76 = { by lemma 15 }
% 2.28/0.76 ifeq2(ifeq(ifeq((X ==> 1) >= 0, true, ((X ==> 1) + X) >= X, true), true, X >= ((X ==> 1) ==> X), true), true, X, (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 5 (sos_08) }
% 2.28/0.76 ifeq2(ifeq(ifeq(true, true, ((X ==> 1) + X) >= X, true), true, X >= ((X ==> 1) ==> X), true), true, X, (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 7 (ifeq_axiom) }
% 2.28/0.76 ifeq2(ifeq(((X ==> 1) + X) >= X, true, X >= ((X ==> 1) ==> X), true), true, X, (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 14 (sos_07_1) }
% 2.28/0.76 ifeq2(true, true, X, (X ==> 1) ==> X)
% 2.28/0.76 = { by axiom 6 (ifeq_axiom) }
% 2.28/0.76 X
% 2.28/0.76
% 2.28/0.76 Lemma 19: (X ==> 1) ==> 1 = X.
% 2.28/0.76 Proof:
% 2.28/0.76 (X ==> 1) ==> 1
% 2.28/0.76 = { by axiom 6 (ifeq_axiom) R->L }
% 2.28/0.76 ifeq2(true, true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 11 (sos_11) R->L }
% 2.28/0.76 ifeq2(ifeq(1 >= X, true, ((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 3 (sos_12) R->L }
% 2.28/0.76 ifeq2(ifeq((X + 1) >= X, true, ((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 1 (sos_02) R->L }
% 2.28/0.76 ifeq2(ifeq((1 + X) >= X, true, ((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 7 (ifeq_axiom) R->L }
% 2.28/0.76 ifeq2(ifeq(ifeq(true, true, (1 + X) >= X, true), true, ((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 5 (sos_08) R->L }
% 2.28/0.76 ifeq2(ifeq(ifeq(1 >= 0, true, (1 + X) >= X, true), true, ((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by lemma 15 R->L }
% 2.28/0.76 ifeq2(ifeq(ifeq(1 >= 0, true, (1 + X) >= (0 + X), true), true, ((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 12 (sos_09) }
% 2.28/0.76 ifeq2(ifeq(true, true, ((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 7 (ifeq_axiom) }
% 2.28/0.76 ifeq2(((X ==> 1) ==> 1) >= ((X ==> 1) ==> X), true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by lemma 18 }
% 2.28/0.76 ifeq2(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X)
% 2.28/0.76 = { by axiom 6 (ifeq_axiom) R->L }
% 2.28/0.76 ifeq2(true, true, ifeq2(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X), X)
% 2.28/0.76 = { by axiom 14 (sos_07_1) R->L }
% 2.28/0.76 ifeq2(ifeq(((X ==> 1) + X) >= ((X ==> 1) + X), true, X >= ((X ==> 1) ==> ((X ==> 1) + X)), true), true, ifeq2(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X), X)
% 2.28/0.76 = { by axiom 4 (sos_04) }
% 2.28/0.76 ifeq2(ifeq(true, true, X >= ((X ==> 1) ==> ((X ==> 1) + X)), true), true, ifeq2(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X), X)
% 2.28/0.76 = { by axiom 7 (ifeq_axiom) }
% 2.28/0.76 ifeq2(X >= ((X ==> 1) ==> ((X ==> 1) + X)), true, ifeq2(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X), X)
% 2.28/0.76 = { by axiom 1 (sos_02) }
% 2.28/0.76 ifeq2(X >= ((X ==> 1) ==> (X + (X ==> 1))), true, ifeq2(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X), X)
% 2.28/0.76 = { by lemma 16 }
% 2.28/0.76 ifeq2(X >= ((X ==> 1) ==> 1), true, ifeq2(((X ==> 1) ==> 1) >= X, true, (X ==> 1) ==> 1, X), X)
% 2.28/0.76 = { by axiom 10 (sos_06) }
% 2.28/0.76 X
% 2.28/0.76
% 2.28/0.76 Goal 1 (goals_14): x17 + x17 = x17.
% 2.28/0.76 Proof:
% 2.28/0.76 x17 + x17
% 2.28/0.76 = { by lemma 19 R->L }
% 2.28/0.76 ((x17 + x17) ==> 1) ==> 1
% 2.28/0.76 = { by axiom 10 (sos_06) R->L }
% 2.28/0.77 ifeq2(((x17 + x17) ==> 1) >= (x17 ==> 1), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by lemma 18 R->L }
% 2.28/0.77 ifeq2(((x17 + x17) ==> 1) >= (((x17 ==> 1) ==> 1) ==> (x17 ==> 1)), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by lemma 19 }
% 2.28/0.77 ifeq2(((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> 1)), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by lemma 16 R->L }
% 2.28/0.77 ifeq2(((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> ((x17 + x17) + ((x17 + x17) ==> 1)))), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 1 (sos_02) R->L }
% 2.28/0.77 ifeq2(((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> (((x17 + x17) ==> 1) + (x17 + x17)))), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by lemma 17 }
% 2.28/0.77 ifeq2(((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> (x17 + (((x17 + x17) ==> 1) + x17)))), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 8 (sos_01) R->L }
% 2.28/0.77 ifeq2(((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + x17))), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 2.28/0.77 ifeq2(ifeq(true, true, ((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + x17))), true), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 14 (sos_07_1) R->L }
% 2.28/0.77 ifeq2(ifeq(ifeq((x17 + (x17 + ((x17 + x17) ==> 1))) >= (x17 + (x17 + ((x17 + x17) ==> 1))), true, (x17 + ((x17 + x17) ==> 1)) >= (x17 ==> (x17 + (x17 + ((x17 + x17) ==> 1)))), true), true, ((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + x17))), true), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 4 (sos_04) }
% 2.28/0.77 ifeq2(ifeq(ifeq(true, true, (x17 + ((x17 + x17) ==> 1)) >= (x17 ==> (x17 + (x17 + ((x17 + x17) ==> 1)))), true), true, ((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + x17))), true), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 7 (ifeq_axiom) }
% 2.28/0.77 ifeq2(ifeq((x17 + ((x17 + x17) ==> 1)) >= (x17 ==> (x17 + (x17 + ((x17 + x17) ==> 1)))), true, ((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + x17))), true), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 1 (sos_02) }
% 2.28/0.77 ifeq2(ifeq((x17 + ((x17 + x17) ==> 1)) >= (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + x17)), true, ((x17 + x17) ==> 1) >= (x17 ==> (x17 ==> ((x17 + ((x17 + x17) ==> 1)) + x17))), true), true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 14 (sos_07_1) }
% 2.28/0.77 ifeq2(true, true, ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1), (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 6 (ifeq_axiom) }
% 2.28/0.77 ifeq2((x17 ==> 1) >= ((x17 + x17) ==> 1), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 2.28/0.77 ifeq2(ifeq(true, true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 12 (sos_09) R->L }
% 2.28/0.77 ifeq2(ifeq(ifeq(x17 >= 0, true, (x17 + 1) >= (0 + 1), true), true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by lemma 15 }
% 2.28/0.77 ifeq2(ifeq(ifeq(x17 >= 0, true, (x17 + 1) >= 1, true), true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 5 (sos_08) }
% 2.28/0.77 ifeq2(ifeq(ifeq(true, true, (x17 + 1) >= 1, true), true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 7 (ifeq_axiom) }
% 2.28/0.77 ifeq2(ifeq((x17 + 1) >= 1, true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by lemma 16 R->L }
% 2.28/0.77 ifeq2(ifeq((x17 + (x17 + (x17 ==> 1))) >= 1, true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 1 (sos_02) R->L }
% 2.28/0.77 ifeq2(ifeq((x17 + ((x17 ==> 1) + x17)) >= 1, true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by lemma 17 R->L }
% 2.28/0.77 ifeq2(ifeq(((x17 ==> 1) + (x17 + x17)) >= 1, true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 1 (sos_02) }
% 2.28/0.77 ifeq2(ifeq(((x17 + x17) + (x17 ==> 1)) >= 1, true, (x17 ==> 1) >= ((x17 + x17) ==> 1), true), true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 14 (sos_07_1) }
% 2.28/0.77 ifeq2(true, true, x17 ==> 1, (x17 + x17) ==> 1) ==> 1
% 2.28/0.77 = { by axiom 6 (ifeq_axiom) }
% 2.28/0.77 (x17 ==> 1) ==> 1
% 2.28/0.77 = { by lemma 19 }
% 2.28/0.77 x17
% 2.28/0.77 % SZS output end Proof
% 2.28/0.77
% 2.28/0.77 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------