%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : PUZ128+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:30:57 PM UTC 2026
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PUZ128+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n008.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 22:45:09 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.54 Command-line arguments: --flatten-regeneralise
% 0.21/0.54
% 0.21/0.54 % SZS status Theorem
% 0.21/0.54
% 0.62/0.59 % SZS output start Proof
% 0.62/0.59 Axiom 1 (background_1): Oedipus = e2.
% 0.62/0.59 Axiom 2 (background): Oedipus = c.
% 0.62/0.59 Axiom 3 (background_4): Polyneikes = d.
% 0.62/0.59 Axiom 4 (background_2): Iokaste = a.
% 0.62/0.59 Axiom 5 (background_3): Iokaste = b.
% 0.62/0.59 Axiom 6 (background_5): parent(a) = true.
% 0.62/0.59 Axiom 7 (background_7): parent(c) = true.
% 0.62/0.59 Axiom 8 (background_8): parent(d) = true.
% 0.62/0.59 Axiom 9 (background_13): patricide(e2) = true.
% 0.62/0.59 Axiom 10 (background_9): relation(a, of, Oedipus) = true.
% 0.62/0.59 Axiom 11 (background_10): relation(b, of, Polyneikes) = true.
% 0.62/0.59 Axiom 12 (background_11): relation(c, of, Polyneikes) = true.
% 0.62/0.60 Axiom 13 (background_12): relation(d, of, Thersandros) = true.
% 0.62/0.60 Axiom 14 (ifeq_axiom): ifeq4(X, X, Y, Z) = Y.
% 0.62/0.60 Axiom 15 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.62/0.60 Axiom 16 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.62/0.60 Axiom 17 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.62/0.60 Axiom 18 (prove): ifeq2(patricide(X), true, ifeq2(relation(X, of, Y), true, ifeq2(relation(Z, of, X), true, ifeq2(parent(X), true, ifeq2(parent(Z), true, ifeq4(Iokaste, Z, e(Y), Y), Y), Y), Y), Y), Y) = Y.
% 0.62/0.60 Axiom 19 (prove_1): ifeq(patricide(X), true, ifeq(relation(X, of, Y), true, ifeq(relation(Z, of, X), true, ifeq(parent(X), true, ifeq(parent(Z), true, ifeq3(Iokaste, Z, patricide(e(Y)), true), true), true), true), true), true) = true.
% 0.62/0.60
% 0.62/0.60 Lemma 20: c = e2.
% 0.62/0.60 Proof:
% 0.62/0.60 c
% 0.62/0.60 = { by axiom 2 (background) R->L }
% 0.62/0.60 Oedipus
% 0.62/0.60 = { by axiom 1 (background_1) }
% 0.62/0.60 e2
% 0.62/0.60
% 0.62/0.60 Lemma 21: b = a.
% 0.62/0.60 Proof:
% 0.62/0.60 b
% 0.62/0.60 = { by axiom 5 (background_3) R->L }
% 0.62/0.60 Iokaste
% 0.62/0.60 = { by axiom 4 (background_2) }
% 0.62/0.60 a
% 0.62/0.60
% 0.62/0.60 Lemma 22: ifeq2(patricide(X), true, ifeq2(relation(X, of, Y), true, ifeq2(relation(Z, of, X), true, ifeq2(parent(X), true, ifeq2(parent(Z), true, ifeq4(a, Z, e(Y), Y), Y), Y), Y), Y), Y) = Y.
% 0.62/0.60 Proof:
% 0.62/0.60 ifeq2(patricide(X), true, ifeq2(relation(X, of, Y), true, ifeq2(relation(Z, of, X), true, ifeq2(parent(X), true, ifeq2(parent(Z), true, ifeq4(a, Z, e(Y), Y), Y), Y), Y), Y), Y)
% 0.62/0.60 = { by axiom 4 (background_2) R->L }
% 0.62/0.60 ifeq2(patricide(X), true, ifeq2(relation(X, of, Y), true, ifeq2(relation(Z, of, X), true, ifeq2(parent(X), true, ifeq2(parent(Z), true, ifeq4(Iokaste, Z, e(Y), Y), Y), Y), Y), Y), Y)
% 0.62/0.60 = { by axiom 18 (prove) }
% 0.62/0.60 Y
% 0.62/0.60
% 0.62/0.60 Lemma 23: e(Polyneikes) = Polyneikes.
% 0.62/0.60 Proof:
% 0.62/0.60 e(Polyneikes)
% 0.62/0.60 = { by axiom 17 (ifeq_axiom) R->L }
% 0.62/0.60 ifeq2(true, true, e(Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 12 (background_11) R->L }
% 0.62/0.60 ifeq2(relation(c, of, Polyneikes), true, e(Polyneikes), Polyneikes)
% 0.62/0.60 = { by lemma 20 }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, e(Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 14 (ifeq_axiom) R->L }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 17 (ifeq_axiom) R->L }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, ifeq2(true, true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 6 (background_5) R->L }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 17 (ifeq_axiom) R->L }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, ifeq2(true, true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 7 (background_7) R->L }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, ifeq2(parent(c), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by lemma 20 }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, ifeq2(parent(e2), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 17 (ifeq_axiom) R->L }
% 0.62/0.60 ifeq2(relation(e2, of, Polyneikes), true, ifeq2(true, true, ifeq2(parent(e2), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 17 (ifeq_axiom) R->L }
% 0.62/0.60 ifeq2(true, true, ifeq2(relation(e2, of, Polyneikes), true, ifeq2(true, true, ifeq2(parent(e2), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 9 (background_13) R->L }
% 0.62/0.60 ifeq2(patricide(e2), true, ifeq2(relation(e2, of, Polyneikes), true, ifeq2(true, true, ifeq2(parent(e2), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 10 (background_9) R->L }
% 0.62/0.60 ifeq2(patricide(e2), true, ifeq2(relation(e2, of, Polyneikes), true, ifeq2(relation(a, of, Oedipus), true, ifeq2(parent(e2), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by axiom 1 (background_1) }
% 0.62/0.60 ifeq2(patricide(e2), true, ifeq2(relation(e2, of, Polyneikes), true, ifeq2(relation(a, of, e2), true, ifeq2(parent(e2), true, ifeq2(parent(a), true, ifeq4(a, a, e(Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes), Polyneikes)
% 0.62/0.60 = { by lemma 22 }
% 0.62/0.60 Polyneikes
% 0.62/0.60
% 0.62/0.60 Goal 1 (background_14): tuple(Thersandros, patricide(X)) = tuple(X, true).
% 0.62/0.60 The goal is true when:
% 0.62/0.60 X = Thersandros
% 0.62/0.60
% 0.62/0.60 Proof:
% 0.62/0.60 tuple(Thersandros, patricide(Thersandros))
% 0.62/0.60 = { by lemma 22 R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(patricide(Polyneikes), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(relation(a, of, Polyneikes), true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by lemma 21 R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(patricide(Polyneikes), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(relation(b, of, Polyneikes), true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 11 (background_10) }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(patricide(Polyneikes), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by lemma 23 R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(patricide(e(Polyneikes)), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(true, true, patricide(e(Polyneikes)), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 12 (background_11) R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(c, of, Polyneikes), true, patricide(e(Polyneikes)), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by lemma 20 }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, patricide(e(Polyneikes)), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 15 (ifeq_axiom) R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 6 (background_5) R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by axiom 7 (background_7) R->L }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, ifeq(parent(c), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.60 = { by lemma 20 }
% 0.62/0.60 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(ifeq(true, true, ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 9 (background_13) R->L }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 10 (background_9) R->L }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(relation(a, of, Oedipus), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 1 (background_1) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(relation(a, of, e2), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 4 (background_2) R->L }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(relation(a, of, e2), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(Iokaste, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 19 (prove_1) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(true, true, ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 17 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 17 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(parent(Polyneikes), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 3 (background_4) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(parent(d), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 8 (background_8) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 17 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(parent(a), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 6 (background_5) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq2(true, true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 17 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, ifeq4(a, a, e(Thersandros), Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 14 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(Polyneikes, of, Thersandros), true, e(Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 3 (background_4) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(relation(d, of, Thersandros), true, e(Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 13 (background_12) }
% 0.62/0.61 tuple(Thersandros, patricide(ifeq2(true, true, e(Thersandros), Thersandros)))
% 0.62/0.61 = { by axiom 17 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, patricide(e(Thersandros)))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(true, true, patricide(e(Thersandros)), true))
% 0.62/0.61 = { by axiom 13 (background_12) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(d, of, Thersandros), true, patricide(e(Thersandros)), true))
% 0.62/0.61 = { by axiom 3 (background_4) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, patricide(e(Thersandros)), true))
% 0.62/0.61 = { by axiom 15 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq3(a, a, patricide(e(Thersandros)), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true))
% 0.62/0.61 = { by axiom 6 (background_5) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true))
% 0.62/0.61 = { by axiom 8 (background_8) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(parent(d), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true))
% 0.62/0.61 = { by axiom 3 (background_4) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(true, true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 19 (prove_1) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(relation(a, of, e2), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(Iokaste, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 4 (background_2) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(relation(a, of, e2), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 1 (background_1) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(relation(a, of, Oedipus), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 10 (background_9) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(patricide(e2), true, ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 9 (background_13) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(true, true, ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, ifeq(parent(e2), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by lemma 20 R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, ifeq(parent(c), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 7 (background_7) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 6 (background_5) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, ifeq(true, true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, ifeq3(a, a, patricide(e(Polyneikes)), true), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 15 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(e2, of, Polyneikes), true, patricide(e(Polyneikes)), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by lemma 20 R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(relation(c, of, Polyneikes), true, patricide(e(Polyneikes)), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 12 (background_11) }
% 0.62/0.61 tuple(Thersandros, ifeq(ifeq(true, true, patricide(e(Polyneikes)), true), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 16 (ifeq_axiom) }
% 0.62/0.61 tuple(Thersandros, ifeq(patricide(e(Polyneikes)), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by lemma 23 }
% 0.62/0.61 tuple(Thersandros, ifeq(patricide(Polyneikes), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(true, true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 11 (background_10) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(patricide(Polyneikes), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(relation(b, of, Polyneikes), true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by lemma 21 }
% 0.62/0.61 tuple(Thersandros, ifeq(patricide(Polyneikes), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(relation(a, of, Polyneikes), true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(a, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 4 (background_2) R->L }
% 0.62/0.61 tuple(Thersandros, ifeq(patricide(Polyneikes), true, ifeq(relation(Polyneikes, of, Thersandros), true, ifeq(relation(a, of, Polyneikes), true, ifeq(parent(Polyneikes), true, ifeq(parent(a), true, ifeq3(Iokaste, a, patricide(e(Thersandros)), true), true), true), true), true), true))
% 0.62/0.61 = { by axiom 19 (prove_1) }
% 0.62/0.61 tuple(Thersandros, true)
% 0.62/0.61 % SZS output end Proof
% 0.62/0.61
% 0.62/0.61 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------