TSTP Solution File: ALG246-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG246-1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n027.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 : Wed Aug 30 16:42:43 EDT 2023
% Result : Unsatisfiable 48.36s 12.60s
% Output : Proof 48.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.26 % Problem : ALG246-1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.27 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.48 % Computer : n027.cluster.edu
% 0.10/0.48 % Model : x86_64 x86_64
% 0.10/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.48 % Memory : 8042.1875MB
% 0.10/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.48 % CPULimit : 300
% 0.10/0.48 % WCLimit : 300
% 0.10/0.48 % DateTime : Mon Aug 28 06:24:37 EDT 2023
% 0.10/0.50 % CPUTime :
% 48.36/12.60 Command-line arguments: --flatten
% 48.36/12.60
% 48.36/12.60 % SZS status Unsatisfiable
% 48.36/12.61
% 48.77/12.79 % SZS output start Proof
% 48.77/12.79 Axiom 1 (c11): n(X) = m(tptp2(X)).
% 48.77/12.81 Axiom 2 (c12): tptp2(tptp2(X)) = X.
% 48.77/12.81 Axiom 3 (c01): tptp1(X, Y) = tptp1(Y, X).
% 48.77/12.81 Axiom 4 (c02): tptp1(tptp5, X) = X.
% 48.77/12.81 Axiom 5 (c10): m(X) = tptp0(X, tptp3).
% 48.77/12.81 Axiom 6 (c05): tptp0(tptp3, X) = tptp5.
% 48.77/12.81 Axiom 7 (c07): tptp4(X, Y) = tptp1(X, tptp0(X, Y)).
% 48.77/12.81 Axiom 8 (c03): tptp1(X, tptp0(X, Y)) = tptp1(Y, tptp0(Y, X)).
% 48.77/12.81 Axiom 9 (c04): tptp0(tptp1(X, Y), Z) = tptp0(X, tptp0(Y, Z)).
% 48.77/12.81 Axiom 10 (c13): n(tptp0(X, Y)) = n(tptp0(tptp2(Y), tptp2(X))).
% 48.77/12.81 Axiom 11 (c09): tptp0(tptp1(X, Y), tptp3) = v(tptp0(X, tptp3), tptp0(Y, tptp3)).
% 48.77/12.81 Axiom 12 (c08): v(X, Y) = tptp4(tptp0(tptp0(X, Y), Y), tptp0(tptp0(Y, X), X)).
% 48.77/12.81 Axiom 13 (c06): tptp0(tptp0(tptp0(X, Y), Z), tptp0(tptp0(tptp0(Y, X), Z), Z)) = tptp5.
% 48.77/12.81
% 48.77/12.81 Lemma 14: m(tptp3) = tptp5.
% 48.77/12.81 Proof:
% 48.77/12.81 m(tptp3)
% 48.77/12.81 = { by axiom 5 (c10) }
% 48.77/12.81 tptp0(tptp3, tptp3)
% 48.77/12.81 = { by axiom 6 (c05) }
% 48.77/12.81 tptp5
% 48.77/12.81
% 48.77/12.81 Lemma 15: n(tptp0(Y, tptp2(X))) = n(tptp0(X, tptp2(Y))).
% 48.77/12.81 Proof:
% 48.77/12.81 n(tptp0(Y, tptp2(X)))
% 48.77/12.81 = { by axiom 2 (c12) R->L }
% 48.77/12.81 n(tptp0(tptp2(tptp2(Y)), tptp2(X)))
% 48.77/12.81 = { by axiom 10 (c13) R->L }
% 48.77/12.81 n(tptp0(X, tptp2(Y)))
% 48.77/12.81
% 48.77/12.81 Lemma 16: tptp4(Y, X) = tptp4(X, Y).
% 48.77/12.81 Proof:
% 48.77/12.81 tptp4(Y, X)
% 48.77/12.81 = { by axiom 7 (c07) }
% 48.77/12.81 tptp1(Y, tptp0(Y, X))
% 48.77/12.81 = { by axiom 8 (c03) R->L }
% 48.77/12.81 tptp1(X, tptp0(X, Y))
% 48.77/12.81 = { by axiom 7 (c07) R->L }
% 48.77/12.81 tptp4(X, Y)
% 48.77/12.81
% 48.77/12.81 Lemma 17: tptp0(tptp5, X) = tptp4(X, tptp5).
% 48.77/12.81 Proof:
% 48.77/12.81 tptp0(tptp5, X)
% 48.77/12.81 = { by axiom 4 (c02) R->L }
% 48.77/12.81 tptp1(tptp5, tptp0(tptp5, X))
% 48.77/12.81 = { by axiom 7 (c07) R->L }
% 48.77/12.81 tptp4(tptp5, X)
% 48.77/12.81 = { by lemma 16 R->L }
% 48.77/12.81 tptp4(X, tptp5)
% 48.77/12.81
% 48.77/12.81 Lemma 18: v(m(X), m(Y)) = tptp0(X, m(Y)).
% 48.77/12.81 Proof:
% 48.77/12.81 v(m(X), m(Y))
% 48.77/12.81 = { by axiom 5 (c10) }
% 48.77/12.81 v(m(X), tptp0(Y, tptp3))
% 48.77/12.81 = { by axiom 5 (c10) }
% 48.77/12.81 v(tptp0(X, tptp3), tptp0(Y, tptp3))
% 48.77/12.81 = { by axiom 11 (c09) R->L }
% 48.77/12.81 tptp0(tptp1(X, Y), tptp3)
% 48.77/12.81 = { by axiom 9 (c04) }
% 48.77/12.81 tptp0(X, tptp0(Y, tptp3))
% 48.77/12.81 = { by axiom 5 (c10) R->L }
% 48.77/12.81 tptp0(X, m(Y))
% 48.77/12.81
% 48.77/12.81 Lemma 19: tptp0(X, m(Y)) = m(tptp1(X, Y)).
% 48.77/12.81 Proof:
% 48.77/12.81 tptp0(X, m(Y))
% 48.77/12.81 = { by axiom 5 (c10) }
% 48.77/12.81 tptp0(X, tptp0(Y, tptp3))
% 48.77/12.81 = { by axiom 9 (c04) R->L }
% 48.77/12.81 tptp0(tptp1(X, Y), tptp3)
% 48.77/12.81 = { by axiom 5 (c10) R->L }
% 48.77/12.81 m(tptp1(X, Y))
% 48.77/12.81
% 48.77/12.81 Lemma 20: tptp0(X, tptp5) = tptp5.
% 48.77/12.81 Proof:
% 48.77/12.81 tptp0(X, tptp5)
% 48.77/12.81 = { by axiom 6 (c05) R->L }
% 48.77/12.81 tptp0(X, tptp0(tptp3, m(Y)))
% 48.77/12.81 = { by axiom 9 (c04) R->L }
% 48.77/12.81 tptp0(tptp1(X, tptp3), m(Y))
% 48.77/12.81 = { by lemma 18 R->L }
% 48.77/12.81 v(m(tptp1(X, tptp3)), m(Y))
% 48.77/12.81 = { by axiom 3 (c01) R->L }
% 48.77/12.81 v(m(tptp1(tptp3, X)), m(Y))
% 48.77/12.81 = { by lemma 19 R->L }
% 48.77/12.81 v(tptp0(tptp3, m(X)), m(Y))
% 48.77/12.81 = { by axiom 6 (c05) }
% 48.77/12.81 v(tptp5, m(Y))
% 48.77/12.81 = { by lemma 14 R->L }
% 48.77/12.81 v(m(tptp3), m(Y))
% 48.77/12.81 = { by lemma 18 }
% 48.77/12.81 tptp0(tptp3, m(Y))
% 48.77/12.81 = { by axiom 6 (c05) }
% 48.77/12.81 tptp5
% 48.77/12.81
% 48.77/12.81 Lemma 21: tptp1(X, tptp5) = X.
% 48.77/12.81 Proof:
% 48.77/12.81 tptp1(X, tptp5)
% 48.77/12.81 = { by axiom 3 (c01) R->L }
% 48.77/12.81 tptp1(tptp5, X)
% 48.77/12.81 = { by axiom 4 (c02) }
% 48.77/12.81 X
% 48.77/12.81
% 48.77/12.81 Lemma 22: tptp4(X, tptp5) = X.
% 48.77/12.81 Proof:
% 48.77/12.81 tptp4(X, tptp5)
% 48.77/12.81 = { by axiom 7 (c07) }
% 48.77/12.81 tptp1(X, tptp0(X, tptp5))
% 48.77/12.81 = { by lemma 20 }
% 48.77/12.81 tptp1(X, tptp5)
% 48.77/12.81 = { by lemma 21 }
% 48.77/12.81 X
% 48.77/12.81
% 48.77/12.81 Lemma 23: n(tptp2(X)) = m(X).
% 48.77/12.81 Proof:
% 48.77/12.81 n(tptp2(X))
% 48.77/12.81 = { by axiom 1 (c11) }
% 48.77/12.81 m(tptp2(tptp2(X)))
% 48.77/12.81 = { by axiom 2 (c12) }
% 48.77/12.81 m(X)
% 48.77/12.81
% 48.77/12.81 Lemma 24: n(tptp0(X, tptp2(tptp5))) = m(X).
% 48.77/12.81 Proof:
% 48.77/12.81 n(tptp0(X, tptp2(tptp5)))
% 48.77/12.81 = { by lemma 15 }
% 48.77/12.81 n(tptp0(tptp5, tptp2(X)))
% 48.77/12.81 = { by lemma 17 }
% 48.77/12.81 n(tptp4(tptp2(X), tptp5))
% 48.77/12.81 = { by lemma 22 }
% 48.77/12.81 n(tptp2(X))
% 48.77/12.81 = { by lemma 23 }
% 48.77/12.81 m(X)
% 48.77/12.81
% 48.77/12.81 Lemma 25: n(tptp5) = tptp5.
% 48.77/12.81 Proof:
% 48.77/12.81 n(tptp5)
% 48.77/12.81 = { by axiom 6 (c05) R->L }
% 48.77/12.81 n(tptp0(tptp3, tptp2(tptp5)))
% 48.77/12.81 = { by lemma 24 }
% 48.77/12.81 m(tptp3)
% 48.77/12.81 = { by lemma 14 }
% 48.77/12.81 tptp5
% 48.77/12.81
% 48.77/12.81 Lemma 26: tptp4(X, tptp3) = tptp3.
% 48.77/12.81 Proof:
% 48.77/12.81 tptp4(X, tptp3)
% 48.77/12.81 = { by lemma 16 }
% 48.77/12.81 tptp4(tptp3, X)
% 48.77/12.81 = { by axiom 7 (c07) }
% 48.77/12.81 tptp1(tptp3, tptp0(tptp3, X))
% 48.77/12.81 = { by axiom 6 (c05) }
% 48.77/12.81 tptp1(tptp3, tptp5)
% 48.77/12.81 = { by lemma 21 }
% 48.77/12.81 tptp3
% 48.77/12.81
% 48.77/12.81 Lemma 27: tptp1(X, m(X)) = tptp3.
% 48.77/12.81 Proof:
% 48.77/12.81 tptp1(X, m(X))
% 48.77/12.81 = { by axiom 5 (c10) }
% 48.77/12.81 tptp1(X, tptp0(X, tptp3))
% 48.77/12.81 = { by axiom 7 (c07) R->L }
% 48.77/12.81 tptp4(X, tptp3)
% 48.77/12.81 = { by lemma 26 }
% 48.77/12.81 tptp3
% 48.77/12.81
% 48.77/12.82 Lemma 28: tptp1(tptp2(X), n(X)) = tptp3.
% 48.77/12.82 Proof:
% 48.77/12.82 tptp1(tptp2(X), n(X))
% 48.77/12.82 = { by axiom 1 (c11) }
% 48.77/12.82 tptp1(tptp2(X), m(tptp2(X)))
% 48.77/12.82 = { by lemma 27 }
% 48.77/12.82 tptp3
% 48.77/12.82
% 48.77/12.82 Lemma 29: tptp2(tptp5) = tptp3.
% 48.77/12.82 Proof:
% 48.77/12.82 tptp2(tptp5)
% 48.77/12.82 = { by lemma 21 R->L }
% 48.77/12.82 tptp1(tptp2(tptp5), tptp5)
% 48.77/12.82 = { by lemma 25 R->L }
% 48.77/12.82 tptp1(tptp2(tptp5), n(tptp5))
% 48.77/12.82 = { by lemma 28 }
% 48.77/12.82 tptp3
% 48.77/12.82
% 48.77/12.82 Lemma 30: tptp2(tptp3) = tptp5.
% 48.77/12.82 Proof:
% 48.77/12.82 tptp2(tptp3)
% 48.77/12.82 = { by lemma 29 R->L }
% 48.77/12.82 tptp2(tptp2(tptp5))
% 48.77/12.82 = { by axiom 2 (c12) }
% 48.77/12.82 tptp5
% 48.77/12.82
% 48.77/12.82 Lemma 31: tptp0(Y, tptp0(X, Z)) = tptp0(X, tptp0(Y, Z)).
% 48.77/12.82 Proof:
% 48.77/12.82 tptp0(Y, tptp0(X, Z))
% 48.77/12.82 = { by axiom 9 (c04) R->L }
% 48.77/12.82 tptp0(tptp1(Y, X), Z)
% 48.77/12.82 = { by axiom 3 (c01) R->L }
% 48.77/12.82 tptp0(tptp1(X, Y), Z)
% 48.77/12.82 = { by axiom 9 (c04) }
% 48.77/12.82 tptp0(X, tptp0(Y, Z))
% 48.77/12.82
% 48.77/12.82 Lemma 32: tptp0(X, X) = v(X, tptp5).
% 48.77/12.82 Proof:
% 48.77/12.82 tptp0(X, X)
% 48.77/12.82 = { by lemma 22 R->L }
% 48.77/12.82 tptp0(tptp4(X, tptp5), X)
% 48.77/12.82 = { by lemma 17 R->L }
% 48.77/12.82 tptp0(tptp0(tptp5, X), X)
% 48.77/12.82 = { by lemma 22 R->L }
% 48.77/12.82 tptp4(tptp0(tptp0(tptp5, X), X), tptp5)
% 48.77/12.82 = { by lemma 16 R->L }
% 48.77/12.82 tptp4(tptp5, tptp0(tptp0(tptp5, X), X))
% 48.77/12.82 = { by lemma 20 R->L }
% 48.77/12.82 tptp4(tptp0(tptp0(X, tptp5), tptp5), tptp0(tptp0(tptp5, X), X))
% 48.77/12.82 = { by axiom 12 (c08) R->L }
% 48.77/12.82 v(X, tptp5)
% 48.77/12.82
% 48.77/12.82 Lemma 33: v(Y, X) = v(X, Y).
% 48.77/12.82 Proof:
% 48.77/12.82 v(Y, X)
% 48.77/12.82 = { by axiom 12 (c08) }
% 48.77/12.82 tptp4(tptp0(tptp0(Y, X), X), tptp0(tptp0(X, Y), Y))
% 48.77/12.82 = { by lemma 16 }
% 48.77/12.82 tptp4(tptp0(tptp0(X, Y), Y), tptp0(tptp0(Y, X), X))
% 48.77/12.82 = { by axiom 12 (c08) R->L }
% 48.77/12.82 v(X, Y)
% 48.77/12.82
% 48.77/12.82 Lemma 34: tptp0(X, tptp0(tptp0(X, Y), Z)) = tptp0(tptp4(X, Y), Z).
% 48.77/12.82 Proof:
% 48.77/12.82 tptp0(X, tptp0(tptp0(X, Y), Z))
% 48.77/12.82 = { by axiom 9 (c04) R->L }
% 48.77/12.82 tptp0(tptp1(X, tptp0(X, Y)), Z)
% 48.77/12.82 = { by axiom 7 (c07) R->L }
% 48.77/12.82 tptp0(tptp4(X, Y), Z)
% 48.77/12.82
% 48.77/12.82 Lemma 35: tptp0(X, X) = tptp5.
% 48.77/12.82 Proof:
% 48.77/12.82 tptp0(X, X)
% 48.77/12.82 = { by lemma 22 R->L }
% 48.77/12.82 tptp0(X, tptp4(X, tptp5))
% 48.77/12.82 = { by lemma 17 R->L }
% 48.77/12.82 tptp0(X, tptp0(tptp5, X))
% 48.77/12.82 = { by axiom 6 (c05) R->L }
% 48.77/12.82 tptp0(X, tptp0(tptp0(tptp3, X), X))
% 48.77/12.82 = { by lemma 26 R->L }
% 48.77/12.82 tptp0(X, tptp0(tptp0(tptp4(tptp5, tptp3), X), X))
% 48.77/12.82 = { by lemma 16 R->L }
% 48.77/12.82 tptp0(X, tptp0(tptp0(tptp4(tptp3, tptp5), X), X))
% 48.77/12.82 = { by lemma 17 R->L }
% 48.77/12.82 tptp0(X, tptp0(tptp0(tptp0(tptp5, tptp3), X), X))
% 48.77/12.82 = { by axiom 5 (c10) R->L }
% 48.77/12.82 tptp0(X, tptp0(tptp0(m(tptp5), X), X))
% 48.77/12.82 = { by lemma 31 }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), tptp0(X, X))
% 48.77/12.82 = { by lemma 32 }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), v(X, tptp5))
% 48.77/12.82 = { by lemma 33 R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), v(tptp5, X))
% 48.77/12.82 = { by lemma 22 R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), v(tptp5, tptp4(X, tptp5)))
% 48.77/12.82 = { by lemma 17 R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), v(tptp5, tptp0(tptp5, X)))
% 48.77/12.82 = { by lemma 33 }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), v(tptp0(tptp5, X), tptp5))
% 48.77/12.82 = { by lemma 32 R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), tptp0(tptp0(tptp5, X), tptp0(tptp5, X)))
% 48.77/12.82 = { by lemma 31 R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), tptp0(tptp5, tptp0(tptp0(tptp5, X), X)))
% 48.77/12.82 = { by lemma 34 }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), tptp0(tptp4(tptp5, X), X))
% 48.77/12.82 = { by lemma 16 R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), tptp0(tptp4(X, tptp5), X))
% 48.77/12.82 = { by lemma 17 R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), tptp0(tptp0(tptp5, X), X))
% 48.77/12.82 = { by axiom 6 (c05) R->L }
% 48.77/12.82 tptp0(tptp0(m(tptp5), X), tptp0(tptp0(tptp0(tptp3, tptp5), X), X))
% 48.77/12.82 = { by axiom 5 (c10) }
% 48.77/12.82 tptp0(tptp0(tptp0(tptp5, tptp3), X), tptp0(tptp0(tptp0(tptp3, tptp5), X), X))
% 48.77/12.82 = { by axiom 13 (c06) }
% 48.77/12.82 tptp5
% 48.77/12.82
% 48.77/12.82 Lemma 36: tptp0(tptp5, X) = X.
% 48.77/12.82 Proof:
% 48.77/12.82 tptp0(tptp5, X)
% 48.77/12.82 = { by axiom 4 (c02) R->L }
% 48.77/12.82 tptp1(tptp5, tptp0(tptp5, X))
% 48.77/12.82 = { by axiom 7 (c07) R->L }
% 48.77/12.82 tptp4(tptp5, X)
% 48.77/12.82 = { by lemma 16 R->L }
% 48.77/12.82 tptp4(X, tptp5)
% 48.77/12.82 = { by lemma 22 }
% 48.77/12.82 X
% 48.77/12.82
% 48.77/12.82 Lemma 37: n(m(X)) = m(X).
% 48.77/12.82 Proof:
% 48.77/12.82 n(m(X))
% 48.77/12.82 = { by axiom 5 (c10) }
% 48.77/12.82 n(tptp0(X, tptp3))
% 48.77/12.82 = { by lemma 29 R->L }
% 48.77/12.82 n(tptp0(X, tptp2(tptp5)))
% 48.77/12.82 = { by lemma 15 R->L }
% 48.77/12.82 n(tptp0(tptp5, tptp2(X)))
% 48.77/12.82 = { by lemma 17 }
% 48.77/12.82 n(tptp4(tptp2(X), tptp5))
% 48.77/12.82 = { by lemma 22 }
% 48.77/12.82 n(tptp2(X))
% 48.77/12.82 = { by lemma 23 }
% 48.77/12.82 m(X)
% 48.77/12.82
% 48.77/12.82 Lemma 38: tptp0(X, tptp0(m(X), Y)) = tptp5.
% 48.77/12.83 Proof:
% 48.77/12.83 tptp0(X, tptp0(m(X), Y))
% 48.77/12.83 = { by axiom 9 (c04) R->L }
% 48.77/12.83 tptp0(tptp1(X, m(X)), Y)
% 48.77/12.83 = { by lemma 27 }
% 48.77/12.83 tptp0(tptp3, Y)
% 48.77/12.83 = { by axiom 6 (c05) }
% 48.77/12.83 tptp5
% 48.77/12.83
% 48.77/12.83 Lemma 39: tptp4(X, m(m(X))) = X.
% 48.77/12.83 Proof:
% 48.77/12.83 tptp4(X, m(m(X)))
% 48.77/12.83 = { by axiom 5 (c10) }
% 48.77/12.83 tptp4(X, tptp0(m(X), tptp3))
% 48.77/12.83 = { by axiom 7 (c07) }
% 48.77/12.83 tptp1(X, tptp0(X, tptp0(m(X), tptp3)))
% 48.77/12.83 = { by lemma 38 }
% 48.77/12.83 tptp1(X, tptp5)
% 48.77/12.83 = { by lemma 21 }
% 48.77/12.83 X
% 48.77/12.83
% 48.77/12.83 Lemma 40: m(tptp1(X, tptp2(Y))) = tptp0(X, n(Y)).
% 48.77/12.83 Proof:
% 48.77/12.83 m(tptp1(X, tptp2(Y)))
% 48.77/12.83 = { by lemma 19 R->L }
% 48.77/12.83 tptp0(X, m(tptp2(Y)))
% 48.77/12.83 = { by axiom 1 (c11) R->L }
% 48.77/12.83 tptp0(X, n(Y))
% 48.77/12.83
% 48.77/12.83 Lemma 41: n(tptp0(tptp2(m(X)), Y)) = tptp0(X, n(Y)).
% 48.77/12.83 Proof:
% 48.77/12.83 n(tptp0(tptp2(m(X)), Y))
% 48.77/12.83 = { by axiom 2 (c12) R->L }
% 48.77/12.83 n(tptp0(tptp2(m(X)), tptp2(tptp2(Y))))
% 48.77/12.83 = { by axiom 10 (c13) R->L }
% 48.77/12.83 n(tptp0(tptp2(Y), m(X)))
% 48.77/12.83 = { by lemma 19 }
% 48.77/12.83 n(m(tptp1(tptp2(Y), X)))
% 48.77/12.83 = { by lemma 37 }
% 48.77/12.83 m(tptp1(tptp2(Y), X))
% 48.77/12.83 = { by axiom 3 (c01) R->L }
% 48.77/12.83 m(tptp1(X, tptp2(Y)))
% 48.77/12.83 = { by lemma 40 }
% 48.77/12.83 tptp0(X, n(Y))
% 48.77/12.83
% 48.77/12.83 Lemma 42: tptp0(X, n(tptp0(m(X), Y))) = tptp5.
% 48.77/12.83 Proof:
% 48.77/12.83 tptp0(X, n(tptp0(m(X), Y)))
% 48.77/12.83 = { by lemma 37 R->L }
% 48.77/12.83 tptp0(X, n(tptp0(n(m(X)), Y)))
% 48.77/12.83 = { by axiom 1 (c11) }
% 48.77/12.83 tptp0(X, n(tptp0(m(tptp2(m(X))), Y)))
% 48.77/12.83 = { by lemma 41 R->L }
% 48.77/12.83 n(tptp0(tptp2(m(X)), tptp0(m(tptp2(m(X))), Y)))
% 48.77/12.83 = { by lemma 38 }
% 48.77/12.83 n(tptp5)
% 48.77/12.83 = { by lemma 25 }
% 48.77/12.83 tptp5
% 48.77/12.83
% 48.77/12.83 Lemma 43: tptp0(m(X), n(tptp0(X, Y))) = tptp5.
% 48.77/12.83 Proof:
% 48.77/12.83 tptp0(m(X), n(tptp0(X, Y)))
% 48.77/12.83 = { by lemma 39 R->L }
% 48.77/12.83 tptp0(m(X), n(tptp0(tptp4(X, m(m(X))), Y)))
% 48.77/12.83 = { by lemma 16 }
% 48.77/12.83 tptp0(m(X), n(tptp0(tptp4(m(m(X)), X), Y)))
% 48.77/12.83 = { by lemma 34 R->L }
% 48.77/12.83 tptp0(m(X), n(tptp0(m(m(X)), tptp0(tptp0(m(m(X)), X), Y))))
% 48.77/12.83 = { by lemma 42 }
% 48.77/12.83 tptp5
% 48.77/12.83
% 48.77/12.83 Lemma 44: tptp1(m(X), tptp2(tptp0(X, Y))) = tptp3.
% 48.77/12.83 Proof:
% 48.77/12.83 tptp1(m(X), tptp2(tptp0(X, Y)))
% 48.77/12.83 = { by lemma 21 R->L }
% 48.77/12.83 tptp1(tptp1(m(X), tptp2(tptp0(X, Y))), tptp5)
% 48.77/12.83 = { by lemma 43 R->L }
% 48.77/12.83 tptp1(tptp1(m(X), tptp2(tptp0(X, Y))), tptp0(m(X), n(tptp0(X, Y))))
% 48.77/12.83 = { by lemma 40 R->L }
% 48.77/12.83 tptp1(tptp1(m(X), tptp2(tptp0(X, Y))), m(tptp1(m(X), tptp2(tptp0(X, Y)))))
% 48.77/12.83 = { by lemma 27 }
% 48.77/12.83 tptp3
% 48.77/12.83
% 48.77/12.83 Lemma 45: tptp1(X, tptp0(Y, tptp0(X, Z))) = tptp4(X, tptp0(Y, Z)).
% 48.77/12.83 Proof:
% 48.77/12.83 tptp1(X, tptp0(Y, tptp0(X, Z)))
% 48.77/12.83 = { by lemma 31 }
% 48.77/12.83 tptp1(X, tptp0(X, tptp0(Y, Z)))
% 48.77/12.83 = { by axiom 7 (c07) R->L }
% 48.77/12.83 tptp4(X, tptp0(Y, Z))
% 48.77/12.83
% 48.77/12.83 Lemma 46: tptp4(X, tptp0(tptp0(X, Y), Y)) = X.
% 48.77/12.83 Proof:
% 48.77/12.83 tptp4(X, tptp0(tptp0(X, Y), Y))
% 48.77/12.83 = { by lemma 45 R->L }
% 48.77/12.83 tptp1(X, tptp0(tptp0(X, Y), tptp0(X, Y)))
% 48.77/12.83 = { by lemma 35 }
% 48.77/12.83 tptp1(X, tptp5)
% 48.77/12.83 = { by lemma 21 }
% 48.77/12.83 X
% 48.77/12.83
% 48.77/12.83 Lemma 47: tptp0(X, n(tptp0(X, Y))) = n(tptp0(X, Y)).
% 48.77/12.83 Proof:
% 48.77/12.83 tptp0(X, n(tptp0(X, Y)))
% 48.77/12.83 = { by lemma 40 R->L }
% 48.77/12.83 m(tptp1(X, tptp2(tptp0(X, Y))))
% 48.77/12.83 = { by lemma 19 R->L }
% 48.77/12.83 tptp0(X, m(tptp2(tptp0(X, Y))))
% 48.77/12.83 = { by axiom 5 (c10) }
% 48.77/12.83 tptp0(X, tptp0(tptp2(tptp0(X, Y)), tptp3))
% 48.77/12.83 = { by axiom 9 (c04) R->L }
% 48.77/12.83 tptp0(tptp1(X, tptp2(tptp0(X, Y))), tptp3)
% 48.77/12.83 = { by axiom 11 (c09) }
% 48.77/12.83 v(tptp0(X, tptp3), tptp0(tptp2(tptp0(X, Y)), tptp3))
% 48.77/12.83 = { by axiom 5 (c10) R->L }
% 48.77/12.83 v(m(X), tptp0(tptp2(tptp0(X, Y)), tptp3))
% 48.77/12.83 = { by lemma 44 R->L }
% 48.77/12.83 v(m(X), tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y)))))
% 48.77/12.83 = { by axiom 12 (c08) }
% 48.77/12.83 tptp4(tptp0(tptp0(m(X), tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y))))), tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y))))), tptp0(tptp0(tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y)))), m(X)), m(X)))
% 48.77/12.83 = { by axiom 9 (c04) R->L }
% 48.77/12.83 tptp4(tptp0(tptp0(tptp1(m(X), tptp2(tptp0(X, Y))), tptp1(m(X), tptp2(tptp0(X, Y)))), tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y))))), tptp0(tptp0(tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y)))), m(X)), m(X)))
% 48.77/12.83 = { by lemma 35 }
% 48.77/12.83 tptp4(tptp0(tptp5, tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y))))), tptp0(tptp0(tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y)))), m(X)), m(X)))
% 48.77/12.83 = { by lemma 36 }
% 48.77/12.83 tptp4(tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y)))), tptp0(tptp0(tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y)))), m(X)), m(X)))
% 48.77/12.83 = { by lemma 46 }
% 48.77/12.83 tptp0(tptp2(tptp0(X, Y)), tptp1(m(X), tptp2(tptp0(X, Y))))
% 48.77/12.83 = { by lemma 44 }
% 48.77/12.83 tptp0(tptp2(tptp0(X, Y)), tptp3)
% 48.77/12.83 = { by axiom 5 (c10) R->L }
% 48.77/12.83 m(tptp2(tptp0(X, Y)))
% 48.77/12.83 = { by axiom 1 (c11) R->L }
% 48.77/12.84 n(tptp0(X, Y))
% 48.77/12.84
% 48.77/12.84 Lemma 48: tptp0(n(X), X) = tptp5.
% 48.77/12.84 Proof:
% 48.77/12.84 tptp0(n(X), X)
% 48.77/12.84 = { by axiom 2 (c12) R->L }
% 48.77/12.84 tptp2(tptp2(tptp0(n(X), X)))
% 48.77/12.84 = { by lemma 21 R->L }
% 48.77/12.84 tptp2(tptp1(tptp2(tptp0(n(X), X)), tptp5))
% 48.77/12.84 = { by lemma 43 R->L }
% 48.77/12.84 tptp2(tptp1(tptp2(tptp0(n(X), X)), tptp0(m(tptp2(X)), n(tptp0(tptp2(X), tptp2(n(X)))))))
% 48.77/12.84 = { by axiom 10 (c13) R->L }
% 48.77/12.84 tptp2(tptp1(tptp2(tptp0(n(X), X)), tptp0(m(tptp2(X)), n(tptp0(n(X), X)))))
% 48.77/12.84 = { by axiom 1 (c11) R->L }
% 48.77/12.84 tptp2(tptp1(tptp2(tptp0(n(X), X)), tptp0(n(X), n(tptp0(n(X), X)))))
% 48.77/12.84 = { by lemma 47 }
% 48.77/12.84 tptp2(tptp1(tptp2(tptp0(n(X), X)), n(tptp0(n(X), X))))
% 48.77/12.84 = { by lemma 28 }
% 48.77/12.84 tptp2(tptp3)
% 48.77/12.84 = { by lemma 30 }
% 48.77/12.84 tptp5
% 48.77/12.84
% 48.77/12.84 Lemma 49: tptp4(m(m(X)), tptp2(m(X))) = tptp2(m(X)).
% 48.77/12.84 Proof:
% 48.77/12.84 tptp4(m(m(X)), tptp2(m(X)))
% 48.77/12.84 = { by lemma 16 }
% 48.77/12.84 tptp4(tptp2(m(X)), m(m(X)))
% 48.77/12.84 = { by axiom 5 (c10) }
% 48.77/12.84 tptp4(tptp2(tptp0(X, tptp3)), m(m(X)))
% 48.77/12.84 = { by lemma 29 R->L }
% 48.77/12.84 tptp4(tptp2(tptp0(X, tptp2(tptp5))), m(m(X)))
% 48.77/12.84 = { by lemma 24 R->L }
% 48.77/12.84 tptp4(tptp2(tptp0(X, tptp2(tptp5))), m(n(tptp0(X, tptp2(tptp5)))))
% 48.77/12.84 = { by axiom 7 (c07) }
% 48.77/12.84 tptp1(tptp2(tptp0(X, tptp2(tptp5))), tptp0(tptp2(tptp0(X, tptp2(tptp5))), m(n(tptp0(X, tptp2(tptp5))))))
% 48.77/12.84 = { by lemma 19 }
% 48.77/12.84 tptp1(tptp2(tptp0(X, tptp2(tptp5))), m(tptp1(tptp2(tptp0(X, tptp2(tptp5))), n(tptp0(X, tptp2(tptp5))))))
% 48.77/12.84 = { by lemma 28 }
% 48.77/12.84 tptp1(tptp2(tptp0(X, tptp2(tptp5))), m(tptp3))
% 48.77/12.84 = { by lemma 14 }
% 48.77/12.84 tptp1(tptp2(tptp0(X, tptp2(tptp5))), tptp5)
% 48.77/12.84 = { by lemma 21 }
% 48.77/12.84 tptp2(tptp0(X, tptp2(tptp5)))
% 48.77/12.84 = { by lemma 29 }
% 48.77/12.84 tptp2(tptp0(X, tptp3))
% 48.77/12.84 = { by axiom 5 (c10) R->L }
% 48.77/12.84 tptp2(m(X))
% 48.77/12.85
% 48.77/12.85 Lemma 50: m(m(n(X))) = n(X).
% 48.77/12.85 Proof:
% 48.77/12.85 m(m(n(X)))
% 48.77/12.85 = { by axiom 1 (c11) }
% 48.77/12.85 m(m(m(tptp2(X))))
% 48.77/12.85 = { by lemma 21 R->L }
% 48.77/12.85 tptp1(m(m(m(tptp2(X)))), tptp5)
% 48.77/12.85 = { by lemma 38 R->L }
% 48.77/12.85 tptp1(m(m(m(tptp2(X)))), tptp0(m(m(tptp2(X))), tptp0(m(m(m(tptp2(X)))), m(tptp0(m(m(tptp2(X))), tptp2(m(tptp2(X))))))))
% 48.77/12.85 = { by lemma 45 }
% 48.77/12.85 tptp4(m(m(m(tptp2(X)))), tptp0(m(m(tptp2(X))), m(tptp0(m(m(tptp2(X))), tptp2(m(tptp2(X)))))))
% 48.77/12.85 = { by lemma 19 }
% 48.77/12.85 tptp4(m(m(m(tptp2(X)))), m(tptp1(m(m(tptp2(X))), tptp0(m(m(tptp2(X))), tptp2(m(tptp2(X)))))))
% 48.77/12.85 = { by axiom 7 (c07) R->L }
% 48.77/12.85 tptp4(m(m(m(tptp2(X)))), m(tptp4(m(m(tptp2(X))), tptp2(m(tptp2(X))))))
% 48.77/12.85 = { by lemma 49 }
% 48.77/12.85 tptp4(m(m(m(tptp2(X)))), m(tptp2(m(tptp2(X)))))
% 48.77/12.85 = { by axiom 1 (c11) R->L }
% 48.77/12.85 tptp4(m(m(m(tptp2(X)))), n(m(tptp2(X))))
% 48.77/12.85 = { by lemma 37 }
% 48.77/12.85 tptp4(m(m(m(tptp2(X)))), m(tptp2(X)))
% 48.77/12.85 = { by lemma 16 R->L }
% 48.77/12.85 tptp4(m(tptp2(X)), m(m(m(tptp2(X)))))
% 48.77/12.85 = { by lemma 39 }
% 48.77/12.85 m(tptp2(X))
% 48.77/12.85 = { by axiom 1 (c11) R->L }
% 48.77/12.85 n(X)
% 48.77/12.85
% 48.77/12.85 Lemma 51: tptp0(n(X), n(Y)) = n(tptp0(n(X), Y)).
% 48.77/12.85 Proof:
% 48.77/12.85 tptp0(n(X), n(Y))
% 48.77/12.85 = { by lemma 40 R->L }
% 48.77/12.85 m(tptp1(n(X), tptp2(Y)))
% 48.77/12.85 = { by lemma 19 R->L }
% 48.77/12.85 tptp0(n(X), m(tptp2(Y)))
% 48.77/12.85 = { by lemma 18 R->L }
% 48.77/12.85 v(m(n(X)), m(tptp2(Y)))
% 48.77/12.85 = { by axiom 1 (c11) R->L }
% 48.77/12.85 v(m(n(X)), n(Y))
% 48.77/12.85 = { by lemma 23 R->L }
% 48.77/12.85 v(n(tptp2(n(X))), n(Y))
% 48.77/12.85 = { by lemma 36 R->L }
% 48.77/12.85 v(n(tptp2(n(X))), n(tptp0(tptp5, Y)))
% 48.77/12.85 = { by lemma 33 }
% 48.77/12.85 v(n(tptp0(tptp5, Y)), n(tptp2(n(X))))
% 48.77/12.85 = { by axiom 1 (c11) }
% 48.77/12.85 v(n(tptp0(tptp5, Y)), m(tptp2(tptp2(n(X)))))
% 48.77/12.85 = { by lemma 33 }
% 48.77/12.85 v(m(tptp2(tptp2(n(X)))), n(tptp0(tptp5, Y)))
% 48.77/12.85 = { by axiom 1 (c11) }
% 48.77/12.85 v(m(tptp2(tptp2(n(X)))), m(tptp2(tptp0(tptp5, Y))))
% 48.77/12.85 = { by lemma 18 }
% 48.77/12.85 tptp0(tptp2(tptp2(n(X))), m(tptp2(tptp0(tptp5, Y))))
% 48.77/12.85 = { by lemma 19 }
% 48.77/12.85 m(tptp1(tptp2(tptp2(n(X))), tptp2(tptp0(tptp5, Y))))
% 48.77/12.85 = { by lemma 40 }
% 48.77/12.85 tptp0(tptp2(tptp2(n(X))), n(tptp0(tptp5, Y)))
% 48.77/12.85 = { by lemma 41 R->L }
% 48.77/12.85 n(tptp0(tptp2(m(tptp2(tptp2(n(X))))), tptp0(tptp5, Y)))
% 48.77/12.85 = { by axiom 1 (c11) R->L }
% 48.77/12.85 n(tptp0(tptp2(n(tptp2(n(X)))), tptp0(tptp5, Y)))
% 48.77/12.85 = { by lemma 31 R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp2(n(tptp2(n(X)))), Y)))
% 48.77/12.85 = { by axiom 1 (c11) }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp2(m(tptp2(tptp2(n(X))))), Y)))
% 48.77/12.85 = { by lemma 49 R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp4(m(m(tptp2(tptp2(n(X))))), tptp2(m(tptp2(tptp2(n(X)))))), Y)))
% 48.77/12.85 = { by axiom 1 (c11) R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp4(m(n(tptp2(n(X)))), tptp2(m(tptp2(tptp2(n(X)))))), Y)))
% 48.77/12.85 = { by axiom 1 (c11) R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp4(m(n(tptp2(n(X)))), tptp2(n(tptp2(n(X))))), Y)))
% 48.77/12.85 = { by lemma 50 R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp4(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X))))))), Y)))
% 48.77/12.85 = { by axiom 7 (c07) }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X)))))))), Y)))
% 48.77/12.85 = { by axiom 2 (c12) R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp2(tptp2(tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X)))))))))), Y)))
% 48.77/12.85 = { by lemma 21 R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp2(tptp1(tptp2(tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X)))))))), tptp5))), Y)))
% 48.77/12.85 = { by lemma 42 R->L }
% 48.77/12.85 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp2(tptp1(tptp2(tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X)))))))), tptp0(m(n(tptp2(n(X)))), n(tptp0(m(m(n(tptp2(n(X))))), tptp2(m(n(tptp2(n(X))))))))))), Y)))
% 48.77/12.86 = { by lemma 15 R->L }
% 48.77/12.86 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp2(tptp1(tptp2(tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X)))))))), tptp0(m(n(tptp2(n(X)))), n(tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X)))))))))))), Y)))
% 48.77/12.86 = { by lemma 47 }
% 48.77/12.86 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp2(tptp1(tptp2(tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X)))))))), n(tptp0(m(n(tptp2(n(X)))), tptp2(m(m(n(tptp2(n(X))))))))))), Y)))
% 48.77/12.86 = { by lemma 28 }
% 48.77/12.86 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp2(tptp3)), Y)))
% 48.77/12.86 = { by lemma 30 }
% 48.77/12.86 n(tptp0(tptp5, tptp0(tptp1(m(n(tptp2(n(X)))), tptp5), Y)))
% 48.77/12.86 = { by lemma 21 }
% 48.77/12.86 n(tptp0(tptp5, tptp0(m(n(tptp2(n(X)))), Y)))
% 48.77/12.86 = { by lemma 36 }
% 48.77/12.86 n(tptp0(m(n(tptp2(n(X)))), Y))
% 48.77/12.86 = { by lemma 23 }
% 48.77/12.86 n(tptp0(m(m(n(X))), Y))
% 48.77/12.86 = { by lemma 50 }
% 48.77/12.86 n(tptp0(n(X), Y))
% 48.77/12.86
% 48.77/12.86 Lemma 52: tptp0(tptp1(Y, X), Z) = tptp0(X, tptp0(Y, Z)).
% 48.77/12.86 Proof:
% 48.77/12.86 tptp0(tptp1(Y, X), Z)
% 48.77/12.86 = { by axiom 3 (c01) }
% 48.77/12.86 tptp0(tptp1(X, Y), Z)
% 48.77/12.86 = { by axiom 9 (c04) }
% 48.77/12.86 tptp0(X, tptp0(Y, Z))
% 48.77/12.86
% 48.77/12.86 Goal 1 (goals): v(tptp1(n(a), n(tptp0(a, b))), n(b)) = n(b).
% 48.77/12.86 Proof:
% 48.77/12.86 v(tptp1(n(a), n(tptp0(a, b))), n(b))
% 48.77/12.86 = { by axiom 12 (c08) }
% 48.77/12.86 tptp4(tptp0(tptp0(tptp1(n(a), n(tptp0(a, b))), n(b)), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 52 }
% 48.77/12.86 tptp4(tptp0(tptp0(n(tptp0(a, b)), tptp0(n(a), n(b))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 51 }
% 48.77/12.86 tptp4(tptp0(tptp0(n(tptp0(a, b)), n(tptp0(n(a), b))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 51 }
% 48.77/12.86 tptp4(tptp0(n(tptp0(n(tptp0(a, b)), tptp0(n(a), b))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 52 R->L }
% 48.77/12.86 tptp4(tptp0(n(tptp0(tptp1(n(a), n(tptp0(a, b))), b)), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 36 R->L }
% 48.77/12.86 tptp4(tptp0(n(tptp0(tptp1(n(a), n(tptp0(a, b))), tptp0(tptp5, b))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 48 R->L }
% 48.77/12.86 tptp4(tptp0(n(tptp0(tptp1(n(a), n(tptp0(a, b))), tptp0(tptp0(n(a), a), b))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 52 }
% 48.77/12.86 tptp4(tptp0(n(tptp0(n(tptp0(a, b)), tptp0(n(a), tptp0(tptp0(n(a), a), b)))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 34 }
% 48.77/12.86 tptp4(tptp0(n(tptp0(n(tptp0(a, b)), tptp0(tptp4(n(a), a), b))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 16 }
% 48.77/12.86 tptp4(tptp0(n(tptp0(n(tptp0(a, b)), tptp0(tptp4(a, n(a)), b))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 34 R->L }
% 48.77/12.86 tptp4(tptp0(n(tptp0(n(tptp0(a, b)), tptp0(a, tptp0(tptp0(a, n(a)), b)))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 31 }
% 48.77/12.86 tptp4(tptp0(n(tptp0(n(tptp0(a, b)), tptp0(tptp0(a, n(a)), tptp0(a, b)))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 31 R->L }
% 48.77/12.86 tptp4(tptp0(n(tptp0(tptp0(a, n(a)), tptp0(n(tptp0(a, b)), tptp0(a, b)))), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 48 }
% 48.77/12.86 tptp4(tptp0(n(tptp0(tptp0(a, n(a)), tptp5)), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.86 = { by lemma 20 }
% 48.77/12.86 tptp4(tptp0(n(tptp5), n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.87 = { by lemma 25 }
% 48.77/12.87 tptp4(tptp0(tptp5, n(b)), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.87 = { by lemma 36 }
% 48.77/12.87 tptp4(n(b), tptp0(tptp0(n(b), tptp1(n(a), n(tptp0(a, b)))), tptp1(n(a), n(tptp0(a, b)))))
% 48.77/12.87 = { by lemma 46 }
% 48.77/12.87 n(b)
% 48.77/12.87 % SZS output end Proof
% 48.77/12.87
% 48.77/12.87 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------