TSTP Solution File: LCL016-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL016-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:17:03 EDT 2023
% Result : Unsatisfiable 79.31s 10.57s
% Output : Proof 80.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.35 % Computer : n012.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Aug 25 06:32:41 EDT 2023
% 0.12/0.35 % CPUTime :
% 79.31/10.57 Command-line arguments: --no-flatten-goal
% 79.31/10.57
% 79.31/10.57 % SZS status Unsatisfiable
% 79.31/10.57
% 80.01/10.68 % SZS output start Proof
% 80.01/10.68 Take the following subset of the input axioms:
% 80.01/10.68 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 80.01/10.68 fof(prove_yrm, negated_conjecture, ~is_a_theorem(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))).
% 80.01/10.68 fof(yro, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, Y2), equivalent(Z, equivalent(equivalent(Z, Y2), X2))))).
% 80.01/10.68
% 80.01/10.68 Now clausify the problem and encode Horn clauses using encoding 3 of
% 80.01/10.68 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 80.01/10.68 We repeatedly replace C & s=t => u=v by the two clauses:
% 80.01/10.68 fresh(y, y, x1...xn) = u
% 80.01/10.68 C => fresh(s, t, x1...xn) = v
% 80.01/10.68 where fresh is a fresh function symbol and x1..xn are the free
% 80.01/10.68 variables of u and v.
% 80.01/10.68 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 80.01/10.68 input problem has no model of domain size 1).
% 80.01/10.68
% 80.01/10.68 The encoding turns the above axioms into the following unit equations and goals:
% 80.01/10.68
% 80.01/10.68 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 80.01/10.68 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 80.01/10.68 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 80.01/10.68 Axiom 4 (yro): is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X)))) = true.
% 80.01/10.68
% 80.01/10.68 Lemma 5: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Z, equivalent(equivalent(Z, Y), X))) = is_a_theorem(equivalent(Z, equivalent(equivalent(Z, Y), X))).
% 80.01/10.68 Proof:
% 80.01/10.68 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Z, equivalent(equivalent(Z, Y), X)))
% 80.01/10.68 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.68 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X)))), true, equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X)))
% 80.35/10.68 = { by axiom 4 (yro) }
% 80.35/10.68 fresh(true, true, equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X)))
% 80.35/10.68 = { by axiom 2 (condensed_detachment) }
% 80.35/10.68 is_a_theorem(equivalent(Z, equivalent(equivalent(Z, Y), X)))
% 80.35/10.68
% 80.35/10.68 Lemma 6: is_a_theorem(equivalent(X, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z)))) = true.
% 80.35/10.68 Proof:
% 80.35/10.68 is_a_theorem(equivalent(X, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z))))
% 80.35/10.69 = { by lemma 5 R->L }
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(W, Z), equivalent(Y, equivalent(equivalent(Y, Z), W)))), true, equivalent(X, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z))))
% 80.35/10.69 = { by axiom 4 (yro) }
% 80.35/10.69 fresh2(true, true, equivalent(X, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z))))
% 80.35/10.69 = { by axiom 1 (condensed_detachment) }
% 80.35/10.69 true
% 80.35/10.69
% 80.35/10.69 Lemma 7: fresh2(is_a_theorem(X), true, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z))) = is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z))).
% 80.35/10.69 Proof:
% 80.35/10.69 fresh2(is_a_theorem(X), true, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z)))
% 80.35/10.69 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.69 fresh(is_a_theorem(equivalent(X, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z)))), true, X, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z)))
% 80.35/10.69 = { by lemma 6 }
% 80.35/10.69 fresh(true, true, X, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z)))
% 80.35/10.69 = { by axiom 2 (condensed_detachment) }
% 80.35/10.69 is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Y, Z), W))), equivalent(W, Z)))
% 80.35/10.69
% 80.35/10.69 Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))) = true.
% 80.35/10.69 Proof:
% 80.35/10.69 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V)))
% 80.35/10.69 = { by lemma 7 R->L }
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V)))
% 80.35/10.69 = { by axiom 4 (yro) }
% 80.35/10.69 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V)))
% 80.35/10.69 = { by axiom 1 (condensed_detachment) }
% 80.35/10.69 true
% 80.35/10.69
% 80.35/10.69 Lemma 9: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U)))), true, equivalent(U, V)) = is_a_theorem(equivalent(U, V)).
% 80.35/10.69 Proof:
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U)))), true, equivalent(U, V))
% 80.35/10.69 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.69 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))
% 80.35/10.69 = { by lemma 8 }
% 80.35/10.69 fresh(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))
% 80.35/10.69 = { by axiom 2 (condensed_detachment) }
% 80.35/10.69 is_a_theorem(equivalent(U, V))
% 80.35/10.69
% 80.35/10.69 Lemma 10: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z)) = true.
% 80.35/10.69 Proof:
% 80.35/10.69 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z))
% 80.35/10.69 = { by lemma 9 R->L }
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X))), equivalent(W, equivalent(equivalent(W, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X))), equivalent(X, Y)))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z))
% 80.35/10.69 = { by lemma 8 }
% 80.35/10.69 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z))
% 80.35/10.69 = { by axiom 1 (condensed_detachment) }
% 80.35/10.69 true
% 80.35/10.69
% 80.35/10.69 Lemma 11: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))) = true.
% 80.35/10.69 Proof:
% 80.35/10.69 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V)))
% 80.35/10.69 = { by lemma 7 R->L }
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z)), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V)))
% 80.35/10.69 = { by lemma 10 }
% 80.35/10.69 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V)))
% 80.35/10.69 = { by axiom 1 (condensed_detachment) }
% 80.35/10.69 true
% 80.35/10.69
% 80.35/10.69 Lemma 12: fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U)))), true, equivalent(U, V)) = is_a_theorem(equivalent(U, V)).
% 80.35/10.69 Proof:
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U)))), true, equivalent(U, V))
% 80.35/10.69 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.69 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))
% 80.35/10.69 = { by lemma 11 }
% 80.35/10.69 fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(W, equivalent(equivalent(W, V), U))), equivalent(U, V))
% 80.35/10.69 = { by axiom 2 (condensed_detachment) }
% 80.35/10.69 is_a_theorem(equivalent(U, V))
% 80.35/10.69
% 80.35/10.69 Lemma 13: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z)) = true.
% 80.35/10.69 Proof:
% 80.35/10.69 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z))
% 80.35/10.69 = { by lemma 12 R->L }
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(Z, Y), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(Z, Y), Y)), Z), equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))))))), true, equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z))
% 80.35/10.69 = { by lemma 5 R->L }
% 80.35/10.69 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(Z, Y), Y)), Z), equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y)))), equivalent(equivalent(Z, Y), Y))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(Z, Y), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(Z, Y), Y)), Z), equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))))))), true, equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z))
% 80.35/10.69 = { by lemma 11 }
% 80.35/10.69 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(Z, Y), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, Y), Y), Y), Z), Y), equivalent(equivalent(Z, Y), Y)), Z), equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))))))), true, equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z))
% 80.35/10.69 = { by axiom 1 (condensed_detachment) }
% 80.35/10.69 fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z))
% 80.35/10.69 = { by axiom 1 (condensed_detachment) }
% 80.35/10.69 true
% 80.35/10.69
% 80.35/10.69 Lemma 14: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y)))), true, Z) = is_a_theorem(Z).
% 80.35/10.69 Proof:
% 80.35/10.69 fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y)))), true, Z)
% 80.35/10.69 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.69 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z)), true, equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z)
% 80.35/10.69 = { by lemma 13 }
% 80.35/10.69 fresh(true, true, equivalent(X, equivalent(equivalent(X, Y), equivalent(Z, Y))), Z)
% 80.35/10.69 = { by axiom 2 (condensed_detachment) }
% 80.35/10.69 is_a_theorem(Z)
% 80.35/10.69
% 80.35/10.69 Lemma 15: is_a_theorem(equivalent(equivalent(equivalent(X, Y), X), Y)) = true.
% 80.35/10.69 Proof:
% 80.35/10.69 is_a_theorem(equivalent(equivalent(equivalent(X, Y), X), Y))
% 80.35/10.69 = { by lemma 14 R->L }
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), X), equivalent(equivalent(equivalent(equivalent(X, Y), X), Y), X)))), true, equivalent(equivalent(equivalent(X, Y), X), Y))
% 80.35/10.69 = { by axiom 4 (yro) }
% 80.35/10.69 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), X), Y))
% 80.35/10.69 = { by axiom 1 (condensed_detachment) }
% 80.35/10.69 true
% 80.35/10.69
% 80.35/10.69 Lemma 16: is_a_theorem(equivalent(X, equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), Z)))) = true.
% 80.35/10.69 Proof:
% 80.35/10.69 is_a_theorem(equivalent(X, equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), Z))))
% 80.35/10.69 = { by lemma 5 R->L }
% 80.35/10.69 fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, Y), Z), Y)), true, equivalent(X, equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), Z))))
% 80.35/10.70 = { by lemma 15 }
% 80.35/10.70 fresh2(true, true, equivalent(X, equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), Z))))
% 80.35/10.70 = { by axiom 1 (condensed_detachment) }
% 80.35/10.70 true
% 80.35/10.70
% 80.35/10.70 Lemma 17: is_a_theorem(equivalent(X, X)) = true.
% 80.35/10.70 Proof:
% 80.35/10.70 is_a_theorem(equivalent(X, X))
% 80.35/10.70 = { by lemma 14 R->L }
% 80.35/10.70 fresh2(is_a_theorem(equivalent(Y, equivalent(equivalent(Y, X), equivalent(equivalent(X, X), X)))), true, equivalent(X, X))
% 80.35/10.70 = { by lemma 16 }
% 80.35/10.70 fresh2(true, true, equivalent(X, X))
% 80.35/10.70 = { by axiom 1 (condensed_detachment) }
% 80.35/10.70 true
% 80.35/10.70
% 80.35/10.70 Lemma 18: is_a_theorem(equivalent(X, equivalent(equivalent(X, Y), Y))) = true.
% 80.35/10.70 Proof:
% 80.35/10.70 is_a_theorem(equivalent(X, equivalent(equivalent(X, Y), Y)))
% 80.35/10.70 = { by lemma 5 R->L }
% 80.35/10.70 fresh2(is_a_theorem(equivalent(Y, Y)), true, equivalent(X, equivalent(equivalent(X, Y), Y)))
% 80.35/10.70 = { by lemma 17 }
% 80.35/10.70 fresh2(true, true, equivalent(X, equivalent(equivalent(X, Y), Y)))
% 80.35/10.70 = { by axiom 1 (condensed_detachment) }
% 80.35/10.70 true
% 80.35/10.70
% 80.35/10.70 Lemma 19: fresh2(is_a_theorem(X), true, equivalent(equivalent(X, Y), Y)) = is_a_theorem(equivalent(equivalent(X, Y), Y)).
% 80.35/10.70 Proof:
% 80.35/10.70 fresh2(is_a_theorem(X), true, equivalent(equivalent(X, Y), Y))
% 80.35/10.70 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.70 fresh(is_a_theorem(equivalent(X, equivalent(equivalent(X, Y), Y))), true, X, equivalent(equivalent(X, Y), Y))
% 80.35/10.70 = { by lemma 18 }
% 80.35/10.70 fresh(true, true, X, equivalent(equivalent(X, Y), Y))
% 80.35/10.70 = { by axiom 2 (condensed_detachment) }
% 80.35/10.70 is_a_theorem(equivalent(equivalent(X, Y), Y))
% 80.35/10.70
% 80.35/10.70 Lemma 20: fresh2(is_a_theorem(equivalent(equivalent(X, X), Y)), true, Y) = is_a_theorem(Y).
% 80.35/10.70 Proof:
% 80.35/10.70 fresh2(is_a_theorem(equivalent(equivalent(X, X), Y)), true, Y)
% 80.35/10.70 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.70 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, X), Y), Y)), true, equivalent(equivalent(X, X), Y), Y)
% 80.35/10.70 = { by lemma 19 R->L }
% 80.35/10.70 fresh(fresh2(is_a_theorem(equivalent(X, X)), true, equivalent(equivalent(equivalent(X, X), Y), Y)), true, equivalent(equivalent(X, X), Y), Y)
% 80.35/10.70 = { by lemma 17 }
% 80.35/10.70 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, X), Y), Y)), true, equivalent(equivalent(X, X), Y), Y)
% 80.35/10.70 = { by axiom 1 (condensed_detachment) }
% 80.35/10.70 fresh(true, true, equivalent(equivalent(X, X), Y), Y)
% 80.35/10.70 = { by axiom 2 (condensed_detachment) }
% 80.35/10.70 is_a_theorem(Y)
% 80.35/10.70
% 80.35/10.70 Lemma 21: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z))), true, X) = is_a_theorem(X).
% 80.35/10.70 Proof:
% 80.35/10.70 fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z))), true, X)
% 80.35/10.70 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.70 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by lemma 20 R->L }
% 80.35/10.70 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(Y, Z), Y), Z)), equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by axiom 2 (condensed_detachment) R->L }
% 80.35/10.70 fresh(fresh2(fresh(true, true, equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(Y, Z), Y), Z)), equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by lemma 16 R->L }
% 80.35/10.70 fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(Y, Z), Y), Z)), equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)))), true, equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(Y, Z), Y), Z)), equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by axiom 3 (condensed_detachment) }
% 80.35/10.70 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, Z), Y), Z)), true, equivalent(equivalent(equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(Y, Z), Y), Z)), equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by lemma 15 }
% 80.35/10.70 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(Y, Z), Y), Z), equivalent(equivalent(equivalent(Y, Z), Y), Z)), equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by axiom 1 (condensed_detachment) }
% 80.35/10.70 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by axiom 1 (condensed_detachment) }
% 80.35/10.70 fresh(true, true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), Y), Z)), X)
% 80.35/10.70 = { by axiom 2 (condensed_detachment) }
% 80.35/10.70 is_a_theorem(X)
% 80.35/10.70
% 80.35/10.70 Lemma 22: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z))), true, Y) = is_a_theorem(Y).
% 80.35/10.70 Proof:
% 80.35/10.70 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z))), true, Y)
% 80.35/10.70 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.70 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.70 = { by axiom 2 (condensed_detachment) R->L }
% 80.35/10.70 fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.70 = { by axiom 1 (condensed_detachment) R->L }
% 80.35/10.70 fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.70 = { by lemma 16 R->L }
% 80.35/10.71 fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by lemma 12 }
% 80.35/10.71 fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by axiom 3 (condensed_detachment) }
% 80.35/10.71 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by lemma 21 R->L }
% 80.35/10.71 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z))), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by lemma 5 R->L }
% 80.35/10.71 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z))), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by lemma 16 }
% 80.35/10.71 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z))), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by axiom 1 (condensed_detachment) }
% 80.35/10.71 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y), X), equivalent(equivalent(Z, X), Z)), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by axiom 1 (condensed_detachment) }
% 80.35/10.71 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by axiom 1 (condensed_detachment) }
% 80.35/10.71 fresh(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), Z)), Y)
% 80.35/10.71 = { by axiom 2 (condensed_detachment) }
% 80.35/10.71 is_a_theorem(Y)
% 80.35/10.71
% 80.35/10.71 Lemma 23: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, X), Z), Y))) = true.
% 80.35/10.71 Proof:
% 80.35/10.71 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, X), Z), Y)))
% 80.35/10.71 = { by lemma 22 R->L }
% 80.35/10.71 fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, X), Z), Y))), equivalent(equivalent(Z, X), Z))), true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, X), Z), Y)))
% 80.35/10.71 = { by lemma 13 }
% 80.35/10.71 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, X), Z), Y)))
% 80.35/10.71 = { by axiom 1 (condensed_detachment) }
% 80.35/10.71 true
% 80.35/10.71
% 80.35/10.71 Lemma 24: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W)) = true.
% 80.35/10.71 Proof:
% 80.35/10.71 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))
% 80.35/10.71 = { by axiom 2 (condensed_detachment) R->L }
% 80.35/10.71 fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))
% 80.35/10.71 = { by axiom 1 (condensed_detachment) R->L }
% 80.35/10.71 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))
% 80.35/10.71 = { by lemma 6 R->L }
% 80.35/10.71 fresh(fresh2(is_a_theorem(equivalent(W, equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))
% 80.35/10.71 = { by lemma 5 }
% 80.35/10.71 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))
% 80.35/10.71 = { by axiom 3 (condensed_detachment) }
% 80.35/10.71 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z)), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))
% 80.35/10.71 = { by lemma 10 }
% 80.35/10.71 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), Y), X), Z), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(V, U), T))), equivalent(T, U))), W))
% 80.35/10.71 = { by axiom 1 (condensed_detachment) }
% 80.35/10.72 true
% 80.35/10.72
% 80.35/10.72 Lemma 25: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y))) = true.
% 80.35/10.72 Proof:
% 80.35/10.72 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.72 = { by axiom 2 (condensed_detachment) R->L }
% 80.35/10.72 fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.72 = { by axiom 1 (condensed_detachment) R->L }
% 80.35/10.72 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.72 = { by axiom 1 (condensed_detachment) R->L }
% 80.35/10.72 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.72 = { by lemma 18 R->L }
% 80.35/10.72 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.73 = { by lemma 5 }
% 80.35/10.73 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.73 = { by lemma 20 }
% 80.35/10.73 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y))), equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.73 = { by axiom 3 (condensed_detachment) }
% 80.35/10.73 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(X, equivalent(equivalent(X, Y), Z))), equivalent(Z, Y))), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)), equivalent(Z, Y)), equivalent(Z, Y)))), true, equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.73 = { by lemma 24 }
% 80.35/10.73 fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(X, Y), Z)), equivalent(Z, Y)))
% 80.35/10.73 = { by axiom 1 (condensed_detachment) }
% 80.35/10.73 true
% 80.35/10.73
% 80.35/10.73 Lemma 26: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(Z, Y), X)) = is_a_theorem(equivalent(equivalent(Z, Y), X)).
% 80.35/10.73 Proof:
% 80.35/10.73 fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(Z, Y), X))
% 80.35/10.73 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.73 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.35/10.73 = { by axiom 2 (condensed_detachment) R->L }
% 80.35/10.73 fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.35/10.73 = { by axiom 1 (condensed_detachment) R->L }
% 80.35/10.73 fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.35/10.73 = { by lemma 25 R->L }
% 80.35/10.73 fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.35/10.73 = { by axiom 3 (condensed_detachment) R->L }
% 80.35/10.73 fresh(fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.35/10.73 = { by lemma 15 }
% 80.35/10.74 fresh(fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.35/10.74 = { by axiom 2 (condensed_detachment) }
% 80.35/10.74 fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.35/10.74 = { by axiom 3 (condensed_detachment) }
% 80.77/10.74 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.77/10.74 = { by lemma 9 R->L }
% 80.77/10.74 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.77/10.74 = { by axiom 2 (condensed_detachment) R->L }
% 80.77/10.74 fresh(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.77/10.75 = { by axiom 1 (condensed_detachment) R->L }
% 80.77/10.75 fresh(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)))))), true, equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.75 = { by lemma 13 R->L }
% 80.87/10.75 fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y))), true, equivalent(equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)))))), true, equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by lemma 19 }
% 80.87/10.76 fresh(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)))))), true, equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by axiom 3 (condensed_detachment) }
% 80.87/10.76 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)))))), true, equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by lemma 20 R->L }
% 80.87/10.76 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(X, Y)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(Z, equivalent(equivalent(Z, Y), X))), equivalent(X, Y))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))))), true, equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)))))), true, equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by lemma 24 }
% 80.87/10.76 fresh(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), equivalent(X, Y)), equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z)))))), true, equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by axiom 1 (condensed_detachment) }
% 80.87/10.76 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(Z, equivalent(equivalent(Z, Y), X)), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by axiom 1 (condensed_detachment) }
% 80.87/10.76 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X)), Z), Z)), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by axiom 1 (condensed_detachment) }
% 80.87/10.76 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by axiom 1 (condensed_detachment) }
% 80.87/10.76 fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(Z, Y), X))
% 80.87/10.76 = { by axiom 2 (condensed_detachment) }
% 80.87/10.77 is_a_theorem(equivalent(equivalent(Z, Y), X))
% 80.87/10.77
% 80.87/10.77 Goal 1 (prove_yrm): is_a_theorem(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a)))) = true.
% 80.87/10.77 Proof:
% 80.87/10.77 is_a_theorem(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.77 = { by lemma 26 R->L }
% 80.87/10.77 fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.77 = { by axiom 2 (condensed_detachment) R->L }
% 80.87/10.77 fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.77 = { by axiom 1 (condensed_detachment) R->L }
% 80.87/10.77 fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.77 = { by axiom 1 (condensed_detachment) R->L }
% 80.87/10.77 fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.77 = { by lemma 23 R->L }
% 80.87/10.77 fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.77 = { by axiom 3 (condensed_detachment) R->L }
% 80.87/10.77 fresh2(fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by lemma 19 R->L }
% 80.87/10.78 fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by lemma 21 R->L }
% 80.87/10.78 fresh2(fresh(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), a), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))))), true, equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by lemma 16 }
% 80.87/10.78 fresh2(fresh(fresh2(fresh(fresh2(fresh2(true, true, equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by axiom 1 (condensed_detachment) }
% 80.87/10.78 fresh2(fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))))), true, equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by axiom 1 (condensed_detachment) }
% 80.87/10.78 fresh2(fresh(fresh2(fresh(true, true, equivalent(equivalent(a, equivalent(equivalent(equivalent(b, c), a), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by axiom 2 (condensed_detachment) }
% 80.87/10.78 fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by lemma 26 }
% 80.87/10.78 fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.78 = { by axiom 3 (condensed_detachment) }
% 80.87/10.79 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.79 = { by lemma 26 R->L }
% 80.87/10.79 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.79 = { by lemma 9 R->L }
% 80.87/10.79 fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.79 = { by axiom 2 (condensed_detachment) R->L }
% 80.87/10.79 fresh2(fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.79 = { by axiom 1 (condensed_detachment) R->L }
% 80.87/10.79 fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))))), true, equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.80 = { by lemma 25 R->L }
% 80.87/10.80 fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))))), true, equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.80 = { by lemma 22 }
% 80.87/10.80 fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))))), true, equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.80 = { by axiom 3 (condensed_detachment) }
% 80.87/10.81 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.81 = { by lemma 23 }
% 80.87/10.81 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(b, c), b), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))), equivalent(c, equivalent(equivalent(c, equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.81 = { by axiom 1 (condensed_detachment) }
% 80.87/10.81 fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), equivalent(b, c)), equivalent(equivalent(b, c), a))), true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.81 = { by axiom 1 (condensed_detachment) }
% 80.87/10.81 fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(b, c)), equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b))), true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.81 = { by axiom 1 (condensed_detachment) }
% 80.87/10.81 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, equivalent(equivalent(b, c), a)), b), a)), true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.81 = { by axiom 1 (condensed_detachment) }
% 80.87/10.81 fresh2(true, true, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(b, c), a))))
% 80.87/10.81 = { by axiom 1 (condensed_detachment) }
% 80.87/10.81 true
% 80.87/10.81 % SZS output end Proof
% 80.87/10.81
% 80.87/10.81 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------