TSTP Solution File: LCL051-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL051-1 : 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 : n011.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 08:17:11 EDT 2023
% Result : Unsatisfiable 48.83s 6.65s
% Output : Proof 50.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL051-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 04:45:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 48.83/6.65 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 48.83/6.65
% 48.83/6.65 % SZS status Unsatisfiable
% 48.83/6.65
% 49.85/6.73 % SZS output start Proof
% 49.85/6.73 Take the following subset of the input axioms:
% 49.85/6.73 fof(cn_1, axiom, ![X, Y, Z]: is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))).
% 49.85/6.73 fof(cn_2, axiom, ![X2]: is_a_theorem(implies(implies(not(X2), X2), X2))).
% 49.85/6.73 fof(cn_3, axiom, ![X2, Y2]: is_a_theorem(implies(X2, implies(not(X2), Y2)))).
% 49.85/6.73 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 49.85/6.73 fof(prove_cn_22, negated_conjecture, ~is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c))))).
% 49.85/6.73
% 49.85/6.73 Now clausify the problem and encode Horn clauses using encoding 3 of
% 49.85/6.73 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 49.85/6.73 We repeatedly replace C & s=t => u=v by the two clauses:
% 49.85/6.73 fresh(y, y, x1...xn) = u
% 49.85/6.73 C => fresh(s, t, x1...xn) = v
% 49.85/6.73 where fresh is a fresh function symbol and x1..xn are the free
% 49.85/6.73 variables of u and v.
% 49.85/6.73 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 49.85/6.73 input problem has no model of domain size 1).
% 49.85/6.73
% 49.85/6.73 The encoding turns the above axioms into the following unit equations and goals:
% 49.85/6.73
% 49.85/6.73 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 49.85/6.73 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 49.85/6.73 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 49.85/6.73 Axiom 4 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 49.85/6.73 Axiom 5 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 49.85/6.73 Axiom 6 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 49.85/6.73
% 49.85/6.73 Lemma 7: fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z))) = is_a_theorem(implies(implies(Y, Z), implies(X, Z))).
% 49.85/6.73 Proof:
% 49.85/6.73 fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z)))
% 50.13/6.73 = { by axiom 5 (condensed_detachment) R->L }
% 50.13/6.73 fresh(is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))), true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 50.13/6.73 = { by axiom 6 (cn_1) }
% 50.13/6.73 fresh(true, true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 50.13/6.73 = { by axiom 2 (condensed_detachment) }
% 50.13/6.73 is_a_theorem(implies(implies(Y, Z), implies(X, Z)))
% 50.13/6.73
% 50.13/6.73 Lemma 8: is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))) = true.
% 50.13/6.73 Proof:
% 50.13/6.73 is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 50.13/6.73 = { by lemma 7 R->L }
% 50.13/6.73 fresh2(is_a_theorem(implies(X, implies(not(X), Y))), true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 50.13/6.73 = { by axiom 3 (cn_3) }
% 50.13/6.73 fresh2(true, true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 50.13/6.73 = { by axiom 1 (condensed_detachment) }
% 50.13/6.73 true
% 50.13/6.73
% 50.13/6.73 Lemma 9: fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z)) = is_a_theorem(implies(X, Z)).
% 50.13/6.73 Proof:
% 50.13/6.73 fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z))
% 50.13/6.73 = { by axiom 5 (condensed_detachment) R->L }
% 50.13/6.73 fresh(is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))), true, implies(implies(not(X), Y), Z), implies(X, Z))
% 50.13/6.73 = { by lemma 8 }
% 50.13/6.73 fresh(true, true, implies(implies(not(X), Y), Z), implies(X, Z))
% 50.13/6.73 = { by axiom 2 (condensed_detachment) }
% 50.13/6.73 is_a_theorem(implies(X, Z))
% 50.13/6.73
% 50.13/6.73 Lemma 10: is_a_theorem(implies(X, X)) = true.
% 50.13/6.73 Proof:
% 50.13/6.73 is_a_theorem(implies(X, X))
% 50.13/6.73 = { by lemma 9 R->L }
% 50.13/6.73 fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(X, X))
% 50.13/6.73 = { by axiom 4 (cn_2) }
% 50.13/6.73 fresh2(true, true, implies(X, X))
% 50.13/6.73 = { by axiom 1 (condensed_detachment) }
% 50.13/6.73 true
% 50.13/6.73
% 50.13/6.73 Lemma 11: fresh2(is_a_theorem(implies(not(X), X)), true, X) = is_a_theorem(X).
% 50.13/6.73 Proof:
% 50.13/6.73 fresh2(is_a_theorem(implies(not(X), X)), true, X)
% 50.13/6.73 = { by axiom 5 (condensed_detachment) R->L }
% 50.13/6.73 fresh(is_a_theorem(implies(implies(not(X), X), X)), true, implies(not(X), X), X)
% 50.13/6.73 = { by axiom 4 (cn_2) }
% 50.13/6.73 fresh(true, true, implies(not(X), X), X)
% 50.13/6.73 = { by axiom 2 (condensed_detachment) }
% 50.13/6.73 is_a_theorem(X)
% 50.13/6.73
% 50.13/6.73 Lemma 12: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))) = true.
% 50.13/6.73 Proof:
% 50.13/6.73 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 50.13/6.73 = { by lemma 7 R->L }
% 50.13/6.73 fresh2(is_a_theorem(implies(implies(Z, X), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 50.13/6.73 = { by axiom 6 (cn_1) }
% 50.13/6.73 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 50.13/6.73 = { by axiom 1 (condensed_detachment) }
% 50.13/6.73 true
% 50.13/6.73
% 50.13/6.73 Lemma 13: fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W)) = is_a_theorem(implies(implies(Z, X), W)).
% 50.13/6.73 Proof:
% 50.13/6.73 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W))
% 50.13/6.73 = { by axiom 5 (condensed_detachment) R->L }
% 50.13/6.73 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 50.13/6.73 = { by lemma 12 }
% 50.13/6.73 fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 50.13/6.73 = { by axiom 2 (condensed_detachment) }
% 50.13/6.73 is_a_theorem(implies(implies(Z, X), W))
% 50.13/6.73
% 50.13/6.73 Lemma 14: fresh2(is_a_theorem(implies(implies(X, implies(not(Y), Z)), W)), true, implies(Y, W)) = is_a_theorem(implies(Y, W)).
% 50.13/6.73 Proof:
% 50.13/6.73 fresh2(is_a_theorem(implies(implies(X, implies(not(Y), Z)), W)), true, implies(Y, W))
% 50.13/6.73 = { by axiom 5 (condensed_detachment) R->L }
% 50.13/6.73 fresh(is_a_theorem(implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.13/6.73 = { by lemma 7 R->L }
% 50.15/6.73 fresh(fresh2(is_a_theorem(implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.15/6.73 = { by lemma 9 R->L }
% 50.15/6.73 fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(Y), not(X)), implies(X, implies(not(Y), Z)))), true, implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.15/6.73 = { by lemma 13 R->L }
% 50.15/6.73 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(X), Z), implies(not(Y), Z)), implies(X, implies(not(Y), Z)))), true, implies(implies(not(Y), not(X)), implies(X, implies(not(Y), Z)))), true, implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.15/6.73 = { by lemma 8 }
% 50.15/6.73 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(not(Y), not(X)), implies(X, implies(not(Y), Z)))), true, implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 fresh(fresh2(fresh2(true, true, implies(Y, implies(X, implies(not(Y), Z)))), true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 fresh(fresh2(true, true, implies(implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))), true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 fresh(true, true, implies(implies(X, implies(not(Y), Z)), W), implies(Y, W))
% 50.15/6.73 = { by axiom 2 (condensed_detachment) }
% 50.15/6.73 is_a_theorem(implies(Y, W))
% 50.15/6.73
% 50.15/6.73 Lemma 15: is_a_theorem(implies(X, implies(implies(X, Y), implies(Z, Y)))) = true.
% 50.15/6.73 Proof:
% 50.15/6.73 is_a_theorem(implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by lemma 14 R->L }
% 50.15/6.73 fresh2(is_a_theorem(implies(implies(Z, implies(not(X), X)), implies(implies(X, Y), implies(Z, Y)))), true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by lemma 13 R->L }
% 50.15/6.73 fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(X), X), Y), implies(Z, Y)), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(Z, implies(not(X), X)), implies(implies(X, Y), implies(Z, Y)))), true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by lemma 7 R->L }
% 50.15/6.73 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), implies(Z, Y)), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(Z, implies(not(X), X)), implies(implies(X, Y), implies(Z, Y)))), true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by lemma 7 R->L }
% 50.15/6.73 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), implies(Z, Y)), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(Z, implies(not(X), X)), implies(implies(X, Y), implies(Z, Y)))), true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by axiom 4 (cn_2) }
% 50.15/6.73 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), implies(Z, Y)), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(Z, implies(not(X), X)), implies(implies(X, Y), implies(Z, Y)))), true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(not(X), X), Y), implies(Z, Y)), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(Z, implies(not(X), X)), implies(implies(X, Y), implies(Z, Y)))), true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 fresh2(fresh2(true, true, implies(implies(Z, implies(not(X), X)), implies(implies(X, Y), implies(Z, Y)))), true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 fresh2(true, true, implies(X, implies(implies(X, Y), implies(Z, Y))))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 true
% 50.15/6.73
% 50.15/6.73 Lemma 16: fresh2(is_a_theorem(X), true, implies(implies(X, Y), implies(Z, Y))) = is_a_theorem(implies(implies(X, Y), implies(Z, Y))).
% 50.15/6.73 Proof:
% 50.15/6.73 fresh2(is_a_theorem(X), true, implies(implies(X, Y), implies(Z, Y)))
% 50.15/6.73 = { by axiom 5 (condensed_detachment) R->L }
% 50.15/6.73 fresh(is_a_theorem(implies(X, implies(implies(X, Y), implies(Z, Y)))), true, X, implies(implies(X, Y), implies(Z, Y)))
% 50.15/6.73 = { by lemma 15 }
% 50.15/6.73 fresh(true, true, X, implies(implies(X, Y), implies(Z, Y)))
% 50.15/6.73 = { by axiom 2 (condensed_detachment) }
% 50.15/6.73 is_a_theorem(implies(implies(X, Y), implies(Z, Y)))
% 50.15/6.73
% 50.15/6.73 Lemma 17: is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))) = true.
% 50.15/6.73 Proof:
% 50.15/6.73 is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 50.15/6.73 = { by lemma 13 R->L }
% 50.15/6.73 fresh2(is_a_theorem(implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 50.15/6.73 = { by lemma 16 R->L }
% 50.15/6.73 fresh2(fresh2(is_a_theorem(implies(implies(not(Y), Y), Y)), true, implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 50.15/6.73 = { by axiom 4 (cn_2) }
% 50.15/6.73 fresh2(fresh2(true, true, implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 fresh2(true, true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.73 true
% 50.15/6.73
% 50.15/6.73 Lemma 18: is_a_theorem(implies(implies(not(X), Y), implies(Z, implies(implies(Y, X), X)))) = true.
% 50.15/6.73 Proof:
% 50.15/6.73 is_a_theorem(implies(implies(not(X), Y), implies(Z, implies(implies(Y, X), X))))
% 50.15/6.73 = { by lemma 13 R->L }
% 50.15/6.73 fresh2(is_a_theorem(implies(implies(implies(Y, X), implies(not(X), X)), implies(Z, implies(implies(Y, X), X)))), true, implies(implies(not(X), Y), implies(Z, implies(implies(Y, X), X))))
% 50.15/6.73 = { by lemma 17 }
% 50.15/6.73 fresh2(true, true, implies(implies(not(X), Y), implies(Z, implies(implies(Y, X), X))))
% 50.15/6.73 = { by axiom 1 (condensed_detachment) }
% 50.15/6.74 true
% 50.15/6.74
% 50.15/6.74 Goal 1 (prove_cn_22): is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))) = true.
% 50.15/6.74 Proof:
% 50.15/6.74 is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.74 = { by axiom 2 (condensed_detachment) R->L }
% 50.15/6.74 fresh(true, true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.74 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.74 fresh(fresh2(true, true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.74 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.74 fresh(fresh2(fresh2(true, true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.75 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.75 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.75 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.75 fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.75 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.75 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.75 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.75 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.75 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.75 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.75 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.75 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.75 = { by lemma 18 R->L }
% 50.15/6.75 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.76 = { by axiom 5 (condensed_detachment) R->L }
% 50.15/6.76 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.76 = { by lemma 16 R->L }
% 50.15/6.76 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(not(implies(a, c)), implies(X, X))), true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.76 = { by axiom 2 (condensed_detachment) R->L }
% 50.15/6.76 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(true, true, implies(implies(X, X), implies(X, X)), implies(not(implies(a, c)), implies(X, X))), true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.76 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.77 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(X, X), implies(X, X)), implies(not(implies(a, c)), implies(X, X)))), true, implies(implies(X, X), implies(X, X)), implies(not(implies(a, c)), implies(X, X))), true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.77 = { by lemma 10 R->L }
% 50.15/6.77 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(X, X)), true, implies(implies(implies(X, X), implies(X, X)), implies(not(implies(a, c)), implies(X, X)))), true, implies(implies(X, X), implies(X, X)), implies(not(implies(a, c)), implies(X, X))), true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.77 = { by lemma 16 }
% 50.15/6.77 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(X, X), implies(X, X)), implies(not(implies(a, c)), implies(X, X)))), true, implies(implies(X, X), implies(X, X)), implies(not(implies(a, c)), implies(X, X))), true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.77 = { by axiom 5 (condensed_detachment) }
% 50.15/6.77 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(X, X), implies(X, X))), true, implies(not(implies(a, c)), implies(X, X))), true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.77 = { by lemma 10 }
% 50.15/6.78 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(not(implies(a, c)), implies(X, X))), true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.78 = { by axiom 1 (condensed_detachment) }
% 50.15/6.78 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.78 = { by axiom 1 (condensed_detachment) }
% 50.15/6.78 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(not(implies(a, c)), implies(X, X)), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.78 = { by axiom 2 (condensed_detachment) }
% 50.15/6.78 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.78 = { by lemma 11 }
% 50.15/6.78 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.78 = { by lemma 11 }
% 50.15/6.78 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), true, implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.79 = { by axiom 5 (condensed_detachment) R->L }
% 50.15/6.79 fresh(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.79 = { by axiom 2 (condensed_detachment) R->L }
% 50.15/6.79 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(true, true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.79 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.79 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.80 = { by axiom 1 (condensed_detachment) R->L }
% 50.15/6.80 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.81 = { by axiom 4 (cn_2) R->L }
% 50.15/6.81 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.81 = { by axiom 5 (condensed_detachment) R->L }
% 50.15/6.81 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.82 = { by lemma 7 R->L }
% 50.15/6.82 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.82 = { by lemma 14 R->L }
% 50.15/6.83 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.83 = { by lemma 17 }
% 50.15/6.83 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.84 = { by axiom 1 (condensed_detachment) }
% 50.15/6.84 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))))), true, implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.84 = { by axiom 1 (condensed_detachment) }
% 50.15/6.84 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(fresh(true, true, implies(implies(not(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.84 = { by axiom 2 (condensed_detachment) }
% 50.15/6.85 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))))), true, implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.85 = { by lemma 7 }
% 50.15/6.85 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))))), true, implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.85 = { by axiom 5 (condensed_detachment) }
% 50.15/6.85 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(not(implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(X, X), implies(a, c)), implies(a, c))), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.85 = { by lemma 18 }
% 50.15/6.85 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))))), true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.85 = { by axiom 1 (condensed_detachment) }
% 50.15/6.85 fresh(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.85 = { by axiom 2 (condensed_detachment) }
% 50.15/6.85 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.85 = { by lemma 11 }
% 50.15/6.85 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(implies(X, X), implies(a, c)), implies(a, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.85 = { by lemma 13 }
% 50.15/6.86 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by axiom 5 (condensed_detachment) R->L }
% 50.15/6.86 fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by lemma 7 R->L }
% 50.15/6.86 fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by lemma 15 }
% 50.15/6.86 fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by axiom 1 (condensed_detachment) }
% 50.15/6.86 fresh(fresh2(fresh(true, true, implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(X, X), implies(a, c))), implies(implies(implies(b, c), implies(a, c)), implies(a, c))), implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by axiom 2 (condensed_detachment) }
% 50.15/6.86 fresh(fresh2(is_a_theorem(implies(implies(b, c), implies(implies(implies(b, c), implies(a, c)), implies(a, c)))), true, implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by lemma 7 }
% 50.15/6.86 fresh(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by axiom 5 (condensed_detachment) }
% 50.15/6.86 fresh2(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c)))), true, implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by lemma 12 }
% 50.15/6.86 fresh2(true, true, implies(implies(b, c), implies(implies(a, b), implies(a, c))))
% 50.15/6.86 = { by axiom 1 (condensed_detachment) }
% 50.15/6.86 true
% 50.15/6.86 % SZS output end Proof
% 50.15/6.86
% 50.15/6.86 RESULT: Unsatisfiable (the axioms are contradictory).
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