TSTP Solution File: LCL025-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL025-1 : 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 : n021.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 08:17:05 EDT 2023
% Result : Unsatisfiable 6.36s 1.23s
% Output : Proof 7.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL025-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 17:53:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.36/1.23 Command-line arguments: --no-flatten-goal
% 6.36/1.23
% 6.36/1.23 % SZS status Unsatisfiable
% 6.36/1.23
% 6.36/1.26 % SZS output start Proof
% 6.36/1.26 Take the following subset of the input axioms:
% 6.36/1.26 fof(c0_2, axiom, ![X, Y]: is_a_theorem(implies(X, implies(Y, X)))).
% 6.36/1.26 fof(c0_6, axiom, ![Z, X2, Y2]: is_a_theorem(implies(implies(X2, implies(Y2, Z)), implies(implies(X2, Y2), implies(X2, Z))))).
% 6.36/1.26 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 6.36/1.26 fof(prove_c0_1, negated_conjecture, ~is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))).
% 6.36/1.26
% 6.36/1.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.36/1.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.36/1.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.36/1.26 fresh(y, y, x1...xn) = u
% 6.36/1.26 C => fresh(s, t, x1...xn) = v
% 6.36/1.26 where fresh is a fresh function symbol and x1..xn are the free
% 6.36/1.26 variables of u and v.
% 6.36/1.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.36/1.26 input problem has no model of domain size 1).
% 6.36/1.26
% 6.36/1.26 The encoding turns the above axioms into the following unit equations and goals:
% 6.36/1.26
% 6.36/1.26 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 6.36/1.26 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 6.36/1.26 Axiom 3 (c0_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 6.36/1.26 Axiom 4 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 6.36/1.26 Axiom 5 (c0_6): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 6.36/1.26
% 6.36/1.26 Lemma 6: fresh2(is_a_theorem(X), true, implies(Y, X)) = is_a_theorem(implies(Y, X)).
% 6.36/1.26 Proof:
% 6.36/1.26 fresh2(is_a_theorem(X), true, implies(Y, X))
% 6.36/1.26 = { by axiom 4 (condensed_detachment) R->L }
% 6.36/1.26 fresh(is_a_theorem(implies(X, implies(Y, X))), true, X, implies(Y, X))
% 6.36/1.26 = { by axiom 3 (c0_2) }
% 6.36/1.26 fresh(true, true, X, implies(Y, X))
% 6.36/1.26 = { by axiom 2 (condensed_detachment) }
% 6.36/1.26 is_a_theorem(implies(Y, X))
% 6.36/1.26
% 6.36/1.26 Lemma 7: is_a_theorem(implies(X, implies(Y, implies(Z, Y)))) = true.
% 6.36/1.26 Proof:
% 6.36/1.26 is_a_theorem(implies(X, implies(Y, implies(Z, Y))))
% 6.36/1.26 = { by lemma 6 R->L }
% 6.36/1.26 fresh2(is_a_theorem(implies(Y, implies(Z, Y))), true, implies(X, implies(Y, implies(Z, Y))))
% 6.36/1.26 = { by axiom 3 (c0_2) }
% 6.36/1.26 fresh2(true, true, implies(X, implies(Y, implies(Z, Y))))
% 6.36/1.26 = { by axiom 1 (condensed_detachment) }
% 6.36/1.26 true
% 6.36/1.26
% 6.36/1.26 Lemma 8: is_a_theorem(implies(X, implies(Y, implies(Z, implies(W, Z))))) = true.
% 6.36/1.26 Proof:
% 6.36/1.26 is_a_theorem(implies(X, implies(Y, implies(Z, implies(W, Z)))))
% 6.36/1.26 = { by lemma 6 R->L }
% 6.36/1.26 fresh2(is_a_theorem(implies(Y, implies(Z, implies(W, Z)))), true, implies(X, implies(Y, implies(Z, implies(W, Z)))))
% 6.36/1.26 = { by lemma 7 }
% 6.36/1.26 fresh2(true, true, implies(X, implies(Y, implies(Z, implies(W, Z)))))
% 6.36/1.26 = { by axiom 1 (condensed_detachment) }
% 6.36/1.26 true
% 6.36/1.26
% 6.36/1.26 Lemma 9: fresh2(is_a_theorem(implies(X, implies(Y, Z))), true, implies(implies(X, Y), implies(X, Z))) = is_a_theorem(implies(implies(X, Y), implies(X, Z))).
% 6.36/1.26 Proof:
% 6.36/1.26 fresh2(is_a_theorem(implies(X, implies(Y, Z))), true, implies(implies(X, Y), implies(X, Z)))
% 6.36/1.26 = { by axiom 4 (condensed_detachment) R->L }
% 6.36/1.26 fresh(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))), true, implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))
% 6.36/1.26 = { by axiom 5 (c0_6) }
% 6.36/1.26 fresh(true, true, implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))
% 6.36/1.26 = { by axiom 2 (condensed_detachment) }
% 6.36/1.26 is_a_theorem(implies(implies(X, Y), implies(X, Z)))
% 6.36/1.26
% 6.36/1.26 Lemma 10: fresh2(is_a_theorem(implies(implies(X, Y), X)), true, implies(implies(X, Y), Y)) = is_a_theorem(implies(implies(X, Y), Y)).
% 6.36/1.26 Proof:
% 6.36/1.26 fresh2(is_a_theorem(implies(implies(X, Y), X)), true, implies(implies(X, Y), Y))
% 6.36/1.26 = { by axiom 4 (condensed_detachment) R->L }
% 6.36/1.26 fresh(is_a_theorem(implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 6.36/1.26 = { by lemma 9 R->L }
% 6.36/1.26 fresh(fresh2(is_a_theorem(implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 6.36/1.26 = { by axiom 2 (condensed_detachment) R->L }
% 6.36/1.26 fresh(fresh2(fresh(true, true, implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 6.36/1.26 = { by axiom 1 (condensed_detachment) R->L }
% 6.36/1.26 fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(X, Y)))), true, implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 6.36/1.26 = { by axiom 3 (c0_2) R->L }
% 7.09/1.27 fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(Z, implies(X, Y)), implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(X, Y)))), true, implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 7.09/1.27 = { by lemma 9 }
% 7.09/1.27 fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(X, Y)))), true, implies(implies(X, Y), implies(Z, implies(X, Y))), implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 7.09/1.27 = { by axiom 4 (condensed_detachment) }
% 7.09/1.27 fresh(fresh2(fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, implies(X, Y)))), true, implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 7.09/1.27 = { by axiom 3 (c0_2) }
% 7.09/1.27 fresh(fresh2(fresh2(true, true, implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 7.09/1.27 = { by axiom 1 (condensed_detachment) }
% 7.09/1.27 fresh(fresh2(true, true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 7.09/1.27 = { by axiom 1 (condensed_detachment) }
% 7.09/1.27 fresh(true, true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 7.09/1.27 = { by axiom 2 (condensed_detachment) }
% 7.09/1.27 is_a_theorem(implies(implies(X, Y), Y))
% 7.09/1.27
% 7.09/1.27 Lemma 11: is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(X, Y)), implies(implies(X, implies(Y, Z)), implies(X, Z)))) = true.
% 7.09/1.27 Proof:
% 7.09/1.27 is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(X, Y)), implies(implies(X, implies(Y, Z)), implies(X, Z))))
% 7.09/1.27 = { by lemma 9 R->L }
% 7.09/1.27 fresh2(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))), true, implies(implies(implies(X, implies(Y, Z)), implies(X, Y)), implies(implies(X, implies(Y, Z)), implies(X, Z))))
% 7.09/1.27 = { by axiom 5 (c0_6) }
% 7.09/1.27 fresh2(true, true, implies(implies(implies(X, implies(Y, Z)), implies(X, Y)), implies(implies(X, implies(Y, Z)), implies(X, Z))))
% 7.09/1.27 = { by axiom 1 (condensed_detachment) }
% 7.09/1.27 true
% 7.09/1.27
% 7.09/1.27 Goal 1 (prove_c0_1): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 7.09/1.27 Proof:
% 7.09/1.27 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.27 = { by axiom 2 (condensed_detachment) R->L }
% 7.09/1.27 fresh(true, true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.27 = { by axiom 1 (condensed_detachment) R->L }
% 7.09/1.27 fresh(fresh2(true, true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.27 = { by axiom 1 (condensed_detachment) R->L }
% 7.09/1.27 fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.27 = { by lemma 11 R->L }
% 7.09/1.27 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.27 = { by axiom 4 (condensed_detachment) R->L }
% 7.09/1.27 fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.28 = { by axiom 2 (condensed_detachment) R->L }
% 7.09/1.28 fresh(fresh2(fresh(fresh(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.28 = { by axiom 1 (condensed_detachment) R->L }
% 7.09/1.28 fresh(fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.09/1.28 = { by axiom 1 (condensed_detachment) R->L }
% 7.09/1.29 fresh(fresh2(fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.29 = { by lemma 7 R->L }
% 7.26/1.29 fresh(fresh2(fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.29 = { by lemma 9 }
% 7.26/1.30 fresh(fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.30 = { by lemma 9 }
% 7.26/1.30 fresh(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.30 = { by axiom 4 (condensed_detachment) }
% 7.26/1.30 fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))))), true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.30 = { by lemma 8 }
% 7.26/1.30 fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.30 = { by axiom 1 (condensed_detachment) }
% 7.26/1.30 fresh(fresh2(fresh(true, true, implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.30 = { by axiom 2 (condensed_detachment) }
% 7.26/1.30 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.31 = { by axiom 4 (condensed_detachment) R->L }
% 7.26/1.31 fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.31 = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.31 fresh(fresh(fresh(true, true, implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.31 = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.31 fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.31 = { by lemma 8 R->L }
% 7.26/1.31 fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))))), true, implies(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by lemma 10 }
% 7.26/1.32 fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 4 (condensed_detachment) }
% 7.26/1.32 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by lemma 11 }
% 7.26/1.32 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 1 (condensed_detachment) }
% 7.26/1.32 fresh(fresh(true, true, implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 2 (condensed_detachment) }
% 7.26/1.32 fresh(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 4 (condensed_detachment) }
% 7.26/1.32 fresh2(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by lemma 9 R->L }
% 7.26/1.32 fresh2(fresh2(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 2 (condensed_detachment) R->L }
% 7.26/1.32 fresh2(fresh2(fresh(true, true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 1 (condensed_detachment) R->L }
% 7.26/1.32 fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by lemma 7 R->L }
% 7.26/1.32 fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true, implies(implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by lemma 10 }
% 7.26/1.32 fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 4 (condensed_detachment) }
% 7.26/1.32 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by lemma 9 R->L }
% 7.26/1.32 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by lemma 6 R->L }
% 7.26/1.32 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true, implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 5 (c0_6) }
% 7.26/1.32 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 1 (condensed_detachment) }
% 7.26/1.32 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 1 (condensed_detachment) }
% 7.26/1.32 fresh2(fresh2(fresh2(true, true, implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 1 (condensed_detachment) }
% 7.26/1.32 fresh2(fresh2(true, true, implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 1 (condensed_detachment) }
% 7.26/1.32 fresh2(true, true, implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 7.26/1.32 = { by axiom 1 (condensed_detachment) }
% 7.26/1.32 true
% 7.26/1.32 % SZS output end Proof
% 7.26/1.32
% 7.26/1.32 RESULT: Unsatisfiable (the axioms are contradictory).
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