TSTP Solution File: LCL405-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL405-1 : TPTP v8.1.2. Released v2.3.0.
% 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 : n032.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 08:18:48 EDT 2023
% Result : Unsatisfiable 3.94s 0.81s
% Output : Proof 4.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LCL405-1 : TPTP v8.1.2. Released v2.3.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Aug 25 06:23:42 EDT 2023
% 0.09/0.28 % CPUTime :
% 3.94/0.81 Command-line arguments: --no-flatten-goal
% 3.94/0.81
% 3.94/0.81 % SZS status Unsatisfiable
% 3.94/0.81
% 3.94/0.85 % SZS output start Proof
% 3.94/0.85 Take the following subset of the input axioms:
% 3.94/0.85 fof(cn_1, axiom, ![X, Y, Z]: is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))).
% 3.94/0.85 fof(cn_2, axiom, ![X2]: is_a_theorem(implies(implies(not(X2), X2), X2))).
% 3.94/0.85 fof(cn_3, axiom, ![X2, Y2]: is_a_theorem(implies(X2, implies(not(X2), Y2)))).
% 3.94/0.85 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 3.94/0.85 fof(prove_cn_71, negated_conjecture, ~is_a_theorem(not(implies(implies(x, x), not(implies(y, y)))))).
% 3.94/0.85
% 3.94/0.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.94/0.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.94/0.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.94/0.85 fresh(y, y, x1...xn) = u
% 3.94/0.85 C => fresh(s, t, x1...xn) = v
% 3.94/0.85 where fresh is a fresh function symbol and x1..xn are the free
% 3.94/0.85 variables of u and v.
% 3.94/0.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.94/0.85 input problem has no model of domain size 1).
% 3.94/0.85
% 3.94/0.85 The encoding turns the above axioms into the following unit equations and goals:
% 3.94/0.85
% 3.94/0.85 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 3.94/0.85 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 3.94/0.85 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 3.94/0.85 Axiom 4 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 3.94/0.85 Axiom 5 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 3.94/0.85 Axiom 6 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 3.94/0.85
% 3.94/0.85 Lemma 7: fresh2(is_a_theorem(X), true, implies(not(X), Y)) = is_a_theorem(implies(not(X), Y)).
% 3.94/0.85 Proof:
% 3.94/0.85 fresh2(is_a_theorem(X), true, implies(not(X), Y))
% 3.94/0.85 = { by axiom 5 (condensed_detachment) R->L }
% 3.94/0.85 fresh(is_a_theorem(implies(X, implies(not(X), Y))), true, X, implies(not(X), Y))
% 3.94/0.85 = { by axiom 3 (cn_3) }
% 3.94/0.85 fresh(true, true, X, implies(not(X), Y))
% 3.94/0.85 = { by axiom 2 (condensed_detachment) }
% 3.94/0.85 is_a_theorem(implies(not(X), Y))
% 3.94/0.85
% 3.94/0.85 Lemma 8: fresh2(is_a_theorem(implies(not(X), X)), true, X) = is_a_theorem(X).
% 3.94/0.85 Proof:
% 3.94/0.85 fresh2(is_a_theorem(implies(not(X), X)), true, X)
% 3.94/0.85 = { by axiom 5 (condensed_detachment) R->L }
% 3.94/0.85 fresh(is_a_theorem(implies(implies(not(X), X), X)), true, implies(not(X), X), X)
% 3.94/0.85 = { by axiom 4 (cn_2) }
% 3.94/0.85 fresh(true, true, implies(not(X), X), X)
% 3.94/0.85 = { by axiom 2 (condensed_detachment) }
% 3.94/0.85 is_a_theorem(X)
% 3.94/0.85
% 3.94/0.85 Lemma 9: 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))).
% 3.94/0.85 Proof:
% 3.94/0.85 fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z)))
% 3.94/0.85 = { by axiom 5 (condensed_detachment) R->L }
% 3.94/0.85 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)))
% 3.94/0.85 = { by axiom 6 (cn_1) }
% 3.94/0.85 fresh(true, true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 3.94/0.85 = { by axiom 2 (condensed_detachment) }
% 3.94/0.85 is_a_theorem(implies(implies(Y, Z), implies(X, Z)))
% 3.94/0.85
% 3.94/0.85 Lemma 10: is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y))) = true.
% 3.94/0.85 Proof:
% 3.94/0.85 is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y)))
% 3.94/0.85 = { by lemma 9 R->L }
% 3.94/0.85 fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(implies(X, Y), implies(implies(not(X), X), Y)))
% 3.94/0.85 = { by axiom 4 (cn_2) }
% 3.94/0.85 fresh2(true, true, implies(implies(X, Y), implies(implies(not(X), X), Y)))
% 3.94/0.85 = { by axiom 1 (condensed_detachment) }
% 3.94/0.85 true
% 3.94/0.85
% 3.94/0.85 Lemma 11: is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))) = true.
% 3.94/0.85 Proof:
% 3.94/0.85 is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 3.94/0.85 = { by lemma 9 R->L }
% 3.94/0.85 fresh2(is_a_theorem(implies(X, implies(not(X), Y))), true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 3.94/0.85 = { by axiom 3 (cn_3) }
% 3.94/0.85 fresh2(true, true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 3.94/0.85 = { by axiom 1 (condensed_detachment) }
% 3.94/0.85 true
% 3.94/0.85
% 3.94/0.85 Lemma 12: fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z)) = is_a_theorem(implies(X, Z)).
% 3.94/0.85 Proof:
% 3.94/0.85 fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z))
% 3.94/0.85 = { by axiom 5 (condensed_detachment) R->L }
% 3.94/0.85 fresh(is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))), true, implies(implies(not(X), Y), Z), implies(X, Z))
% 3.94/0.85 = { by lemma 11 }
% 3.94/0.85 fresh(true, true, implies(implies(not(X), Y), Z), implies(X, Z))
% 3.94/0.85 = { by axiom 2 (condensed_detachment) }
% 3.94/0.85 is_a_theorem(implies(X, Z))
% 3.94/0.85
% 3.94/0.85 Lemma 13: is_a_theorem(implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z))) = true.
% 3.94/0.85 Proof:
% 3.94/0.85 is_a_theorem(implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by lemma 9 R->L }
% 3.94/0.85 fresh2(is_a_theorem(implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by lemma 12 R->L }
% 3.94/0.85 fresh2(fresh2(is_a_theorem(implies(implies(not(W), Y), implies(not(implies(X, X)), Y))), true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by lemma 9 R->L }
% 3.94/0.85 fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(X, X)), not(W))), true, implies(implies(not(W), Y), implies(not(implies(X, X)), Y))), true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by lemma 7 R->L }
% 3.94/0.85 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(X, X)), true, implies(not(implies(X, X)), not(W))), true, implies(implies(not(W), Y), implies(not(implies(X, X)), Y))), true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by lemma 12 R->L }
% 3.94/0.85 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(X, X)), true, implies(not(implies(X, X)), not(W))), true, implies(implies(not(W), Y), implies(not(implies(X, X)), Y))), true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by axiom 4 (cn_2) }
% 3.94/0.85 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(X, X)), true, implies(not(implies(X, X)), not(W))), true, implies(implies(not(W), Y), implies(not(implies(X, X)), Y))), true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by axiom 1 (condensed_detachment) }
% 3.94/0.85 fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(X, X)), not(W))), true, implies(implies(not(W), Y), implies(not(implies(X, X)), Y))), true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.85 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh2(fresh2(fresh2(true, true, implies(implies(not(W), Y), implies(not(implies(X, X)), Y))), true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh2(fresh2(true, true, implies(W, implies(not(implies(X, X)), Y))), true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh2(true, true, implies(implies(implies(not(implies(X, X)), Y), Z), implies(W, Z)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 true
% 3.94/0.86
% 3.94/0.86 Lemma 14: 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)).
% 3.94/0.86 Proof:
% 3.94/0.86 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W))
% 3.94/0.86 = { by axiom 5 (condensed_detachment) R->L }
% 3.94/0.86 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))
% 3.94/0.86 = { by lemma 9 R->L }
% 3.94/0.86 fresh(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))), true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 3.94/0.86 = { by axiom 6 (cn_1) }
% 3.94/0.86 fresh(fresh2(true, true, 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))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 3.94/0.86 = { by axiom 2 (condensed_detachment) }
% 3.94/0.86 is_a_theorem(implies(implies(Z, X), W))
% 3.94/0.86
% 3.94/0.86 Lemma 15: fresh2(is_a_theorem(implies(implies(implies(not(X), X), Y), Z)), true, implies(implies(X, Y), Z)) = is_a_theorem(implies(implies(X, Y), Z)).
% 3.94/0.86 Proof:
% 3.94/0.86 fresh2(is_a_theorem(implies(implies(implies(not(X), X), Y), Z)), true, implies(implies(X, Y), Z))
% 3.94/0.86 = { by axiom 5 (condensed_detachment) R->L }
% 3.94/0.86 fresh(is_a_theorem(implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 3.94/0.86 = { by lemma 9 R->L }
% 3.94/0.86 fresh(fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 3.94/0.86 = { by lemma 10 }
% 3.94/0.86 fresh(fresh2(true, true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(true, true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 3.94/0.86 = { by axiom 2 (condensed_detachment) }
% 3.94/0.86 is_a_theorem(implies(implies(X, Y), Z))
% 3.94/0.86
% 3.94/0.86 Lemma 16: fresh2(is_a_theorem(implies(X, implies(not(Y), Y))), true, implies(Z, implies(X, Y))) = is_a_theorem(implies(Z, implies(X, Y))).
% 3.94/0.86 Proof:
% 3.94/0.86 fresh2(is_a_theorem(implies(X, implies(not(Y), Y))), true, implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 5 (condensed_detachment) R->L }
% 3.94/0.86 fresh(is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by lemma 14 R->L }
% 3.94/0.86 fresh(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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by lemma 15 R->L }
% 3.94/0.86 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by lemma 9 R->L }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by lemma 12 R->L }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by lemma 9 R->L }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(not(Y), Y), Y)), not(Z))), true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by lemma 7 R->L }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(Y), Y), Y)), true, implies(not(implies(implies(not(Y), Y), Y)), not(Z))), true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 4 (cn_2) }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(not(Y), Y), Y)), not(Z))), true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(fresh2(true, true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) }
% 3.94/0.86 fresh(true, true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.94/0.86 = { by axiom 2 (condensed_detachment) }
% 3.94/0.86 is_a_theorem(implies(Z, implies(X, Y)))
% 3.94/0.86
% 3.94/0.86 Goal 1 (prove_cn_71): is_a_theorem(not(implies(implies(x, x), not(implies(y, y))))) = true.
% 3.94/0.86 Proof:
% 3.94/0.86 is_a_theorem(not(implies(implies(x, x), not(implies(y, y)))))
% 3.94/0.86 = { by axiom 2 (condensed_detachment) R->L }
% 3.94/0.86 fresh(true, true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 3.94/0.86 = { by axiom 1 (condensed_detachment) R->L }
% 3.94/0.86 fresh(fresh2(true, true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 3.94/0.87 = { by axiom 1 (condensed_detachment) R->L }
% 3.94/0.87 fresh(fresh2(fresh2(true, true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 3.94/0.87 = { by axiom 1 (condensed_detachment) R->L }
% 3.94/0.87 fresh(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 3.94/0.87 = { by axiom 1 (condensed_detachment) R->L }
% 3.94/0.87 fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 3.94/0.87 = { by axiom 1 (condensed_detachment) R->L }
% 3.94/0.87 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 3.94/0.87 = { by axiom 1 (condensed_detachment) R->L }
% 3.94/0.87 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.88 = { by axiom 1 (condensed_detachment) R->L }
% 4.54/0.88 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))), implies(implies(x, x), not(implies(y, y)))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.88 = { by axiom 1 (condensed_detachment) R->L }
% 4.54/0.88 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))))), true, implies(implies(implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))), implies(implies(x, x), not(implies(y, y)))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.88 = { by lemma 10 R->L }
% 4.54/0.88 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(y, y))), implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))))), true, implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))))), true, implies(implies(implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))), implies(implies(x, x), not(implies(y, y)))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.88 = { by lemma 12 }
% 4.54/0.88 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))))), true, implies(implies(implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))), implies(implies(x, x), not(implies(y, y)))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.89 = { by lemma 9 }
% 4.54/0.89 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(y, y))), implies(implies(x, x), not(implies(y, y)))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.89 = { by lemma 14 }
% 4.54/0.89 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.89 = { by axiom 5 (condensed_detachment) R->L }
% 4.54/0.89 fresh(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.89 = { by lemma 9 R->L }
% 4.54/0.90 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.90 = { by lemma 12 R->L }
% 4.54/0.90 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(x, x))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.90 = { by lemma 14 R->L }
% 4.54/0.90 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(x, x)), not(not(implies(implies(x, x), not(implies(y, y)))))), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(x, x))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.90 = { by lemma 11 }
% 4.54/0.90 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(implies(x, x))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.90 = { by axiom 1 (condensed_detachment) }
% 4.54/0.91 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))))), true, implies(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by axiom 1 (condensed_detachment) }
% 4.54/0.91 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by axiom 1 (condensed_detachment) }
% 4.54/0.91 fresh(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(x, x), implies(not(not(not(implies(implies(x, x), not(implies(y, y)))))), not(not(implies(implies(x, x), not(implies(y, y))))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by axiom 2 (condensed_detachment) }
% 4.54/0.91 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(not(implies(implies(x, x), not(implies(y, y))))), implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by lemma 9 }
% 4.54/0.91 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), implies(not(not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by lemma 16 }
% 4.54/0.91 fresh(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by lemma 8 }
% 4.54/0.91 fresh(fresh2(is_a_theorem(implies(implies(implies(not(implies(implies(x, x), not(implies(y, y)))), implies(implies(x, x), not(implies(y, y)))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by lemma 15 }
% 4.54/0.91 fresh(is_a_theorem(implies(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by axiom 5 (condensed_detachment) }
% 4.54/0.91 fresh2(is_a_theorem(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by axiom 2 (condensed_detachment) R->L }
% 4.54/0.91 fresh2(fresh(true, true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by axiom 1 (condensed_detachment) R->L }
% 4.54/0.91 fresh2(fresh(fresh2(true, true, implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.91 = { by axiom 1 (condensed_detachment) R->L }
% 4.54/0.91 fresh2(fresh(fresh2(fresh2(true, true, implies(not(implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))))), true, implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by lemma 13 R->L }
% 4.54/0.92 fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(not(implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))))), true, implies(not(implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))))), true, implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by lemma 16 }
% 4.54/0.92 fresh2(fresh(fresh2(is_a_theorem(implies(not(implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))))), true, implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by lemma 8 }
% 4.54/0.92 fresh2(fresh(is_a_theorem(implies(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by axiom 5 (condensed_detachment) }
% 4.54/0.92 fresh2(fresh2(is_a_theorem(implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by lemma 15 R->L }
% 4.54/0.92 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(not(implies(y, y))), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by lemma 9 R->L }
% 4.54/0.92 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(x, x), not(implies(y, y))), implies(not(not(implies(y, y))), not(implies(y, y))))), true, implies(implies(implies(not(not(implies(y, y))), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by lemma 15 R->L }
% 4.54/0.92 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), not(implies(y, y))), implies(not(not(implies(y, y))), not(implies(y, y))))), true, implies(implies(implies(x, x), not(implies(y, y))), implies(not(not(implies(y, y))), not(implies(y, y))))), true, implies(implies(implies(not(not(implies(y, y))), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by lemma 13 }
% 4.54/0.92 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(x, x), not(implies(y, y))), implies(not(not(implies(y, y))), not(implies(y, y))))), true, implies(implies(implies(not(not(implies(y, y))), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by axiom 1 (condensed_detachment) }
% 4.54/0.92 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(not(implies(y, y))), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by axiom 1 (condensed_detachment) }
% 4.54/0.92 fresh2(fresh2(fresh2(true, true, implies(implies(not(implies(y, y)), not(implies(implies(x, x), not(implies(y, y))))), implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y))))))), true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by axiom 1 (condensed_detachment) }
% 4.54/0.92 fresh2(fresh2(true, true, implies(implies(implies(x, x), not(implies(y, y))), not(implies(implies(x, x), not(implies(y, y)))))), true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by axiom 1 (condensed_detachment) }
% 4.54/0.92 fresh2(true, true, not(implies(implies(x, x), not(implies(y, y)))))
% 4.54/0.92 = { by axiom 1 (condensed_detachment) }
% 4.54/0.92 true
% 4.54/0.92 % SZS output end Proof
% 4.54/0.92
% 4.54/0.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------