TSTP Solution File: LCL166-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL166-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:17:43 EDT 2023
% Result : Unsatisfiable 218.94s 28.29s
% Output : Proof 222.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.16 % Problem : LCL166-1 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.17 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.40 % Computer : n011.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8042.1875MB
% 0.16/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Thu Aug 24 17:18:38 EDT 2023
% 0.16/0.41 % CPUTime :
% 218.94/28.29 Command-line arguments: --no-flatten-goal
% 218.94/28.29
% 218.94/28.29 % SZS status Unsatisfiable
% 218.94/28.29
% 220.56/28.48 % SZS output start Proof
% 220.56/28.48 Take the following subset of the input axioms:
% 220.56/28.48 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 220.56/28.48 fof(prove_um, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))).
% 220.56/28.48 fof(xhn, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(X2, equivalent(equivalent(Y2, Z), equivalent(equivalent(Z, X2), Y2))))).
% 220.56/28.48
% 220.56/28.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 220.56/28.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 220.56/28.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 220.56/28.48 fresh(y, y, x1...xn) = u
% 220.56/28.48 C => fresh(s, t, x1...xn) = v
% 220.56/28.48 where fresh is a fresh function symbol and x1..xn are the free
% 220.56/28.48 variables of u and v.
% 220.56/28.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 220.56/28.48 input problem has no model of domain size 1).
% 220.56/28.48
% 220.56/28.48 The encoding turns the above axioms into the following unit equations and goals:
% 220.56/28.48
% 220.56/28.48 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 220.56/28.48 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 220.56/28.48 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 220.56/28.48 Axiom 4 (xhn): is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))) = true.
% 220.56/28.48
% 220.56/28.48 Lemma 5: fresh2(is_a_theorem(X), true, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))) = is_a_theorem(equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))).
% 220.56/28.48 Proof:
% 220.56/28.48 fresh2(is_a_theorem(X), true, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))
% 220.56/28.48 = { by axiom 3 (condensed_detachment) R->L }
% 220.56/28.48 fresh(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), true, X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))
% 220.56/28.48 = { by axiom 4 (xhn) }
% 220.56/28.48 fresh(true, true, X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))
% 220.56/28.48 = { by axiom 2 (condensed_detachment) }
% 220.56/28.48 is_a_theorem(equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))
% 220.56/28.48
% 220.56/28.48 Lemma 6: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))) = true.
% 220.56/28.48 Proof:
% 220.56/28.48 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)))
% 220.56/28.48 = { by lemma 5 R->L }
% 220.56/28.48 fresh2(is_a_theorem(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)))
% 220.56/28.48 = { by axiom 4 (xhn) }
% 220.56/28.48 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)))
% 220.56/28.48 = { by axiom 1 (condensed_detachment) }
% 220.56/28.48 true
% 220.56/28.48
% 220.56/28.48 Lemma 7: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)) = is_a_theorem(equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)).
% 220.56/28.48 Proof:
% 220.56/28.48 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))
% 220.56/28.48 = { by axiom 3 (condensed_detachment) R->L }
% 220.56/28.48 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))), true, equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))
% 220.56/28.48 = { by lemma 6 }
% 220.56/28.48 fresh(true, true, equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))
% 220.56/28.48 = { by axiom 2 (condensed_detachment) }
% 220.56/28.48 is_a_theorem(equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))
% 220.56/28.48
% 220.56/28.48 Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Z)) = true.
% 220.56/28.48 Proof:
% 220.56/28.48 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Z))
% 220.56/28.48 = { by lemma 7 R->L }
% 220.56/28.48 fresh2(is_a_theorem(equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Z))
% 220.56/28.48 = { by axiom 4 (xhn) }
% 220.56/28.48 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Z))
% 220.56/28.48 = { by axiom 1 (condensed_detachment) }
% 220.56/28.48 true
% 220.56/28.48
% 220.56/28.48 Lemma 9: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U))) = true.
% 220.56/28.48 Proof:
% 220.56/28.48 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))
% 220.56/28.48 = { by axiom 2 (condensed_detachment) R->L }
% 220.56/28.48 fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))
% 220.56/28.48 = { by axiom 1 (condensed_detachment) R->L }
% 220.56/28.48 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))
% 220.56/28.48 = { by lemma 6 R->L }
% 220.56/28.48 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)), equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))
% 220.56/28.48 = { by lemma 7 }
% 220.56/28.48 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))
% 220.56/28.48 = { by axiom 3 (condensed_detachment) }
% 220.56/28.48 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U), equivalent(equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)))), equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y)))), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))
% 220.56/28.48 = { by lemma 8 }
% 220.56/28.48 fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, X), Y))), equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(U, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), W)), U)))
% 220.56/28.48 = { by axiom 1 (condensed_detachment) }
% 220.56/28.48 true
% 220.56/28.48
% 220.56/28.48 Lemma 10: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z)) = true.
% 220.56/28.48 Proof:
% 220.56/28.48 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z))
% 220.56/28.48 = { by axiom 2 (condensed_detachment) R->L }
% 220.56/28.48 fresh(true, true, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z))
% 220.56/28.48 = { by lemma 9 R->L }
% 220.56/28.48 fresh(is_a_theorem(equivalent(equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z))), true, equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z))
% 220.56/28.48 = { by axiom 3 (condensed_detachment) }
% 220.56/28.49 fresh2(is_a_theorem(equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z))
% 220.56/28.49 = { by axiom 4 (xhn) }
% 220.56/28.49 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 true
% 220.56/28.49
% 220.56/28.49 Lemma 11: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X))), true, Z) = is_a_theorem(Z).
% 220.56/28.49 Proof:
% 220.56/28.49 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X))), true, Z)
% 220.56/28.49 = { by axiom 3 (condensed_detachment) R->L }
% 220.56/28.49 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z)), true, equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z)
% 220.56/28.49 = { by lemma 10 }
% 220.56/28.49 fresh(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), X)), Z)
% 220.56/28.49 = { by axiom 2 (condensed_detachment) }
% 220.56/28.49 is_a_theorem(Z)
% 220.56/28.49
% 220.56/28.49 Lemma 12: fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z)), true, equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U))))) = is_a_theorem(equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U))))).
% 220.56/28.49 Proof:
% 220.56/28.49 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z)), true, equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))
% 220.56/28.49 = { by axiom 3 (condensed_detachment) R->L }
% 220.56/28.49 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))
% 220.56/28.49 = { by lemma 11 R->L }
% 220.56/28.49 fresh(fresh2(is_a_theorem(equivalent(equivalent(W, equivalent(equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z)), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U))))), equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))))), W))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))
% 220.56/28.49 = { by lemma 9 }
% 220.56/28.49 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), W), Z), equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))
% 220.56/28.49 = { by axiom 2 (condensed_detachment) }
% 220.56/28.49 is_a_theorem(equivalent(W, equivalent(V, equivalent(equivalent(U, T), equivalent(equivalent(T, V), U)))))
% 220.56/28.49
% 220.56/28.49 Lemma 13: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), equivalent(Z, X)), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))) = true.
% 220.56/28.49 Proof:
% 220.56/28.49 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), equivalent(Z, X)), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))))
% 220.56/28.49 = { by lemma 12 R->L }
% 220.56/28.49 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), equivalent(Z, X))), Y)), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), equivalent(Z, X)), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))))
% 220.56/28.49 = { by lemma 10 }
% 220.56/28.49 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), equivalent(Z, X)), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S)))))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 true
% 220.56/28.49
% 220.56/28.49 Lemma 14: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W)) = true.
% 220.56/28.49 Proof:
% 220.56/28.49 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W))
% 220.56/28.49 = { by lemma 11 R->L }
% 220.56/28.49 fresh2(is_a_theorem(equivalent(equivalent(V, U), equivalent(equivalent(U, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), V))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W))
% 220.56/28.49 = { by lemma 5 R->L }
% 220.56/28.49 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), true, equivalent(equivalent(V, U), equivalent(equivalent(U, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), V))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W))
% 220.56/28.49 = { by lemma 12 R->L }
% 220.56/28.49 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), equivalent(equivalent(Z, W), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X))))), equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), equivalent(equivalent(Z, W), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)))), equivalent(W, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), equivalent(equivalent(Z, W), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X))))))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W)), equivalent(equivalent(Z, W), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), true, equivalent(equivalent(V, U), equivalent(equivalent(U, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), V))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W))
% 220.56/28.49 = { by lemma 13 }
% 220.56/28.49 fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), true, equivalent(equivalent(V, U), equivalent(equivalent(U, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), V))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 fresh2(fresh2(true, true, equivalent(equivalent(V, U), equivalent(equivalent(U, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W), equivalent(T, equivalent(equivalent(S, X2), equivalent(equivalent(X2, T), S))))), V))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, W)), X)), Z), W))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 true
% 220.56/28.49
% 220.56/28.49 Lemma 15: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U))) = true.
% 220.56/28.49 Proof:
% 220.56/28.49 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)))
% 220.56/28.49 = { by lemma 11 R->L }
% 220.56/28.49 fresh2(is_a_theorem(equivalent(equivalent(U, equivalent(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)), equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))))), U))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)))
% 220.56/28.49 = { by lemma 7 R->L }
% 220.56/28.49 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)), equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))))), U), U)), true, equivalent(equivalent(U, equivalent(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)), equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))))), U))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)))
% 220.56/28.49 = { by lemma 14 }
% 220.56/28.49 fresh2(fresh2(true, true, equivalent(equivalent(U, equivalent(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)))), equivalent(equivalent(equivalent(equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)), equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W))))), U))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, equivalent(equivalent(W, V), equivalent(equivalent(V, Z), W)))), X)), equivalent(U, U)))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 true
% 220.56/28.49
% 220.56/28.49 Lemma 16: is_a_theorem(equivalent(X, X)) = true.
% 220.56/28.49 Proof:
% 220.56/28.49 is_a_theorem(equivalent(X, X))
% 220.56/28.49 = { by axiom 2 (condensed_detachment) R->L }
% 220.56/28.49 fresh(true, true, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Y)), equivalent(X, X))
% 220.56/28.49 = { by lemma 15 R->L }
% 220.56/28.49 fresh(is_a_theorem(equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Y)), equivalent(X, X))), true, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Y)), equivalent(X, X))
% 220.56/28.49 = { by axiom 3 (condensed_detachment) }
% 220.56/28.49 fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(equivalent(Z, equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Y))), true, equivalent(X, X))
% 220.56/28.49 = { by lemma 6 }
% 220.56/28.49 fresh2(true, true, equivalent(X, X))
% 220.56/28.49 = { by axiom 1 (condensed_detachment) }
% 220.56/28.49 true
% 220.56/28.49
% 220.56/28.49 Lemma 17: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), true, Z) = is_a_theorem(Z).
% 220.56/28.49 Proof:
% 220.56/28.49 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V))))), true, Z)
% 220.56/28.49 = { by axiom 3 (condensed_detachment) R->L }
% 220.56/28.49 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Z)), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Z)
% 220.56/28.49 = { by lemma 8 }
% 220.56/28.49 fresh(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), equivalent(W, equivalent(equivalent(V, U), equivalent(equivalent(U, W), V)))), Z)
% 220.56/28.49 = { by axiom 2 (condensed_detachment) }
% 220.56/28.50 is_a_theorem(Z)
% 220.56/28.50
% 220.56/28.50 Lemma 18: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X))) = true.
% 220.56/28.50 Proof:
% 220.56/28.50 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))
% 220.56/28.50 = { by axiom 2 (condensed_detachment) R->L }
% 220.56/28.50 fresh(true, true, equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(equivalent(Z, Z), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))), W)), equivalent(Z, Z)), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))
% 220.56/28.50 = { by lemma 14 R->L }
% 220.56/28.50 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(equivalent(Z, Z), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))), W)), equivalent(Z, Z)), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))), true, equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(equivalent(Z, Z), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))), W)), equivalent(Z, Z)), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))
% 220.56/28.50 = { by axiom 3 (condensed_detachment) }
% 220.56/28.50 fresh2(is_a_theorem(equivalent(equivalent(equivalent(W, V), equivalent(equivalent(V, equivalent(equivalent(Z, Z), equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))), W)), equivalent(Z, Z))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))
% 220.56/28.50 = { by lemma 15 }
% 220.56/28.50 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X)))
% 220.56/28.50 = { by axiom 1 (condensed_detachment) }
% 220.56/28.50 true
% 220.56/28.50
% 220.56/28.50 Lemma 19: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Y, equivalent(Z, Z)), X)) = is_a_theorem(equivalent(equivalent(Y, equivalent(Z, Z)), X)).
% 220.56/28.50 Proof:
% 220.56/28.50 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(Y, equivalent(Z, Z)), X))
% 220.56/28.50 = { by axiom 3 (condensed_detachment) R->L }
% 220.56/28.50 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X))), true, equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X))
% 220.56/28.50 = { by lemma 18 }
% 220.56/28.50 fresh(true, true, equivalent(X, Y), equivalent(equivalent(Y, equivalent(Z, Z)), X))
% 220.56/28.50 = { by axiom 2 (condensed_detachment) }
% 220.56/28.50 is_a_theorem(equivalent(equivalent(Y, equivalent(Z, Z)), X))
% 220.56/28.50
% 220.56/28.50 Lemma 20: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Y))), true, X) = is_a_theorem(X).
% 220.56/28.50 Proof:
% 220.56/28.50 fresh2(is_a_theorem(equivalent(X, equivalent(Y, Y))), true, X)
% 220.56/28.50 = { by axiom 3 (condensed_detachment) R->L }
% 220.56/28.50 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), X)), true, equivalent(X, equivalent(Y, Y)), X)
% 220.56/28.50 = { by lemma 19 R->L }
% 220.56/28.50 fresh(fresh2(is_a_theorem(equivalent(X, X)), true, equivalent(equivalent(X, equivalent(Y, Y)), X)), true, equivalent(X, equivalent(Y, Y)), X)
% 220.56/28.50 = { by lemma 16 }
% 220.56/28.50 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Y)), X)), true, equivalent(X, equivalent(Y, Y)), X)
% 220.56/28.50 = { by axiom 1 (condensed_detachment) }
% 220.56/28.50 fresh(true, true, equivalent(X, equivalent(Y, Y)), X)
% 220.56/28.50 = { by axiom 2 (condensed_detachment) }
% 220.56/28.50 is_a_theorem(X)
% 220.56/28.50
% 220.56/28.50 Lemma 21: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))) = true.
% 220.56/28.50 Proof:
% 220.56/28.50 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))
% 220.56/28.50 = { by lemma 17 R->L }
% 220.56/28.50 fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))
% 220.56/28.50 = { by axiom 2 (condensed_detachment) R->L }
% 220.56/28.50 fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)))), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y), equivalent(equivalent(Y, equivalent(W, W)), equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))
% 220.56/28.50 = { by axiom 1 (condensed_detachment) R->L }
% 220.56/28.50 fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)))), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y), equivalent(equivalent(Y, equivalent(W, W)), equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)))))), true, equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)))), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y), equivalent(equivalent(Y, equivalent(W, W)), equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))
% 220.56/28.51 = { by axiom 1 (condensed_detachment) R->L }
% 220.56/28.51 fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)))), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y), equivalent(equivalent(Y, equivalent(W, W)), equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z))), equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y)), equivalent(Y, equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)))), equivalent(equivalent(equivalent(equivalent(equivalent(Z, X), equivalent(equivalent(X, Y), Z)), equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X))), Y), equivalent(equivalent(Y, equivalent(W, W)), equivalent(equivalent(equivalent(Z, X), 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% 221.16/28.55 = { by axiom 1 (condensed_detachment) }
% 221.16/28.55 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(Y, equivalent(W, W))), equivalent(Z, X)))
% 221.16/28.55 = { by axiom 1 (condensed_detachment) }
% 221.16/28.55 true
% 221.16/28.55
% 221.16/28.55 Lemma 22: is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)) = true.
% 221.16/28.55 Proof:
% 221.16/28.55 is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y))
% 221.16/28.55 = { by lemma 17 R->L }
% 221.16/28.55 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y, X), equivalent(equivalent(X, equivalent(Y, X)), Y)), equivalent(equivalent(Y, X), equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, X)), equivalent(equivalent(equivalent(Y, X), equivalent(equivalent(X, equivalent(Y, X)), Y)), equivalent(equivalent(equivalent(Y, X), equivalent(equivalent(X, equivalent(Y, X)), Y)), equivalent(equivalent(Y, X), equivalent(equivalent(X, equivalent(Y, X)), Y))))), equivalent(equivalent(Y, X), equivalent(equivalent(Y, X), equivalent(equivalent(X, equivalent(Y, X)), Y))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y))
% 221.16/28.55 = { by lemma 21 }
% 221.16/28.55 fresh2(true, true, equivalent(equivalent(X, equivalent(Y, X)), Y))
% 221.16/28.55 = { by axiom 1 (condensed_detachment) }
% 221.16/28.55 true
% 221.16/28.55
% 221.16/28.55 Lemma 23: fresh2(is_a_theorem(equivalent(X, equivalent(Y, X))), true, Y) = is_a_theorem(Y).
% 221.16/28.55 Proof:
% 221.16/28.55 fresh2(is_a_theorem(equivalent(X, equivalent(Y, X))), true, Y)
% 221.16/28.55 = { by axiom 3 (condensed_detachment) R->L }
% 221.16/28.55 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 221.16/28.55 = { by lemma 22 }
% 221.16/28.55 fresh(true, true, equivalent(X, equivalent(Y, X)), Y)
% 221.16/28.55 = { by axiom 2 (condensed_detachment) }
% 221.16/28.56 is_a_theorem(Y)
% 221.16/28.56
% 221.16/28.56 Lemma 24: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), Z)) = true.
% 221.16/28.56 Proof:
% 221.16/28.56 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), Z))
% 221.16/28.56 = { by lemma 23 R->L }
% 221.16/28.56 fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), Z), equivalent(equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), Z))
% 221.16/28.56 = { by axiom 2 (condensed_detachment) R->L }
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% 221.33/28.57 = { by axiom 1 (condensed_detachment) R->L }
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% 221.33/28.58 = { by axiom 4 (xhn) R->L }
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% 221.33/28.60 = { by axiom 3 (condensed_detachment) R->L }
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% 222.45/28.73 = { by axiom 1 (condensed_detachment) }
% 222.45/28.73 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), Z), equivalent(equivalent(Z, equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X))), equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), Z))
% 222.45/28.73 = { by axiom 1 (condensed_detachment) }
% 222.45/28.73 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, Z), X)), Z))
% 222.45/28.73 = { by axiom 1 (condensed_detachment) }
% 222.45/28.73 true
% 222.45/28.73
% 222.45/28.73 Goal 1 (prove_um): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))) = true.
% 222.45/28.73 Proof:
% 222.45/28.73 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.73 = { by axiom 2 (condensed_detachment) R->L }
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% 222.45/28.73 = { by axiom 1 (condensed_detachment) R->L }
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% 222.45/28.73 = { by axiom 1 (condensed_detachment) R->L }
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% 222.45/28.73 = { by axiom 1 (condensed_detachment) R->L }
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% 222.45/28.74 = { by lemma 24 R->L }
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% 222.45/28.74 = { by axiom 3 (condensed_detachment) R->L }
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% 222.45/28.74 = { by lemma 23 R->L }
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% 222.45/28.75 = { by axiom 2 (condensed_detachment) R->L }
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% 222.45/28.76 = { by lemma 18 R->L }
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% 222.45/28.77 = { by lemma 19 }
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% 222.45/28.77 = { by axiom 3 (condensed_detachment) }
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% 222.45/28.77 = { by lemma 14 }
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% 222.45/28.78 = { by axiom 1 (condensed_detachment) }
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% 222.45/28.78 = { by axiom 1 (condensed_detachment) }
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% 222.45/28.78 = { by axiom 2 (condensed_detachment) }
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% 222.45/28.78 = { by axiom 3 (condensed_detachment) R->L }
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% 222.45/28.78 = { by lemma 19 R->L }
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% 222.45/28.79 = { by lemma 22 }
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% 222.45/28.79 = { by axiom 1 (condensed_detachment) }
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% 222.45/28.79 = { by axiom 2 (condensed_detachment) }
% 222.45/28.79 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by axiom 3 (condensed_detachment) R->L }
% 222.45/28.79 fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by lemma 21 }
% 222.45/28.79 fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by axiom 2 (condensed_detachment) }
% 222.45/28.79 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true, equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by axiom 3 (condensed_detachment) }
% 222.45/28.79 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by lemma 5 R->L }
% 222.45/28.79 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), true, equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by lemma 24 }
% 222.45/28.79 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), c)), b)), equivalent(equivalent(a, b), c)))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by axiom 1 (condensed_detachment) }
% 222.45/28.79 fresh2(true, true, equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 222.45/28.79 = { by axiom 1 (condensed_detachment) }
% 222.45/28.79 true
% 222.45/28.79 % SZS output end Proof
% 222.45/28.79
% 222.45/28.79 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------