TSTP Solution File: LCL014-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL014-1 : 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 : n020.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 08:17:02 EDT 2023
% Result : Unsatisfiable 35.47s 5.11s
% Output : Proof 36.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17 % Problem : LCL014-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.18 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.39 % Computer : n020.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Thu Aug 24 20:01:45 EDT 2023
% 0.18/0.39 % CPUTime :
% 35.47/5.11 Command-line arguments: --no-flatten-goal
% 35.47/5.11
% 35.47/5.11 % SZS status Unsatisfiable
% 35.47/5.11
% 35.47/5.17 % SZS output start Proof
% 35.47/5.17 Take the following subset of the input axioms:
% 35.47/5.17 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 35.47/5.17 fof(prove_xgf, negated_conjecture, ~is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))).
% 35.47/5.17 fof(wn, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, equivalent(Y2, Z)), equivalent(Z, equivalent(X2, Y2))))).
% 35.47/5.17
% 35.47/5.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 35.47/5.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 35.47/5.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 35.47/5.17 fresh(y, y, x1...xn) = u
% 35.47/5.17 C => fresh(s, t, x1...xn) = v
% 35.47/5.17 where fresh is a fresh function symbol and x1..xn are the free
% 35.47/5.17 variables of u and v.
% 35.47/5.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 35.47/5.17 input problem has no model of domain size 1).
% 35.47/5.17
% 35.47/5.17 The encoding turns the above axioms into the following unit equations and goals:
% 35.47/5.17
% 35.47/5.17 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 35.47/5.17 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 35.47/5.17 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 35.47/5.17 Axiom 4 (wn): is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(X, Y)))) = true.
% 35.47/5.17
% 35.47/5.17 Lemma 5: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(Z, equivalent(X, Y))) = is_a_theorem(equivalent(Z, equivalent(X, Y))).
% 35.47/5.17 Proof:
% 35.47/5.17 fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(Z, equivalent(X, Y)))
% 35.47/5.17 = { by axiom 3 (condensed_detachment) R->L }
% 35.47/5.17 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(X, Y)))), true, equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(X, Y)))
% 35.47/5.17 = { by axiom 4 (wn) }
% 35.47/5.17 fresh(true, true, equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(X, Y)))
% 35.47/5.17 = { by axiom 2 (condensed_detachment) }
% 35.47/5.17 is_a_theorem(equivalent(Z, equivalent(X, Y)))
% 35.47/5.17
% 35.47/5.17 Lemma 6: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(Y, Z)), Z))) = true.
% 35.47/5.17 Proof:
% 35.47/5.17 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(Y, Z)), Z)))
% 35.47/5.17 = { by lemma 5 R->L }
% 35.47/5.17 fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(Y, Z)), Z)))
% 35.47/5.17 = { by axiom 4 (wn) }
% 35.47/5.17 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(Y, Z)), Z)))
% 35.47/5.17 = { by axiom 1 (condensed_detachment) }
% 35.47/5.17 true
% 35.47/5.17
% 35.47/5.18 Lemma 7: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(X, equivalent(Y, Z)), Z)) = is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), Z)).
% 35.47/5.18 Proof:
% 35.47/5.18 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(X, equivalent(Y, Z)), Z))
% 35.47/5.18 = { by axiom 3 (condensed_detachment) R->L }
% 35.47/5.18 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, equivalent(Y, Z)), Z))), true, equivalent(X, Y), equivalent(equivalent(X, equivalent(Y, Z)), Z))
% 35.47/5.18 = { by lemma 6 }
% 35.47/5.18 fresh(true, true, equivalent(X, Y), equivalent(equivalent(X, equivalent(Y, Z)), Z))
% 35.47/5.18 = { by axiom 2 (condensed_detachment) }
% 35.47/5.18 is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), Z))
% 35.47/5.18
% 35.47/5.18 Lemma 8: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W))), true, W) = is_a_theorem(W).
% 35.47/5.18 Proof:
% 35.47/5.18 fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W))), true, W)
% 35.47/5.18 = { by axiom 3 (condensed_detachment) R->L }
% 35.47/5.18 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)
% 35.47/5.18 = { by lemma 7 R->L }
% 35.47/5.18 fresh(fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)
% 35.47/5.18 = { by lemma 5 R->L }
% 35.47/5.18 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(equivalent(Y, equivalent(Z, X)), X))), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)
% 35.47/5.18 = { by lemma 6 }
% 35.47/5.18 fresh(fresh2(fresh2(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)), true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 fresh(true, true, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(Y, equivalent(Z, X))), W)), W)
% 35.47/5.18 = { by axiom 2 (condensed_detachment) }
% 35.47/5.18 is_a_theorem(W)
% 35.47/5.18
% 35.47/5.18 Lemma 9: is_a_theorem(equivalent(X, equivalent(equivalent(Y, X), Y))) = true.
% 35.47/5.18 Proof:
% 35.47/5.18 is_a_theorem(equivalent(X, equivalent(equivalent(Y, X), Y)))
% 35.47/5.18 = { by lemma 8 R->L }
% 35.47/5.18 fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, X), Y), equivalent(equivalent(equivalent(Y, X), equivalent(Y, equivalent(X, equivalent(equivalent(Y, X), Y)))), equivalent(X, equivalent(equivalent(Y, X), Y))))), true, equivalent(X, equivalent(equivalent(Y, X), Y)))
% 35.47/5.18 = { by lemma 6 }
% 35.47/5.18 fresh2(true, true, equivalent(X, equivalent(equivalent(Y, X), Y)))
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 true
% 35.47/5.18
% 35.47/5.18 Lemma 10: is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))) = true.
% 35.47/5.18 Proof:
% 35.47/5.18 is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y))))
% 35.47/5.18 = { by lemma 5 R->L }
% 35.47/5.18 fresh2(is_a_theorem(equivalent(Y, equivalent(equivalent(X, Y), X))), true, equivalent(X, equivalent(Y, equivalent(X, Y))))
% 35.47/5.18 = { by lemma 9 }
% 35.47/5.18 fresh2(true, true, equivalent(X, equivalent(Y, equivalent(X, Y))))
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 true
% 35.47/5.18
% 35.47/5.18 Lemma 11: is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y))) = true.
% 35.47/5.18 Proof:
% 35.47/5.18 is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Y)))
% 35.47/5.18 = { by lemma 5 R->L }
% 35.47/5.18 fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(X, Y)))
% 35.47/5.18 = { by lemma 10 }
% 35.47/5.18 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(X, Y)))
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 true
% 35.47/5.18
% 35.47/5.18 Lemma 12: is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, X), Y), Z)), Z)) = true.
% 35.47/5.18 Proof:
% 35.47/5.18 is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, X), Y), Z)), Z))
% 35.47/5.18 = { by lemma 7 R->L }
% 35.47/5.18 fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, X), Y))), true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, X), Y), Z)), Z))
% 35.47/5.18 = { by lemma 9 }
% 35.47/5.18 fresh2(true, true, equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, X), Y), Z)), Z))
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 true
% 35.47/5.18
% 35.47/5.18 Lemma 13: fresh2(is_a_theorem(X), true, equivalent(Y, equivalent(X, Y))) = is_a_theorem(equivalent(Y, equivalent(X, Y))).
% 35.47/5.18 Proof:
% 35.47/5.18 fresh2(is_a_theorem(X), true, equivalent(Y, equivalent(X, Y)))
% 35.47/5.18 = { by axiom 3 (condensed_detachment) R->L }
% 35.47/5.18 fresh(is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))), true, X, equivalent(Y, equivalent(X, Y)))
% 35.47/5.18 = { by lemma 10 }
% 35.47/5.18 fresh(true, true, X, equivalent(Y, equivalent(X, Y)))
% 35.47/5.18 = { by axiom 2 (condensed_detachment) }
% 35.47/5.18 is_a_theorem(equivalent(Y, equivalent(X, Y)))
% 35.47/5.18
% 35.47/5.18 Lemma 14: is_a_theorem(equivalent(equivalent(equivalent(X, Y), X), Y)) = true.
% 35.47/5.18 Proof:
% 35.47/5.18 is_a_theorem(equivalent(equivalent(equivalent(X, Y), X), Y))
% 35.47/5.18 = { by axiom 2 (condensed_detachment) R->L }
% 35.47/5.18 fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), X), Y), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(X, Y), X), Y)), Y), equivalent(equivalent(equivalent(X, Y), X), Y))), equivalent(equivalent(equivalent(X, Y), X), Y))
% 35.47/5.18 = { by lemma 12 R->L }
% 35.47/5.18 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), X), Y), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(X, Y), X), Y)), Y), equivalent(equivalent(equivalent(X, Y), X), Y))), equivalent(equivalent(equivalent(X, Y), X), Y))), true, equivalent(equivalent(equivalent(equivalent(X, Y), X), Y), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(X, Y), X), Y)), Y), equivalent(equivalent(equivalent(X, Y), X), Y))), equivalent(equivalent(equivalent(X, Y), X), Y))
% 35.47/5.18 = { by axiom 3 (condensed_detachment) }
% 35.47/5.18 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), X), Y), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(X, Y), X), Y)), Y), equivalent(equivalent(equivalent(X, Y), X), Y)))), true, equivalent(equivalent(equivalent(X, Y), X), Y))
% 35.47/5.18 = { by lemma 13 R->L }
% 35.47/5.18 fresh2(fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(equivalent(equivalent(X, Y), X), Y)), Y)), true, equivalent(equivalent(equivalent(equivalent(X, Y), X), Y), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(X, Y), X), Y)), Y), equivalent(equivalent(equivalent(X, Y), X), Y)))), true, equivalent(equivalent(equivalent(X, Y), X), Y))
% 35.47/5.18 = { by lemma 12 }
% 35.47/5.18 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), X), Y), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(X, Y), X), Y)), Y), equivalent(equivalent(equivalent(X, Y), X), Y)))), true, equivalent(equivalent(equivalent(X, Y), X), Y))
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), X), Y))
% 35.47/5.18 = { by axiom 1 (condensed_detachment) }
% 35.47/5.18 true
% 35.47/5.18
% 35.47/5.18 Lemma 15: fresh2(is_a_theorem(equivalent(equivalent(X, Y), X)), true, Y) = is_a_theorem(Y).
% 35.47/5.18 Proof:
% 35.47/5.18 fresh2(is_a_theorem(equivalent(equivalent(X, Y), X)), true, Y)
% 35.47/5.18 = { by axiom 3 (condensed_detachment) R->L }
% 35.47/5.18 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), X), Y)), true, equivalent(equivalent(X, Y), X), Y)
% 35.47/5.18 = { by lemma 14 }
% 35.47/5.18 fresh(true, true, equivalent(equivalent(X, Y), X), Y)
% 35.47/5.18 = { by axiom 2 (condensed_detachment) }
% 35.47/5.18 is_a_theorem(Y)
% 35.47/5.18
% 35.47/5.18 Lemma 16: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Y, X)) = is_a_theorem(equivalent(Y, X)).
% 35.47/5.18 Proof:
% 35.47/5.18 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Y, X))
% 35.47/5.18 = { by axiom 3 (condensed_detachment) R->L }
% 35.47/5.18 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.18 = { by lemma 5 R->L }
% 35.47/5.18 fresh(fresh2(is_a_theorem(equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.18 = { by lemma 15 R->L }
% 35.47/5.18 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.18 = { by lemma 7 R->L }
% 35.47/5.18 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.18 = { by lemma 7 R->L }
% 35.47/5.18 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 2 (condensed_detachment) R->L }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) R->L }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X))), true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) R->L }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, equivalent(X, equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, W))))), true, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X))), true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) R->L }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), X))), true, equivalent(X, equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, W))))), true, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X))), true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by lemma 11 R->L }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(Z, W), equivalent(Z, W))), true, equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), X))), true, equivalent(X, equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, W))))), true, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X))), true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by lemma 13 }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), X))), true, equivalent(X, equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, W))))), true, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X))), true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by lemma 5 }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, W))))), true, equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X))), true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by lemma 5 }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X))), true, equivalent(equivalent(Z, W), equivalent(Z, W)), equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 3 (condensed_detachment) }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(Z, W), equivalent(Z, W))), true, equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by lemma 11 }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(X, X)), true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(X, equivalent(X, Y)), Y)), true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) }
% 35.47/5.19 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(X, Y)), equivalent(Y, equivalent(X, equivalent(X, Y)))), equivalent(X, equivalent(X, Y)))), true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) }
% 35.47/5.19 fresh(fresh2(fresh2(true, true, equivalent(Y, equivalent(X, equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) }
% 35.47/5.19 fresh(fresh2(true, true, equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) }
% 35.47/5.19 fresh(true, true, equivalent(X, Y), equivalent(Y, X))
% 35.47/5.19 = { by axiom 2 (condensed_detachment) }
% 35.47/5.19 is_a_theorem(equivalent(Y, X))
% 35.47/5.19
% 35.47/5.19 Lemma 17: is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, equivalent(X, Y)), W)), W)) = true.
% 35.47/5.19 Proof:
% 35.47/5.19 is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, equivalent(X, Y)), W)), W))
% 35.47/5.19 = { by lemma 7 R->L }
% 35.47/5.19 fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, equivalent(X, Y)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, equivalent(X, Y)), W)), W))
% 35.47/5.19 = { by axiom 4 (wn) }
% 35.47/5.19 fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(Z, equivalent(X, Y)), W)), W))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) }
% 35.47/5.19 true
% 35.47/5.19
% 35.47/5.19 Goal 1 (prove_xgf): is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))) = true.
% 35.47/5.19 Proof:
% 35.47/5.19 is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.19 = { by lemma 16 R->L }
% 35.47/5.19 fresh2(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.19 = { by axiom 2 (condensed_detachment) R->L }
% 35.47/5.19 fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.19 = { by axiom 1 (condensed_detachment) R->L }
% 35.47/5.20 fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by axiom 1 (condensed_detachment) R->L }
% 35.47/5.20 fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by lemma 6 R->L }
% 35.47/5.20 fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a), equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by lemma 7 }
% 35.47/5.20 fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a), equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by lemma 15 }
% 35.47/5.20 fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c), equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by axiom 3 (condensed_detachment) }
% 35.47/5.20 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by lemma 16 R->L }
% 35.47/5.20 fresh2(fresh2(fresh2(is_a_theorem(equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by axiom 2 (condensed_detachment) R->L }
% 35.47/5.20 fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by axiom 1 (condensed_detachment) R->L }
% 35.47/5.20 fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 35.47/5.20 = { by lemma 17 R->L }
% 36.69/5.20 fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c))))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c))))), true, equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.20 = { by lemma 15 }
% 36.69/5.20 fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.20 = { by axiom 3 (condensed_detachment) }
% 36.69/5.20 fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.20 = { by lemma 8 R->L }
% 36.69/5.21 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.21 = { by lemma 5 R->L }
% 36.69/5.21 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.21 = { by axiom 2 (condensed_detachment) R->L }
% 36.69/5.21 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.21 = { by axiom 1 (condensed_detachment) R->L }
% 36.69/5.21 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.22 = { by lemma 14 R->L }
% 36.69/5.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.22 = { by lemma 7 }
% 36.69/5.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c))))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.22 = { by axiom 3 (condensed_detachment) }
% 36.69/5.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.23 = { by lemma 15 R->L }
% 36.69/5.23 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.23 = { by lemma 7 R->L }
% 36.69/5.23 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.23 = { by lemma 17 }
% 36.69/5.23 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.23 = { by axiom 1 (condensed_detachment) }
% 36.69/5.23 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))))), true, equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.23 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)))), equivalent(a, c)))), true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.24 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, c), equivalent(equivalent(equivalent(c, b), equivalent(c, equivalent(b, equivalent(a, c)))), equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))))), true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.24 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(a, c), equivalent(c, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))), true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.24 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 fresh2(fresh2(fresh2(fresh2(true, true, equivalent(c, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)))), true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.24 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), equivalent(a, c)), c)), true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.24 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b)), a)), true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.24 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 fresh2(true, true, equivalent(a, equivalent(equivalent(b, equivalent(a, c)), equivalent(c, b))))
% 36.69/5.24 = { by axiom 1 (condensed_detachment) }
% 36.69/5.24 true
% 36.69/5.24 % SZS output end Proof
% 36.69/5.24
% 36.69/5.24 RESULT: Unsatisfiable (the axioms are contradictory).
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