TSTP Solution File: LCL107-1 by Twee---2.4.2
View Problem
- Process Solution
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% File : Twee---2.4.2
% Problem : LCL107-1 : 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 : n023.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 08:17:27 EDT 2023
% Result : Unsatisfiable 0.16s 0.37s
% Output : Proof 6.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL107-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31 % Computer : n023.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Aug 25 02:36:42 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.37 Command-line arguments: --no-flatten-goal
% 0.16/0.37
% 0.16/0.37 % SZS status Unsatisfiable
% 0.16/0.37
% 2.40/0.71 % SZS output start Proof
% 2.40/0.71 Take the following subset of the input axioms:
% 2.40/0.71 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 2.40/0.71 fof(lg_27_1690, axiom, ![Z, U, V, W, V6, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2, Y2), Z), equivalent(equivalent(U, V), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), V6))), equivalent(Z, equivalent(equivalent(Y2, X2), V6))))).
% 2.40/0.71 fof(prove_p_1, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))).
% 2.40/0.71
% 2.40/0.71 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.40/0.71 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.40/0.71 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.40/0.71 fresh(y, y, x1...xn) = u
% 2.40/0.71 C => fresh(s, t, x1...xn) = v
% 2.40/0.71 where fresh is a fresh function symbol and x1..xn are the free
% 2.40/0.71 variables of u and v.
% 2.40/0.71 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.40/0.71 input problem has no model of domain size 1).
% 2.40/0.71
% 2.40/0.71 The encoding turns the above axioms into the following unit equations and goals:
% 2.40/0.71
% 2.40/0.71 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 2.40/0.71 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 2.40/0.71 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 2.40/0.71 Axiom 4 (lg_27_1690): is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, V), equivalent(equivalent(equivalent(U, V), equivalent(U, W)), T))), equivalent(Z, equivalent(equivalent(Y, X), T)))) = true.
% 2.40/0.71
% 2.40/0.71 Lemma 5: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, V), equivalent(equivalent(equivalent(U, V), equivalent(U, W)), T)))), true, equivalent(Z, equivalent(equivalent(Y, X), T))) = is_a_theorem(equivalent(Z, equivalent(equivalent(Y, X), T))).
% 2.40/0.71 Proof:
% 2.40/0.71 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, V), equivalent(equivalent(equivalent(U, V), equivalent(U, W)), T)))), true, equivalent(Z, equivalent(equivalent(Y, X), T)))
% 2.40/0.71 = { by axiom 3 (condensed_detachment) R->L }
% 2.40/0.71 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, V), equivalent(equivalent(equivalent(U, V), equivalent(U, W)), T))), equivalent(Z, equivalent(equivalent(Y, X), T)))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, V), equivalent(equivalent(equivalent(U, V), equivalent(U, W)), T))), equivalent(Z, equivalent(equivalent(Y, X), T)))
% 2.40/0.71 = { by axiom 4 (lg_27_1690) }
% 2.40/0.71 fresh(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, V), equivalent(equivalent(equivalent(U, V), equivalent(U, W)), T))), equivalent(Z, equivalent(equivalent(Y, X), T)))
% 2.40/0.71 = { by axiom 2 (condensed_detachment) }
% 2.40/0.71 is_a_theorem(equivalent(Z, equivalent(equivalent(Y, X), T)))
% 2.40/0.71
% 2.40/0.71 Lemma 6: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, X)), W)), equivalent(equivalent(equivalent(V, U), equivalent(equivalent(T, V), equivalent(T, U))), W))) = true.
% 2.40/0.71 Proof:
% 2.40/0.71 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, X)), W)), equivalent(equivalent(equivalent(V, U), equivalent(equivalent(T, V), equivalent(T, U))), W)))
% 2.40/0.71 = { by lemma 5 R->L }
% 2.40/0.72 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(T, V), equivalent(T, U)), equivalent(V, U)), equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, X)), W))), equivalent(equivalent(V, U), equivalent(equivalent(equivalent(T, U), equivalent(T, V)), W)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, X)), W)), equivalent(equivalent(equivalent(V, U), equivalent(equivalent(T, V), equivalent(T, U))), W)))
% 2.40/0.72 = { by axiom 4 (lg_27_1690) }
% 2.40/0.72 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(equivalent(Z, Y), equivalent(Z, X)), W)), equivalent(equivalent(equivalent(V, U), equivalent(equivalent(T, V), equivalent(T, U))), W)))
% 2.40/0.72 = { by axiom 1 (condensed_detachment) }
% 2.40/0.72 true
% 2.40/0.72
% 3.12/0.72 Lemma 7: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(equivalent(W, equivalent(equivalent(V, U), equivalent(V, T))), equivalent(W, equivalent(U, T))), S)), equivalent(equivalent(Y, Z), S))) = true.
% 3.12/0.72 Proof:
% 3.12/0.72 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(equivalent(W, equivalent(equivalent(V, U), equivalent(V, T))), equivalent(W, equivalent(U, T))), S)), equivalent(equivalent(Y, Z), S)))
% 3.12/0.72 = { by lemma 5 R->L }
% 3.12/0.72 fresh2(is_a_theorem(equivalent(equivalent(equivalent(Z, Y), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(equivalent(W, equivalent(equivalent(V, U), equivalent(V, T))), equivalent(W, equivalent(U, T))), S))), equivalent(equivalent(equivalent(U, T), equivalent(equivalent(V, U), equivalent(V, T))), equivalent(equivalent(equivalent(W, equivalent(equivalent(V, U), equivalent(V, T))), equivalent(W, equivalent(U, T))), S)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(equivalent(W, equivalent(equivalent(V, U), equivalent(V, T))), equivalent(W, equivalent(U, T))), S)), equivalent(equivalent(Y, Z), S)))
% 3.12/0.72 = { by lemma 6 }
% 3.12/0.72 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(equivalent(equivalent(W, equivalent(equivalent(V, U), equivalent(V, T))), equivalent(W, equivalent(U, T))), S)), equivalent(equivalent(Y, Z), S)))
% 3.12/0.72 = { by axiom 1 (condensed_detachment) }
% 3.12/0.72 true
% 3.12/0.72
% 3.12/0.72 Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U)) = true.
% 3.12/0.72 Proof:
% 3.12/0.72 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U))
% 3.12/0.72 = { by axiom 2 (condensed_detachment) R->L }
% 3.12/0.72 fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), U)), equivalent(equivalent(equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V))), equivalent(X, equivalent(W, V))), U)), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U))
% 3.12/0.72 = { by lemma 7 R->L }
% 3.12/0.72 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), U)), equivalent(equivalent(equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V))), equivalent(X, equivalent(W, V))), U)), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), U)), equivalent(equivalent(equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V))), equivalent(X, equivalent(W, V))), U)), equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U))
% 3.12/0.72 = { by axiom 3 (condensed_detachment) }
% 3.12/0.72 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V)))), U)), equivalent(equivalent(equivalent(X, equivalent(equivalent(Z, W), equivalent(Z, V))), equivalent(X, equivalent(W, V))), U))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U))
% 3.12/0.72 = { by lemma 7 }
% 3.12/0.72 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U))
% 3.12/0.72 = { by axiom 1 (condensed_detachment) }
% 3.12/0.72 true
% 3.12/0.72
% 3.12/0.72 Lemma 9: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U)), true, U) = is_a_theorem(U).
% 3.12/0.72 Proof:
% 3.12/0.72 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U)), true, U)
% 3.12/0.72 = { by axiom 3 (condensed_detachment) R->L }
% 3.12/0.72 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U)), true, equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U)
% 3.12/0.72 = { by lemma 8 }
% 3.12/0.72 fresh(true, true, equivalent(equivalent(equivalent(X, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Y, equivalent(Z, V)))), equivalent(X, equivalent(W, V))), U), U)
% 3.12/0.72 = { by axiom 2 (condensed_detachment) }
% 3.12/0.72 is_a_theorem(U)
% 3.12/0.72
% 3.12/0.72 Lemma 10: fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U)))), true, equivalent(equivalent(W, V), U)) = is_a_theorem(equivalent(equivalent(W, V), U)).
% 3.12/0.72 Proof:
% 3.12/0.72 fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U)))), true, equivalent(equivalent(W, V), U))
% 3.12/0.72 = { by axiom 3 (condensed_detachment) R->L }
% 3.12/0.72 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U))), true, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U))
% 3.12/0.72 = { by lemma 9 R->L }
% 3.12/0.72 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(V, W), equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U)))), equivalent(equivalent(V, W), equivalent(equivalent(equivalent(Z, W), equivalent(Z, V)), U))), equivalent(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U))), true, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U))
% 3.12/0.72 = { by axiom 4 (lg_27_1690) }
% 3.12/0.72 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U))), true, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U))
% 3.12/0.72 = { by axiom 1 (condensed_detachment) }
% 3.12/0.72 fresh(true, true, equivalent(equivalent(X, equivalent(Y, equivalent(equivalent(Z, W), equivalent(Z, V)))), equivalent(X, equivalent(Y, U))), equivalent(equivalent(W, V), U))
% 3.12/0.72 = { by axiom 2 (condensed_detachment) }
% 3.12/0.73 is_a_theorem(equivalent(equivalent(W, V), U))
% 3.12/0.73
% 3.12/0.73 Lemma 11: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))) = true.
% 3.12/0.73 Proof:
% 3.12/0.73 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 3.12/0.73 = { by lemma 10 R->L }
% 3.12/0.73 fresh2(is_a_theorem(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 3.12/0.73 = { by axiom 2 (condensed_detachment) R->L }
% 3.12/0.73 fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 3.12/0.75 = { by axiom 1 (condensed_detachment) R->L }
% 3.12/0.75 fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 3.69/0.81 = { by axiom 1 (condensed_detachment) R->L }
% 3.69/0.82 fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), T), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), T), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), T), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), 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equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), T), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), T), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))))))), equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), T), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 6.07/1.15 = { by lemma 10 }
% 6.07/1.15 fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 6.07/1.15 = { by axiom 3 (condensed_detachment) }
% 6.07/1.16 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))))), true, equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 6.07/1.16 = { by lemma 10 R->L }
% 6.07/1.16 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))))), true, equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 6.07/1.16 = { by lemma 6 }
% 6.07/1.16 fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U)), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y))))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), U))), equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))))), true, equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 6.07/1.16 = { by axiom 1 (condensed_detachment) }
% 6.07/1.16 fresh2(fresh2(true, true, equivalent(equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))), equivalent(W, equivalent(V, equivalent(equivalent(Z, X), equivalent(Z, Y)))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 6.07/1.16 = { by axiom 1 (condensed_detachment) }
% 6.07/1.16 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y))))
% 6.07/1.16 = { by axiom 1 (condensed_detachment) }
% 6.07/1.16 true
% 6.07/1.16
% 6.07/1.16 Goal 1 (prove_p_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) = true.
% 6.07/1.16 Proof:
% 6.07/1.16 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 6.07/1.16 = { by lemma 5 R->L }
% 6.07/1.16 fresh2(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 6.07/1.16 = { by axiom 2 (condensed_detachment) R->L }
% 6.07/1.16 fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 6.07/1.16 = { by lemma 11 R->L }
% 6.07/1.17 fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 6.07/1.17 = { by axiom 3 (condensed_detachment) }
% 6.07/1.17 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), true, equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 6.07/1.17 = { by lemma 11 }
% 6.07/1.17 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 6.07/1.17 = { by axiom 1 (condensed_detachment) }
% 6.07/1.17 fresh2(true, true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 6.07/1.17 = { by axiom 1 (condensed_detachment) }
% 6.07/1.17 true
% 6.07/1.17 % SZS output end Proof
% 6.07/1.17
% 6.07/1.17 RESULT: Unsatisfiable (the axioms are contradictory).
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