TSTP Solution File: LCL091-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL091-1 : 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 : n013.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 08:17:22 EDT 2023
% Result : Unsatisfiable 0.20s 0.75s
% Output : Proof 3.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL091-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 17:34:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.75 Command-line arguments: --no-flatten-goal
% 0.20/0.75
% 0.20/0.75 % SZS status Unsatisfiable
% 0.20/0.75
% 0.20/0.80 % SZS output start Proof
% 0.20/0.80 Take the following subset of the input axioms:
% 0.20/0.80 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(implies(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.80 fof(ic_JLukasiewicz_5, axiom, ![P, Q, R, S, T]: is_a_theorem(implies(implies(implies(P, Q), implies(R, S)), implies(implies(S, P), implies(T, implies(R, P)))))).
% 0.20/0.80 fof(prove_ic_2, negated_conjecture, ~is_a_theorem(implies(a, implies(b, a)))).
% 0.20/0.80
% 0.20/0.80 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.80 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.80 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.80 fresh(y, y, x1...xn) = u
% 0.20/0.80 C => fresh(s, t, x1...xn) = v
% 0.20/0.80 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.80 variables of u and v.
% 0.20/0.80 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.80 input problem has no model of domain size 1).
% 0.20/0.80
% 0.20/0.80 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.80
% 0.20/0.80 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.80 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.80 Axiom 3 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.80 Axiom 4 (ic_JLukasiewicz_5): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))) = true.
% 0.20/0.80
% 0.20/0.80 Lemma 5: fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(implies(W, X), implies(V, implies(Z, X)))) = is_a_theorem(implies(implies(W, X), implies(V, implies(Z, X)))).
% 0.20/0.80 Proof:
% 0.20/0.80 fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(implies(W, X), implies(V, implies(Z, X))))
% 0.20/0.80 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.80 fresh(is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))), true, implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))
% 0.20/0.80 = { by axiom 4 (ic_JLukasiewicz_5) }
% 0.20/0.80 fresh(true, true, implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))
% 0.20/0.80 = { by axiom 2 (condensed_detachment) }
% 0.20/0.80 is_a_theorem(implies(implies(W, X), implies(V, implies(Z, X))))
% 0.20/0.80
% 0.20/0.80 Lemma 6: is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))) = true.
% 0.20/0.80 Proof:
% 0.20/0.80 is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W)))))
% 0.20/0.80 = { by lemma 5 R->L }
% 0.20/0.80 fresh2(is_a_theorem(implies(implies(implies(Z, W), implies(Y, U)), implies(implies(U, Z), implies(X, implies(Y, Z))))), true, implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W)))))
% 0.20/0.80 = { by axiom 4 (ic_JLukasiewicz_5) }
% 0.20/0.80 fresh2(true, true, implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W)))))
% 0.20/0.80 = { by axiom 1 (condensed_detachment) }
% 0.20/0.80 true
% 0.20/0.80
% 0.20/0.80 Lemma 7: fresh2(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Z, W))), true, implies(V, implies(implies(U, Z), implies(Z, W)))) = is_a_theorem(implies(V, implies(implies(U, Z), implies(Z, W)))).
% 0.20/0.80 Proof:
% 0.20/0.80 fresh2(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Z, W))), true, implies(V, implies(implies(U, Z), implies(Z, W))))
% 0.20/0.80 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.80 fresh(is_a_theorem(implies(implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))), true, implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))
% 0.20/0.80 = { by lemma 6 }
% 0.20/0.80 fresh(true, true, implies(implies(X, implies(Y, Z)), implies(Z, W)), implies(V, implies(implies(U, Z), implies(Z, W))))
% 0.20/0.80 = { by axiom 2 (condensed_detachment) }
% 0.20/0.81 is_a_theorem(implies(V, implies(implies(U, Z), implies(Z, W))))
% 0.20/0.81
% 0.20/0.81 Lemma 8: fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, implies(W, X)))), true, implies(V, implies(U, implies(Z, implies(W, X))))) = is_a_theorem(implies(V, implies(U, implies(Z, implies(W, X))))).
% 0.20/0.81 Proof:
% 0.20/0.81 fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, implies(W, X)))), true, implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.81 fresh(is_a_theorem(implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by lemma 5 R->L }
% 0.20/0.81 fresh(fresh2(is_a_theorem(implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by lemma 5 R->L }
% 0.20/0.81 fresh(fresh2(fresh2(is_a_theorem(implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2))))), true, implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z)))))), true, implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by lemma 7 R->L }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(Z3, implies(W3, V2)), implies(V2, Z)), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z)))))), true, implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by lemma 6 }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z)))))), true, implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 1 (condensed_detachment) }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by axiom 2 (condensed_detachment) }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(W, X), Z), implies(Z, implies(implies(W2, V2), implies(V2, Z))))), true, implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by lemma 5 }
% 0.20/0.81 fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(W2, V2), implies(V2, Z)), implies(W, X)), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.81 = { by lemma 7 }
% 0.20/0.82 fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X)))))), true, implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T)))), implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.82 = { by axiom 3 (condensed_detachment) }
% 0.20/0.82 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(implies(Y2, T), implies(Z2, implies(X2, T))))), true, implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.82 = { by axiom 4 (ic_JLukasiewicz_5) }
% 0.20/0.82 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(Y, X), implies(X, implies(Z, implies(W, X))))), true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.82 = { by axiom 1 (condensed_detachment) }
% 0.20/0.82 fresh(fresh2(fresh2(true, true, implies(implies(implies(Z, implies(W, X)), Y), implies(U, implies(X, Y)))), true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.82 = { by axiom 1 (condensed_detachment) }
% 0.20/0.82 fresh(fresh2(true, true, implies(implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))), true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.82 = { by axiom 1 (condensed_detachment) }
% 0.20/0.82 fresh(true, true, implies(implies(X, Y), implies(Z, implies(W, X))), implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.82 = { by axiom 2 (condensed_detachment) }
% 0.20/0.82 is_a_theorem(implies(V, implies(U, implies(Z, implies(W, X)))))
% 0.20/0.82
% 0.20/0.82 Goal 1 (prove_ic_2): is_a_theorem(implies(a, implies(b, a))) = true.
% 0.20/0.82 Proof:
% 0.20/0.82 is_a_theorem(implies(a, implies(b, a)))
% 0.20/0.82 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.82 fresh(true, true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 0.20/0.82 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.82 fresh(fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 0.20/0.82 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 3.25/0.82 fresh(fresh2(is_a_theorem(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U))))), true, implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.82 = { by axiom 3 (condensed_detachment) R->L }
% 3.25/0.82 fresh(fresh(is_a_theorem(implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.82 = { by lemma 8 R->L }
% 3.25/0.82 fresh(fresh(fresh2(is_a_theorem(implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.82 = { by axiom 2 (condensed_detachment) R->L }
% 3.25/0.82 fresh(fresh(fresh2(fresh(true, true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.82 = { by axiom 1 (condensed_detachment) R->L }
% 3.25/0.82 fresh(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.82 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 3.25/0.82 fresh(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2))))), true, implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.83 = { by axiom 3 (condensed_detachment) R->L }
% 3.25/0.83 fresh(fresh(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.83 = { by axiom 2 (condensed_detachment) R->L }
% 3.25/0.83 fresh(fresh(fresh2(fresh(fresh(fresh(true, true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.83 = { by axiom 1 (condensed_detachment) R->L }
% 3.25/0.83 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.83 = { by axiom 1 (condensed_detachment) R->L }
% 3.25/0.83 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.83 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 3.25/0.83 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4))))), true, implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.84 = { by axiom 3 (condensed_detachment) R->L }
% 3.25/0.84 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.84 = { by axiom 2 (condensed_detachment) R->L }
% 3.25/0.84 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(fresh(true, true, implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.84 = { by axiom 1 (condensed_detachment) R->L }
% 3.25/0.84 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))))), true, implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.85 = { by axiom 4 (ic_JLukasiewicz_5) R->L }
% 3.25/0.85 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))))), true, implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.85 = { by lemma 8 }
% 3.25/0.85 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(fresh(is_a_theorem(implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))))), true, implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.85 = { by axiom 3 (condensed_detachment) }
% 3.25/0.85 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(implies(Y5, T4), implies(Z5, implies(X5, T4))))), true, implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.85 = { by axiom 4 (ic_JLukasiewicz_5) }
% 3.25/0.86 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 1 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(fresh(true, true, implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 2 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(fresh2(fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by lemma 8 }
% 3.25/0.86 fresh(fresh(fresh2(fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))))), true, implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3)))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 3 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(fresh2(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(implies(S3, V3), implies(X4, implies(T3, V3))))), true, implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 4 (ic_JLukasiewicz_5) }
% 3.25/0.86 fresh(fresh(fresh2(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))))), true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 1 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(fresh2(fresh(fresh(true, true, implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(implies(Z3, S2), implies(W3, implies(Y3, S2)))), implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 2 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2)))), implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 3 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(implies(U2, Z2), implies(T2, implies(V2, Z2))))), true, implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 4 (ic_JLukasiewicz_5) }
% 3.25/0.86 fresh(fresh(fresh2(fresh2(true, true, implies(implies(a, implies(b, a)), implies(a, implies(b, a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 1 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 1 (condensed_detachment) }
% 3.25/0.86 fresh(fresh(true, true, implies(implies(implies(U, T), implies(S, X2)), implies(implies(X2, U), implies(Y2, implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 2 (condensed_detachment) }
% 3.25/0.86 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 3 (condensed_detachment) }
% 3.25/0.86 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))), true, implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 4 (ic_JLukasiewicz_5) }
% 3.25/0.86 fresh2(true, true, implies(a, implies(b, a)))
% 3.25/0.86 = { by axiom 1 (condensed_detachment) }
% 3.25/0.86 true
% 3.25/0.86 % SZS output end Proof
% 3.25/0.86
% 3.25/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
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