TSTP Solution File: LCL101-1 by Twee---2.4.2
View Problem
- Process Solution
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% File : Twee---2.4.2
% Problem : LCL101-1 : 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 : n014.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 08:17:25 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL101-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 18:45:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.41 Command-line arguments: --no-flatten-goal
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 Take the following subset of the input axioms:
% 0.20/0.46 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.46 fof(lg_2, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X2, Y2), equivalent(X2, Z)), equivalent(Y2, Z)), U), U))).
% 0.20/0.46 fof(p_4, axiom, ![X2, Y2, Z2, U2]: is_a_theorem(equivalent(X2, equivalent(equivalent(equivalent(equivalent(Y2, Z2), equivalent(Y2, U2)), equivalent(Z2, U2)), X2)))).
% 0.20/0.46 fof(prove_p_1, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))).
% 0.20/0.46
% 0.20/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.46 fresh(y, y, x1...xn) = u
% 0.20/0.46 C => fresh(s, t, x1...xn) = v
% 0.20/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.46 variables of u and v.
% 0.20/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.46 input problem has no model of domain size 1).
% 0.20/0.46
% 0.20/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.46
% 0.20/0.46 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.46 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.46 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.46 Axiom 4 (p_4): is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, W)), equivalent(Z, W)), X))) = true.
% 0.20/0.46 Axiom 5 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 0.20/0.46
% 0.20/0.46 Lemma 6: fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, W) = is_a_theorem(W).
% 0.20/0.46 Proof:
% 0.20/0.46 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W)), true, W)
% 0.20/0.46 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.46 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)
% 0.20/0.46 = { by axiom 5 (lg_2) }
% 0.20/0.46 fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)
% 0.20/0.46 = { by axiom 2 (condensed_detachment) }
% 0.20/0.46 is_a_theorem(W)
% 0.20/0.46
% 0.20/0.46 Lemma 7: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), equivalent(V, U)))) = true.
% 0.20/0.46 Proof:
% 0.20/0.46 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), equivalent(V, U))))
% 0.20/0.46 = { by lemma 6 R->L }
% 0.20/0.46 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(W, U)), equivalent(V, U)), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), equivalent(V, U))))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), equivalent(V, U))))
% 0.20/0.46 = { by axiom 4 (p_4) }
% 0.20/0.46 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(W, V), equivalent(W, U)), equivalent(V, U))))
% 0.20/0.46 = { by axiom 1 (condensed_detachment) }
% 0.20/0.47 true
% 0.20/0.47
% 0.20/0.47 Lemma 8: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z)) = is_a_theorem(equivalent(Y, Z)).
% 0.20/0.47 Proof:
% 0.20/0.47 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(X, Z))), true, equivalent(Y, Z))
% 0.20/0.47 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.47 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 0.20/0.47 = { by lemma 6 R->L }
% 0.20/0.47 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, V), equivalent(W, U)), equivalent(V, U)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 0.20/0.47 = { by lemma 7 }
% 0.20/0.47 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))), true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 0.20/0.47 = { by axiom 1 (condensed_detachment) }
% 0.20/0.47 fresh(true, true, equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))
% 0.20/0.47 = { by axiom 2 (condensed_detachment) }
% 0.20/0.47 is_a_theorem(equivalent(Y, Z))
% 0.20/0.47
% 0.20/0.47 Lemma 9: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))) = true.
% 0.20/0.47 Proof:
% 0.20/0.47 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.47 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.47 fresh(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.47 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.47 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.47 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.47 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.48 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.48 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.48 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.48 fresh(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.49 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.49 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.49 = { by lemma 7 R->L }
% 0.20/0.50 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(U, V), equivalent(U, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), equivalent(equivalent(equivalent(U, V), equivalent(U, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))))), true, equivalent(equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.50 = { by lemma 8 }
% 0.20/0.50 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), equivalent(V, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.50 = { by lemma 8 }
% 0.20/0.50 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.50 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.51 fresh(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), 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Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), 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% 0.20/0.51 = { by axiom 4 (p_4) }
% 0.20/0.51 fresh(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.51 = { by axiom 2 (condensed_detachment) }
% 0.20/0.51 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.51 = { by lemma 8 }
% 0.20/0.51 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)), equivalent(equivalent(Y, Z), W)), equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.51 = { by lemma 6 }
% 0.20/0.51 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W))), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.51 = { by axiom 3 (condensed_detachment) }
% 0.20/0.51 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W)))), true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.51 = { by axiom 4 (p_4) }
% 0.20/0.51 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)))
% 0.20/0.51 = { by axiom 1 (condensed_detachment) }
% 0.20/0.51 true
% 0.20/0.51
% 0.20/0.51 Goal 1 (prove_p_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) = true.
% 0.20/0.51 Proof:
% 0.20/0.51 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.20/0.51 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.51 fresh(true, true, equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.20/0.51 = { by lemma 9 R->L }
% 0.20/0.51 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.20/0.51 = { by axiom 3 (condensed_detachment) }
% 0.20/0.51 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.20/0.51 = { by lemma 9 }
% 0.20/0.51 fresh2(true, true, equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 0.20/0.51 = { by axiom 1 (condensed_detachment) }
% 0.20/0.51 true
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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