TSTP Solution File: LCL130-1 by Twee---2.4.2
View Problem
- Process Solution
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% File : Twee---2.4.2
% Problem : LCL130-1 : 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 : n012.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 08:17:35 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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
% 0.00/0.12 % Problem : LCL130-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % 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 : n012.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 : Fri Aug 25 04:27:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Take the following subset of the input axioms:
% 0.20/0.42 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.42 fof(p_4, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, equivalent(equivalent(Y2, Z), equivalent(equivalent(Y2, U), equivalent(Z, U)))), X2))).
% 0.20/0.42 fof(prove_lg_2, negated_conjecture, ~is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))).
% 0.20/0.42
% 0.20/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.42 fresh(y, y, x1...xn) = u
% 0.20/0.43 C => fresh(s, t, x1...xn) = v
% 0.20/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.43 variables of u and v.
% 0.20/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.43 input problem has no model of domain size 1).
% 0.20/0.43
% 0.20/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.43
% 0.20/0.43 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.43 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.43 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.43 Axiom 4 (p_4): is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W)))), X)) = true.
% 0.20/0.43
% 0.20/0.43 Lemma 5: fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), true, X) = is_a_theorem(X).
% 0.20/0.43 Proof:
% 0.20/0.43 fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W))))), true, X)
% 0.20/0.43 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.43 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W)))), X)), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W)))), X)
% 0.20/0.43 = { by axiom 4 (p_4) }
% 0.20/0.43 fresh(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Y, W), equivalent(Z, W)))), X)
% 0.20/0.43 = { by axiom 2 (condensed_detachment) }
% 0.20/0.43 is_a_theorem(X)
% 0.20/0.43
% 0.20/0.43 Lemma 6: is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))), equivalent(equivalent(W, V), equivalent(equivalent(W, U), equivalent(V, U))))) = true.
% 0.20/0.43 Proof:
% 0.20/0.43 is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))), equivalent(equivalent(W, V), equivalent(equivalent(W, U), equivalent(V, U)))))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))), equivalent(equivalent(W, V), equivalent(equivalent(W, U), equivalent(V, U)))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))), true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))), equivalent(equivalent(W, V), equivalent(equivalent(W, U), equivalent(V, U)))))
% 0.20/0.43 = { by axiom 4 (p_4) }
% 0.20/0.43 fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))), equivalent(equivalent(W, V), equivalent(equivalent(W, U), equivalent(V, U)))))
% 0.20/0.43 = { by axiom 1 (condensed_detachment) }
% 0.20/0.43 true
% 0.20/0.43
% 0.20/0.43 Lemma 7: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))) = true.
% 0.20/0.43 Proof:
% 0.20/0.43 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 0.20/0.43 = { by lemma 5 R->L }
% 0.20/0.43 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))), equivalent(equivalent(W, V), equivalent(equivalent(W, U), equivalent(V, U))))), true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 0.20/0.43 = { by lemma 6 }
% 0.20/0.43 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 0.20/0.43 = { by axiom 1 (condensed_detachment) }
% 0.20/0.43 true
% 0.20/0.43
% 0.20/0.43 Lemma 8: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(X, Z), equivalent(Y, Z))) = is_a_theorem(equivalent(equivalent(X, Z), equivalent(Y, Z))).
% 0.20/0.43 Proof:
% 0.20/0.43 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 0.20/0.43 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.43 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))), true, equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 fresh(true, true, equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 0.20/0.43 = { by axiom 2 (condensed_detachment) }
% 0.20/0.43 is_a_theorem(equivalent(equivalent(X, Z), equivalent(Y, Z)))
% 0.20/0.43
% 0.20/0.43 Lemma 9: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z)) = is_a_theorem(equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z)).
% 0.20/0.43 Proof:
% 0.20/0.43 fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 0.20/0.43 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.43 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 0.20/0.43 = { by lemma 8 R->L }
% 0.20/0.43 fresh(fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, W), equivalent(Y, W)))), true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 0.20/0.43 = { by lemma 7 }
% 0.20/0.43 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))), true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 0.20/0.43 = { by axiom 1 (condensed_detachment) }
% 0.20/0.43 fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 0.20/0.43 = { by axiom 2 (condensed_detachment) }
% 0.20/0.43 is_a_theorem(equivalent(equivalent(equivalent(X, W), equivalent(Y, W)), Z))
% 0.20/0.43
% 0.20/0.43 Goal 1 (prove_lg_2): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) = true.
% 0.20/0.43 Proof:
% 0.20/0.43 is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.43 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.43 fresh(true, true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.43 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.43 fresh(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.43 = { by axiom 4 (p_4) R->L }
% 0.20/0.43 fresh(fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), a)), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.43 = { by lemma 8 }
% 0.20/0.43 fresh(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.43 = { by axiom 3 (condensed_detachment) }
% 0.20/0.43 fresh2(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.44 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.44 fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.44 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.44 fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.44 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.44 fresh2(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.44 = { by lemma 6 R->L }
% 0.20/0.44 fresh2(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.44 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.45 fresh2(fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 fresh2(fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.45 = { by lemma 7 }
% 0.20/0.45 fresh2(fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.45 = { by axiom 1 (condensed_detachment) }
% 0.20/0.45 fresh2(fresh(fresh2(fresh(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, Y), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), Y)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.45 = { by axiom 2 (condensed_detachment) }
% 0.20/0.46 fresh2(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.46 = { by lemma 9 }
% 0.20/0.46 fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.46 = { by axiom 3 (condensed_detachment) }
% 0.20/0.46 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, X), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))), X))))), true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.46 = { by lemma 6 }
% 0.20/0.46 fresh2(fresh2(true, true, equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.46 = { by axiom 1 (condensed_detachment) }
% 0.20/0.46 fresh2(true, true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 0.20/0.46 = { by axiom 1 (condensed_detachment) }
% 0.20/0.46 true
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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