TSTP Solution File: LCL024-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL024-1 : 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 : n021.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 08:17:04 EDT 2023
% Result : Unsatisfiable 18.42s 3.00s
% Output : Proof 19.89s
% 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 : LCL024-1 : 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 : n021.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 05:42:40 EDT 2023
% 0.13/0.36 % CPUTime :
% 18.42/3.00 Command-line arguments: --no-flatten-goal
% 18.42/3.00
% 18.42/3.00 % SZS status Unsatisfiable
% 18.42/3.00
% 19.89/3.02 % SZS output start Proof
% 19.89/3.02 Take the following subset of the input axioms:
% 19.89/3.02 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 19.89/3.02 fof(prove_pyo, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))).
% 19.89/3.02 fof(xgk, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(X2, equivalent(equivalent(Y2, equivalent(Z, X2)), equivalent(Z, Y2))))).
% 19.89/3.02
% 19.89/3.02 Now clausify the problem and encode Horn clauses using encoding 3 of
% 19.89/3.02 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 19.89/3.02 We repeatedly replace C & s=t => u=v by the two clauses:
% 19.89/3.02 fresh(y, y, x1...xn) = u
% 19.89/3.02 C => fresh(s, t, x1...xn) = v
% 19.89/3.02 where fresh is a fresh function symbol and x1..xn are the free
% 19.89/3.02 variables of u and v.
% 19.89/3.02 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 19.89/3.02 input problem has no model of domain size 1).
% 19.89/3.02
% 19.89/3.02 The encoding turns the above axioms into the following unit equations and goals:
% 19.89/3.02
% 19.89/3.02 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 19.89/3.02 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 19.89/3.02 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 19.89/3.02 Axiom 4 (xgk): is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))) = true.
% 19.89/3.02
% 19.89/3.02 Lemma 5: fresh2(is_a_theorem(X), true, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))) = is_a_theorem(equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y))).
% 19.89/3.02 Proof:
% 19.89/3.02 fresh2(is_a_theorem(X), true, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))
% 19.89/3.02 = { by axiom 3 (condensed_detachment) R->L }
% 19.89/3.02 fresh(is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))), true, X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))
% 19.89/3.02 = { by axiom 4 (xgk) }
% 19.89/3.02 fresh(true, true, X, equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))
% 19.89/3.02 = { by axiom 2 (condensed_detachment) }
% 19.89/3.02 is_a_theorem(equivalent(equivalent(Y, equivalent(Z, X)), equivalent(Z, Y)))
% 19.89/3.02
% 19.89/3.02 Lemma 6: fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, equivalent(Y, X)) = is_a_theorem(equivalent(Y, X)).
% 19.89/3.02 Proof:
% 19.89/3.02 fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, equivalent(Y, X))
% 19.89/3.02 = { by axiom 3 (condensed_detachment) R->L }
% 19.89/3.02 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))
% 19.89/3.02 = { by lemma 5 R->L }
% 19.89/3.02 fresh(fresh2(is_a_theorem(equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))
% 19.89/3.02 = { by axiom 4 (xgk) }
% 19.89/3.02 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))
% 19.89/3.02 = { by axiom 1 (condensed_detachment) }
% 19.89/3.02 fresh(true, true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))), equivalent(Y, X))
% 19.89/3.02 = { by axiom 2 (condensed_detachment) }
% 19.89/3.02 is_a_theorem(equivalent(Y, X))
% 19.89/3.02
% 19.89/3.02 Lemma 7: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W)) = true.
% 19.89/3.02 Proof:
% 19.89/3.02 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W))
% 19.89/3.02 = { by lemma 6 R->L }
% 19.89/3.02 fresh2(is_a_theorem(equivalent(W, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), equivalent(Z, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)))))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W))
% 19.89/3.02 = { by axiom 4 (xgk) }
% 19.89/3.02 fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W))
% 19.89/3.02 = { by axiom 1 (condensed_detachment) }
% 19.89/3.02 true
% 19.89/3.02
% 19.89/3.02 Lemma 8: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W))), true, W) = is_a_theorem(W).
% 19.89/3.02 Proof:
% 19.89/3.02 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W))), true, W)
% 19.89/3.02 = { by axiom 3 (condensed_detachment) R->L }
% 19.89/3.02 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W)), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W)
% 19.89/3.02 = { by lemma 7 }
% 19.89/3.02 fresh(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, W)), W)
% 19.89/3.03 = { by axiom 2 (condensed_detachment) }
% 19.89/3.03 is_a_theorem(W)
% 19.89/3.03
% 19.89/3.03 Lemma 9: fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, Z)))), true, equivalent(Y, X)) = is_a_theorem(equivalent(Y, X)).
% 19.89/3.03 Proof:
% 19.89/3.03 fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, Z)))), true, equivalent(Y, X))
% 19.89/3.03 = { by axiom 3 (condensed_detachment) R->L }
% 19.89/3.03 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))
% 19.89/3.03 = { by lemma 5 R->L }
% 19.89/3.03 fresh(fresh2(is_a_theorem(equivalent(Z, Z)), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))
% 19.89/3.03 = { by lemma 8 R->L }
% 19.89/3.03 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(W, equivalent(Z, Z)), equivalent(Z, W)), equivalent(Z, equivalent(W, equivalent(Z, Z)))), equivalent(W, equivalent(Z, Z)))), true, equivalent(Z, Z)), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))
% 19.89/3.03 = { by lemma 7 }
% 19.89/3.03 fresh(fresh2(fresh2(true, true, equivalent(Z, Z)), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 fresh(true, true, equivalent(X, equivalent(Y, equivalent(Z, Z))), equivalent(Y, X))
% 19.89/3.03 = { by axiom 2 (condensed_detachment) }
% 19.89/3.03 is_a_theorem(equivalent(Y, X))
% 19.89/3.03
% 19.89/3.03 Lemma 10: is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y)) = true.
% 19.89/3.03 Proof:
% 19.89/3.03 is_a_theorem(equivalent(equivalent(X, equivalent(X, Y)), Y))
% 19.89/3.03 = { by lemma 9 R->L }
% 19.89/3.03 fresh2(is_a_theorem(equivalent(Y, equivalent(equivalent(X, equivalent(X, Y)), equivalent(X, X)))), true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 19.89/3.03 = { by axiom 4 (xgk) }
% 19.89/3.03 fresh2(true, true, equivalent(equivalent(X, equivalent(X, Y)), Y))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 true
% 19.89/3.03
% 19.89/3.03 Lemma 11: is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)))) = true.
% 19.89/3.03 Proof:
% 19.89/3.03 is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X))))
% 19.89/3.03 = { by lemma 6 R->L }
% 19.89/3.03 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(X, equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(W, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)))))))), true, equivalent(X, equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X))))
% 19.89/3.03 = { by lemma 6 R->L }
% 19.89/3.03 fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(W, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)))))), equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(W, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)))))), true, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(X, equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(W, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)))))))), true, equivalent(X, equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X))))
% 19.89/3.03 = { by lemma 10 }
% 19.89/3.03 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(X, equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X)), equivalent(W, equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)))))))), true, equivalent(X, equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X))))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 fresh2(true, true, equivalent(X, equivalent(equivalent(equivalent(Y, equivalent(Z, W)), equivalent(Z, Y)), equivalent(W, X))))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 true
% 19.89/3.03
% 19.89/3.03 Lemma 12: is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))) = true.
% 19.89/3.03 Proof:
% 19.89/3.03 is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))
% 19.89/3.03 = { by lemma 6 R->L }
% 19.89/3.03 fresh2(is_a_theorem(equivalent(equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)), equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(Z, equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W)))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))
% 19.89/3.03 = { by lemma 11 }
% 19.89/3.03 fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, X)), equivalent(equivalent(W, equivalent(V, Z)), equivalent(V, W))))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 true
% 19.89/3.03
% 19.89/3.03 Lemma 13: is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y)))) = true.
% 19.89/3.03 Proof:
% 19.89/3.03 is_a_theorem(equivalent(X, equivalent(Y, equivalent(X, Y))))
% 19.89/3.03 = { by axiom 2 (condensed_detachment) R->L }
% 19.89/3.03 fresh(true, true, equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y))))), equivalent(X, equivalent(Y, equivalent(X, Y))))
% 19.89/3.03 = { by lemma 10 R->L }
% 19.89/3.03 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y))))), equivalent(X, equivalent(Y, equivalent(X, Y))))), true, equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y))))), equivalent(X, equivalent(Y, equivalent(X, Y))))
% 19.89/3.03 = { by axiom 3 (condensed_detachment) }
% 19.89/3.03 fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(equivalent(equivalent(Y, equivalent(X, Y)), equivalent(X, Y)), equivalent(X, equivalent(Y, equivalent(X, Y)))))), true, equivalent(X, equivalent(Y, equivalent(X, Y))))
% 19.89/3.03 = { by lemma 12 }
% 19.89/3.03 fresh2(true, true, equivalent(X, equivalent(Y, equivalent(X, Y))))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 true
% 19.89/3.03
% 19.89/3.03 Lemma 14: is_a_theorem(equivalent(X, equivalent(Y, equivalent(Y, equivalent(X, equivalent(Z, Z)))))) = true.
% 19.89/3.03 Proof:
% 19.89/3.03 is_a_theorem(equivalent(X, equivalent(Y, equivalent(Y, equivalent(X, equivalent(Z, Z))))))
% 19.89/3.03 = { by lemma 9 R->L }
% 19.89/3.03 fresh2(is_a_theorem(equivalent(equivalent(Y, equivalent(Y, equivalent(X, equivalent(Z, Z)))), equivalent(X, equivalent(Z, Z)))), true, equivalent(X, equivalent(Y, equivalent(Y, equivalent(X, equivalent(Z, Z))))))
% 19.89/3.03 = { by lemma 10 }
% 19.89/3.03 fresh2(true, true, equivalent(X, equivalent(Y, equivalent(Y, equivalent(X, equivalent(Z, Z))))))
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 true
% 19.89/3.03
% 19.89/3.03 Lemma 15: fresh2(is_a_theorem(equivalent(X, equivalent(Y, X))), true, Y) = is_a_theorem(Y).
% 19.89/3.03 Proof:
% 19.89/3.03 fresh2(is_a_theorem(equivalent(X, equivalent(Y, X))), true, Y)
% 19.89/3.03 = { by axiom 3 (condensed_detachment) R->L }
% 19.89/3.03 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 2 (condensed_detachment) R->L }
% 19.89/3.03 fresh(fresh(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 1 (condensed_detachment) R->L }
% 19.89/3.03 fresh(fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 1 (condensed_detachment) R->L }
% 19.89/3.03 fresh(fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), Y), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(Z, Z)))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by lemma 14 R->L }
% 19.89/3.03 fresh(fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), Y), equivalent(equivalent(equivalent(X, equivalent(Y, X)), Y), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(Z, Z)))))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), Y), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(Z, Z)))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by lemma 8 }
% 19.89/3.03 fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, X)), Y), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(Z, Z)))), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by lemma 9 }
% 19.89/3.03 fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))), equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 3 (condensed_detachment) }
% 19.89/3.03 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 2 (condensed_detachment) R->L }
% 19.89/3.03 fresh(fresh2(fresh(true, true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 1 (condensed_detachment) R->L }
% 19.89/3.03 fresh(fresh2(fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by lemma 13 R->L }
% 19.89/3.03 fresh(fresh2(fresh(fresh2(is_a_theorem(equivalent(Y, equivalent(X, equivalent(Y, X)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 3 (condensed_detachment) R->L }
% 19.89/3.03 fresh(fresh2(fresh(fresh(is_a_theorem(equivalent(equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))))), true, equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by lemma 6 R->L }
% 19.89/3.03 fresh(fresh2(fresh(fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), equivalent(equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))))))))), true, equivalent(equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))))), true, equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by lemma 14 }
% 19.89/3.03 fresh(fresh2(fresh(fresh(fresh2(true, true, equivalent(equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))))), true, equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 fresh(fresh2(fresh(fresh(true, true, equivalent(Y, equivalent(X, equivalent(Y, X))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 2 (condensed_detachment) }
% 19.89/3.03 fresh(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X)))))), true, equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 3 (condensed_detachment) }
% 19.89/3.03 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by lemma 13 }
% 19.89/3.03 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, X)), equivalent(Y, equivalent(equivalent(X, equivalent(Y, X)), Y))), equivalent(Y, equivalent(X, equivalent(Y, X))))), true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, X)), Y)), true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 1 (condensed_detachment) }
% 19.89/3.03 fresh(true, true, equivalent(X, equivalent(Y, X)), Y)
% 19.89/3.03 = { by axiom 2 (condensed_detachment) }
% 19.89/3.03 is_a_theorem(Y)
% 19.89/3.03
% 19.89/3.03 Lemma 16: fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W)))))), true, equivalent(Y, X)) = is_a_theorem(equivalent(Y, X)).
% 19.89/3.03 Proof:
% 19.89/3.04 fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W)))))), true, equivalent(Y, X))
% 19.89/3.04 = { by axiom 3 (condensed_detachment) R->L }
% 19.89/3.04 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))
% 19.89/3.04 = { by lemma 5 R->L }
% 19.89/3.04 fresh(fresh2(is_a_theorem(equivalent(Z, equivalent(W, equivalent(Z, W)))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))
% 19.89/3.04 = { by lemma 13 }
% 19.89/3.04 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))), true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))
% 19.89/3.04 = { by axiom 1 (condensed_detachment) }
% 19.89/3.04 fresh(true, true, equivalent(X, equivalent(Y, equivalent(Z, equivalent(W, equivalent(Z, W))))), equivalent(Y, X))
% 19.89/3.04 = { by axiom 2 (condensed_detachment) }
% 19.89/3.04 is_a_theorem(equivalent(Y, X))
% 19.89/3.04
% 19.89/3.04 Goal 1 (prove_pyo): is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))) = true.
% 19.89/3.04 Proof:
% 19.89/3.04 is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by axiom 2 (condensed_detachment) R->L }
% 19.89/3.04 fresh(true, true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by axiom 1 (condensed_detachment) R->L }
% 19.89/3.04 fresh(fresh2(true, true, equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by axiom 1 (condensed_detachment) R->L }
% 19.89/3.04 fresh(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true, equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by axiom 1 (condensed_detachment) R->L }
% 19.89/3.04 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true, equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by lemma 11 R->L }
% 19.89/3.04 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true, equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by lemma 16 }
% 19.89/3.04 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(b, a), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))))))), true, equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true, equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by lemma 16 }
% 19.89/3.04 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), equivalent(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a))), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)))))), true, equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by lemma 15 }
% 19.89/3.04 fresh(is_a_theorem(equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by axiom 3 (condensed_detachment) }
% 19.89/3.04 fresh2(is_a_theorem(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by lemma 15 R->L }
% 19.89/3.04 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(b, a)), equivalent(equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(b, a))))), true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by lemma 12 }
% 19.89/3.04 fresh2(fresh2(true, true, equivalent(equivalent(b, a), equivalent(equivalent(a, equivalent(b, c)), c))), true, equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by axiom 1 (condensed_detachment) }
% 19.89/3.04 fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(b, c)), c), equivalent(b, a)))
% 19.89/3.04 = { by axiom 1 (condensed_detachment) }
% 19.89/3.04 true
% 19.89/3.04 % SZS output end Proof
% 19.89/3.04
% 19.89/3.04 RESULT: Unsatisfiable (the axioms are contradictory).
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