TSTP Solution File: LCL129-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL129-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 08:17:35 EDT 2023
% Result : Unsatisfiable 59.74s 7.93s
% Output : Proof 60.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : LCL129-1 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 18:00:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 59.74/7.93 Command-line arguments: --no-flatten-goal
% 59.74/7.93
% 59.74/7.93 % SZS status Unsatisfiable
% 59.74/7.93
% 59.74/7.95 % SZS output start Proof
% 59.74/7.95 Take the following subset of the input axioms:
% 59.74/7.95 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 59.74/7.95 fof(prove_lg_2, negated_conjecture, ~is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))).
% 59.74/7.95 fof(s_4, axiom, ![Z, U, X2, Y2]: is_a_theorem(equivalent(equivalent(X2, equivalent(Y2, Z)), equivalent(equivalent(X2, equivalent(U, Z)), equivalent(Y2, U))))).
% 59.74/7.95
% 59.74/7.95 Now clausify the problem and encode Horn clauses using encoding 3 of
% 59.74/7.95 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 59.74/7.95 We repeatedly replace C & s=t => u=v by the two clauses:
% 59.74/7.95 fresh(y, y, x1...xn) = u
% 59.74/7.95 C => fresh(s, t, x1...xn) = v
% 59.74/7.95 where fresh is a fresh function symbol and x1..xn are the free
% 59.74/7.95 variables of u and v.
% 59.74/7.95 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 59.74/7.95 input problem has no model of domain size 1).
% 59.74/7.95
% 59.74/7.95 The encoding turns the above axioms into the following unit equations and goals:
% 59.74/7.95
% 59.74/7.95 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 59.74/7.95 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 59.74/7.95 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 59.74/7.95 Axiom 4 (s_4): is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))) = true.
% 59.74/7.95
% 59.74/7.95 Lemma 5: fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W))) = is_a_theorem(equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W))).
% 59.74/7.95 Proof:
% 59.74/7.95 fresh2(is_a_theorem(equivalent(X, equivalent(Y, Z))), true, equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))
% 59.74/7.95 = { by axiom 3 (condensed_detachment) R->L }
% 59.74/7.95 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))), true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))
% 59.74/7.95 = { by axiom 4 (s_4) }
% 59.74/7.95 fresh(true, true, equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))
% 59.74/7.95 = { by axiom 2 (condensed_detachment) }
% 59.74/7.95 is_a_theorem(equivalent(equivalent(X, equivalent(W, Z)), equivalent(Y, W)))
% 59.74/7.95
% 59.74/7.95 Lemma 6: fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V)))), true, equivalent(equivalent(X, equivalent(V, Z)), W)) = is_a_theorem(equivalent(equivalent(X, equivalent(V, Z)), W)).
% 59.74/7.95 Proof:
% 59.74/7.95 fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V)))), true, equivalent(equivalent(X, equivalent(V, Z)), W))
% 59.74/7.95 = { by axiom 3 (condensed_detachment) R->L }
% 59.74/7.95 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V))), equivalent(equivalent(X, equivalent(V, Z)), W))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V))), equivalent(equivalent(X, equivalent(V, Z)), W))
% 59.74/7.95 = { by lemma 5 R->L }
% 59.74/7.95 fresh(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, equivalent(V, Z)), equivalent(Y, V)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V))), equivalent(equivalent(X, equivalent(V, Z)), W))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V))), equivalent(equivalent(X, equivalent(V, Z)), W))
% 59.74/7.95 = { by axiom 4 (s_4) }
% 59.74/7.95 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V))), equivalent(equivalent(X, equivalent(V, Z)), W))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V))), equivalent(equivalent(X, equivalent(V, Z)), W))
% 59.74/7.95 = { by axiom 1 (condensed_detachment) }
% 59.74/7.95 fresh(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(W, equivalent(Y, V))), equivalent(equivalent(X, equivalent(V, Z)), W))
% 59.74/7.95 = { by axiom 2 (condensed_detachment) }
% 59.74/7.95 is_a_theorem(equivalent(equivalent(X, equivalent(V, Z)), W))
% 59.74/7.95
% 59.74/7.95 Lemma 7: is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), X)) = true.
% 59.74/7.95 Proof:
% 59.74/7.95 is_a_theorem(equivalent(equivalent(X, equivalent(Y, Y)), X))
% 59.74/7.95 = { by lemma 6 R->L }
% 59.74/7.95 fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Z, Y)), equivalent(X, equivalent(Z, Y)))), true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 59.74/7.95 = { by lemma 6 R->L }
% 59.74/7.95 fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(W, Y)), equivalent(equivalent(X, equivalent(Z, Y)), equivalent(W, Z)))), true, equivalent(equivalent(X, equivalent(Z, Y)), equivalent(X, equivalent(Z, Y)))), true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 59.74/7.95 = { by axiom 4 (s_4) }
% 59.74/7.95 fresh2(fresh2(true, true, equivalent(equivalent(X, equivalent(Z, Y)), equivalent(X, equivalent(Z, Y)))), true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 59.74/7.95 = { by axiom 1 (condensed_detachment) }
% 59.74/7.95 fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Y)), X))
% 59.74/7.95 = { by axiom 1 (condensed_detachment) }
% 59.74/7.95 true
% 59.74/7.95
% 59.74/7.95 Lemma 8: is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X)) = true.
% 59.74/7.95 Proof:
% 59.74/7.95 is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X))
% 59.74/7.95 = { by lemma 6 R->L }
% 59.74/7.95 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Y, Y)), equivalent(X, equivalent(Y, Z)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X))
% 59.74/7.95 = { by lemma 7 }
% 59.74/7.95 fresh2(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X))
% 59.74/7.95 = { by axiom 1 (condensed_detachment) }
% 59.74/7.95 true
% 59.74/7.95
% 59.74/7.95 Lemma 9: is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))) = true.
% 59.74/7.95 Proof:
% 59.74/7.95 is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by axiom 2 (condensed_detachment) R->L }
% 59.74/7.95 fresh(true, true, equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by axiom 1 (condensed_detachment) R->L }
% 59.74/7.95 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))), true, equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by lemma 8 R->L }
% 59.74/7.95 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))), equivalent(equivalent(X, Z), equivalent(X, Z)))), true, equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))), true, equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by axiom 3 (condensed_detachment) R->L }
% 59.74/7.95 fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))), equivalent(equivalent(X, Z), equivalent(X, Z))), equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))), equivalent(equivalent(X, Z), equivalent(X, Z))), equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))), true, equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by lemma 7 }
% 59.74/7.95 fresh(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z)))), equivalent(equivalent(X, Z), equivalent(X, Z))), equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))), true, equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by axiom 2 (condensed_detachment) }
% 59.74/7.95 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))), true, equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y))), equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by axiom 3 (condensed_detachment) }
% 59.74/7.95 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Z), equivalent(X, Z)), equivalent(equivalent(equivalent(X, Z), equivalent(Y, Z)), equivalent(X, Y)))), true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by axiom 4 (s_4) }
% 59.74/7.95 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Y, Z))))
% 59.74/7.95 = { by axiom 1 (condensed_detachment) }
% 59.74/7.95 true
% 59.74/7.95
% 59.74/7.95 Lemma 10: fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W)))), true, equivalent(equivalent(X, W), Z)) = is_a_theorem(equivalent(equivalent(X, W), Z)).
% 59.74/7.95 Proof:
% 59.74/7.95 fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W)))), true, equivalent(equivalent(X, W), Z))
% 59.74/7.95 = { by axiom 3 (condensed_detachment) R->L }
% 59.74/7.95 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W))), equivalent(equivalent(X, W), Z))), true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W))), equivalent(equivalent(X, W), Z))
% 59.74/7.96 = { by lemma 5 R->L }
% 59.74/7.96 fresh(fresh2(is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, W), equivalent(Y, W)))), true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W))), equivalent(equivalent(X, W), Z))), true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W))), equivalent(equivalent(X, W), Z))
% 59.74/7.96 = { by lemma 9 }
% 59.74/7.96 fresh(fresh2(true, true, equivalent(equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W))), equivalent(equivalent(X, W), Z))), true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W))), equivalent(equivalent(X, W), Z))
% 59.74/7.96 = { by axiom 1 (condensed_detachment) }
% 59.74/7.96 fresh(true, true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(Y, W))), equivalent(equivalent(X, W), Z))
% 59.74/7.96 = { by axiom 2 (condensed_detachment) }
% 59.74/7.96 is_a_theorem(equivalent(equivalent(X, W), Z))
% 59.74/7.96
% 59.74/7.96 Lemma 11: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W)), true, equivalent(X, W)) = is_a_theorem(equivalent(X, W)).
% 59.74/7.96 Proof:
% 59.74/7.96 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W)), true, equivalent(X, W))
% 59.74/7.96 = { by axiom 3 (condensed_detachment) R->L }
% 59.74/7.96 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))
% 59.74/7.96 = { by axiom 2 (condensed_detachment) R->L }
% 59.74/7.96 fresh(fresh(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))
% 59.74/7.96 = { by lemma 9 R->L }
% 59.74/7.96 fresh(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W)))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X), equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))
% 59.74/7.96 = { by axiom 3 (condensed_detachment) }
% 59.74/7.96 fresh(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), X)), true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))
% 59.74/7.96 = { by lemma 8 }
% 59.74/7.96 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))), true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))
% 59.74/7.96 = { by axiom 1 (condensed_detachment) }
% 59.74/7.96 fresh(true, true, equivalent(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(Z, Y)), W), equivalent(X, W))
% 59.74/7.96 = { by axiom 2 (condensed_detachment) }
% 59.74/7.96 is_a_theorem(equivalent(X, W))
% 59.74/7.96
% 59.74/7.96 Goal 1 (prove_lg_2): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) = true.
% 59.74/7.96 Proof:
% 59.74/7.96 is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 59.74/7.96 = { by lemma 11 R->L }
% 59.74/7.96 fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 59.74/7.96 = { by lemma 11 R->L }
% 59.74/7.96 fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(b, c)), 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(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 59.74/7.96 = { by lemma 10 R->L }
% 59.74/7.96 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(b, c)), 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(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 59.74/7.96 = { by axiom 2 (condensed_detachment) R->L }
% 59.74/7.97 fresh2(fresh2(fresh2(fresh(true, true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(c, e)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(b, c)), 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(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 59.74/7.97 = { by axiom 1 (condensed_detachment) R->L }
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% 59.74/7.97 = { by lemma 8 R->L }
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% 60.35/7.97 = { by lemma 5 }
% 60.35/7.97 fresh2(fresh2(fresh2(fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(c, e)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(c, e)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(b, c)), 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(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 60.35/7.97 = { by axiom 3 (condensed_detachment) }
% 60.35/7.97 fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(c, e)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(b, c)), 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(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 60.35/7.97 = { by lemma 10 R->L }
% 60.43/7.99 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(b, e)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(c, e)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(b, c)), 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(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 60.43/7.99 = { by lemma 6 R->L }
% 60.43/7.99 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(c, e)), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(b, e)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(c, b)), equivalent(e, c)), equivalent(c, e)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), true, equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(c, b)), equivalent(b, c)), 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(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 60.43/7.99 = { by lemma 8 }
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% 60.43/7.99 = { by axiom 1 (condensed_detachment) }
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% 60.43/7.99 = { by axiom 1 (condensed_detachment) }
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% 60.43/7.99 = { by axiom 1 (condensed_detachment) }
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% 60.43/7.99 = { by axiom 1 (condensed_detachment) }
% 60.43/7.99 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), 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))))))
% 60.43/7.99 = { by axiom 1 (condensed_detachment) }
% 60.43/7.99 fresh2(true, true, equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 60.43/7.99 = { by axiom 1 (condensed_detachment) }
% 60.43/7.99 true
% 60.43/7.99 % SZS output end Proof
% 60.43/7.99
% 60.43/7.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------