TSTP Solution File: LCL006-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL006-1 : 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 08:17:00 EDT 2023
% Result : Unsatisfiable 5.75s 1.13s
% Output : Proof 6.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL006-1 : 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
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Aug 25 02:21:26 EDT 2023
% 0.12/0.35 % CPUTime :
% 5.75/1.13 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 5.75/1.13
% 5.75/1.13 % SZS status Unsatisfiable
% 5.75/1.13
% 6.36/1.17 % SZS output start Proof
% 6.36/1.17 Take the following subset of the input axioms:
% 6.36/1.17 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(equivalent(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 6.36/1.17 fof(ec_4, axiom, ![X2, Y2]: is_a_theorem(equivalent(equivalent(X2, Y2), equivalent(Y2, X2)))).
% 6.36/1.17 fof(ec_5, axiom, ![Z, X2, Y2]: is_a_theorem(equivalent(equivalent(equivalent(X2, Y2), Z), equivalent(X2, equivalent(Y2, Z))))).
% 6.36/1.17 fof(prove_ec_1, negated_conjecture, ~is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))).
% 6.36/1.17
% 6.36/1.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.36/1.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.36/1.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.36/1.17 fresh(y, y, x1...xn) = u
% 6.36/1.17 C => fresh(s, t, x1...xn) = v
% 6.36/1.17 where fresh is a fresh function symbol and x1..xn are the free
% 6.36/1.17 variables of u and v.
% 6.36/1.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.36/1.17 input problem has no model of domain size 1).
% 6.36/1.17
% 6.36/1.17 The encoding turns the above axioms into the following unit equations and goals:
% 6.36/1.17
% 6.36/1.17 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 6.36/1.17 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 6.36/1.17 Axiom 3 (condensed_detachment): fresh(is_a_theorem(equivalent(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 6.36/1.17 Axiom 4 (ec_4): is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))) = true.
% 6.36/1.17 Axiom 5 (ec_5): is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))) = true.
% 6.36/1.17
% 6.36/1.17 Lemma 6: fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Y, X)) = is_a_theorem(equivalent(Y, X)).
% 6.36/1.17 Proof:
% 6.36/1.17 fresh2(is_a_theorem(equivalent(X, Y)), true, equivalent(Y, X))
% 6.36/1.17 = { by axiom 3 (condensed_detachment) R->L }
% 6.36/1.17 fresh(is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))), true, equivalent(X, Y), equivalent(Y, X))
% 6.36/1.17 = { by axiom 4 (ec_4) }
% 6.36/1.17 fresh(true, true, equivalent(X, Y), equivalent(Y, X))
% 6.36/1.17 = { by axiom 2 (condensed_detachment) }
% 6.36/1.17 is_a_theorem(equivalent(Y, X))
% 6.36/1.17
% 6.36/1.17 Lemma 7: fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(X, equivalent(Y, Z))) = is_a_theorem(equivalent(X, equivalent(Y, Z))).
% 6.36/1.17 Proof:
% 6.36/1.17 fresh2(is_a_theorem(equivalent(equivalent(X, Y), Z)), true, equivalent(X, equivalent(Y, Z)))
% 6.36/1.17 = { by axiom 3 (condensed_detachment) R->L }
% 6.36/1.17 fresh(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))), true, equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))
% 6.36/1.17 = { by axiom 5 (ec_5) }
% 6.36/1.17 fresh(true, true, equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))
% 6.36/1.17 = { by axiom 2 (condensed_detachment) }
% 6.36/1.17 is_a_theorem(equivalent(X, equivalent(Y, Z)))
% 6.36/1.17
% 6.36/1.17 Lemma 8: is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(X, equivalent(Y, Z))))) = true.
% 6.36/1.17 Proof:
% 6.36/1.17 is_a_theorem(equivalent(equivalent(X, Y), equivalent(Z, equivalent(X, equivalent(Y, Z)))))
% 6.36/1.17 = { by lemma 7 R->L }
% 6.36/1.17 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))), true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(X, equivalent(Y, Z)))))
% 6.36/1.17 = { by axiom 5 (ec_5) }
% 6.36/1.17 fresh2(true, true, equivalent(equivalent(X, Y), equivalent(Z, equivalent(X, equivalent(Y, Z)))))
% 6.36/1.17 = { by axiom 1 (condensed_detachment) }
% 6.36/1.17 true
% 6.36/1.17
% 6.36/1.17 Lemma 9: fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, X)))), true, equivalent(Y, Z)) = is_a_theorem(equivalent(Y, Z)).
% 6.36/1.17 Proof:
% 6.36/1.17 fresh2(is_a_theorem(equivalent(X, equivalent(Y, equivalent(Z, X)))), true, equivalent(Y, Z))
% 6.36/1.17 = { by axiom 3 (condensed_detachment) R->L }
% 6.36/1.17 fresh(is_a_theorem(equivalent(equivalent(X, equivalent(Y, equivalent(Z, X))), equivalent(Y, Z))), true, equivalent(X, equivalent(Y, equivalent(Z, X))), equivalent(Y, Z))
% 6.36/1.17 = { by lemma 6 R->L }
% 6.36/1.17 fresh(fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(X, equivalent(Y, equivalent(Z, X))))), true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, X))), equivalent(Y, Z))), true, equivalent(X, equivalent(Y, equivalent(Z, X))), equivalent(Y, Z))
% 6.36/1.17 = { by lemma 8 }
% 6.36/1.17 fresh(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, equivalent(Z, X))), equivalent(Y, Z))), true, equivalent(X, equivalent(Y, equivalent(Z, X))), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 1 (condensed_detachment) }
% 6.36/1.17 fresh(true, true, equivalent(X, equivalent(Y, equivalent(Z, X))), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 2 (condensed_detachment) }
% 6.36/1.17 is_a_theorem(equivalent(Y, Z))
% 6.36/1.17
% 6.36/1.17 Lemma 10: fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), X)), true, equivalent(Y, Z)) = is_a_theorem(equivalent(Y, Z)).
% 6.36/1.17 Proof:
% 6.36/1.17 fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), X)), true, equivalent(Y, Z))
% 6.36/1.17 = { by axiom 3 (condensed_detachment) R->L }
% 6.36/1.17 fresh(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by lemma 6 R->L }
% 6.36/1.17 fresh(fresh2(is_a_theorem(equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by lemma 7 R->L }
% 6.36/1.17 fresh(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)), X)), true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by lemma 6 R->L }
% 6.36/1.17 fresh(fresh2(fresh2(fresh2(is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)))), true, equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)), X)), true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by lemma 7 R->L }
% 6.36/1.17 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, Y), Z))), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)))), true, equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)), X)), true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by lemma 6 R->L }
% 6.36/1.17 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))), true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, Y), Z))), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)))), true, equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)), X)), true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 5 (ec_5) }
% 6.36/1.17 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(X, equivalent(Y, Z)), equivalent(equivalent(X, Y), Z))), true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)))), true, equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)), X)), true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 1 (condensed_detachment) }
% 6.36/1.17 fresh(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)))), true, equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)), X)), true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 1 (condensed_detachment) }
% 6.36/1.17 fresh(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(Y, Z), equivalent(equivalent(X, Y), Z)), X)), true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 1 (condensed_detachment) }
% 6.36/1.17 fresh(fresh2(fresh2(true, true, equivalent(equivalent(Y, Z), equivalent(equivalent(equivalent(X, Y), Z), X))), true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 1 (condensed_detachment) }
% 6.36/1.17 fresh(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))), true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 1 (condensed_detachment) }
% 6.36/1.17 fresh(true, true, equivalent(equivalent(equivalent(X, Y), Z), X), equivalent(Y, Z))
% 6.36/1.17 = { by axiom 2 (condensed_detachment) }
% 6.36/1.17 is_a_theorem(equivalent(Y, Z))
% 6.36/1.17
% 6.36/1.17 Goal 1 (prove_ec_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))) = true.
% 6.36/1.17 Proof:
% 6.36/1.17 is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.17 = { by lemma 7 R->L }
% 6.36/1.17 fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.18 = { by lemma 6 R->L }
% 6.36/1.18 fresh2(fresh2(is_a_theorem(equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.18 = { by lemma 7 R->L }
% 6.36/1.18 fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.18 = { by lemma 6 R->L }
% 6.36/1.18 fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.18 = { by lemma 10 R->L }
% 6.36/1.18 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.18 = { by lemma 6 R->L }
% 6.36/1.18 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.18 = { by lemma 10 R->L }
% 6.36/1.18 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.18 = { by lemma 9 R->L }
% 6.36/1.18 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.19 = { by lemma 7 R->L }
% 6.36/1.19 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.19 = { by lemma 6 R->L }
% 6.36/1.19 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.19 = { by lemma 10 R->L }
% 6.36/1.19 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))))), equivalent(a, b))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.36/1.19 = { by lemma 9 R->L }
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% 6.36/1.20 = { by lemma 7 R->L }
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% 6.36/1.20 = { by lemma 6 R->L }
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% 6.36/1.20 = { by lemma 7 R->L }
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% 6.36/1.21 = { by lemma 8 }
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% 6.71/1.21 = { by axiom 1 (condensed_detachment) }
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% 6.71/1.21 = { by axiom 1 (condensed_detachment) }
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% 6.71/1.21 = { by axiom 1 (condensed_detachment) }
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% 6.71/1.21 = { by axiom 1 (condensed_detachment) }
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% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(c, a), equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), c)), true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(a, equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))))), true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(equivalent(a, b), equivalent(c, equivalent(equivalent(a, b), equivalent(c, a)))), a)), true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, equivalent(b, equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))))), true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(fresh2(true, true, equivalent(equivalent(c, equivalent(equivalent(a, b), equivalent(c, a))), b)), true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(fresh2(true, true, equivalent(c, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b))), true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(fresh2(true, true, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 fresh2(true, true, equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 6.71/1.22 = { by axiom 1 (condensed_detachment) }
% 6.71/1.22 true
% 6.71/1.22 % SZS output end Proof
% 6.71/1.22
% 6.71/1.22 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------