TSTP Solution File: LCL113-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL113-1 : 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 : n009.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 08:17:30 EDT 2023
% Result : Unsatisfiable 7.76s 1.40s
% Output : Proof 8.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL113-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 05:55:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 7.76/1.40 Command-line arguments: --no-flatten-goal
% 7.76/1.40
% 7.76/1.40 % SZS status Unsatisfiable
% 7.76/1.40
% 8.20/1.42 % SZS output start Proof
% 8.20/1.42 Take the following subset of the input axioms:
% 8.20/1.42 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(implies(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 8.20/1.42 fof(mv_1, axiom, ![X2, Y2]: is_a_theorem(implies(X2, implies(Y2, X2)))).
% 8.20/1.42 fof(mv_2, axiom, ![Z, X2, Y2]: is_a_theorem(implies(implies(X2, Y2), implies(implies(Y2, Z), implies(X2, Z))))).
% 8.20/1.42 fof(mv_3, axiom, ![X2, Y2]: is_a_theorem(implies(implies(implies(X2, Y2), Y2), implies(implies(Y2, X2), X2)))).
% 8.20/1.42 fof(mv_5, axiom, ![X2, Y2]: is_a_theorem(implies(implies(not(X2), not(Y2)), implies(Y2, X2)))).
% 8.20/1.42 fof(prove_mv_33, negated_conjecture, ~is_a_theorem(implies(implies(not(a), b), implies(not(b), a)))).
% 8.20/1.42
% 8.20/1.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 8.20/1.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 8.20/1.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 8.20/1.42 fresh(y, y, x1...xn) = u
% 8.20/1.42 C => fresh(s, t, x1...xn) = v
% 8.20/1.42 where fresh is a fresh function symbol and x1..xn are the free
% 8.20/1.42 variables of u and v.
% 8.20/1.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 8.20/1.42 input problem has no model of domain size 1).
% 8.20/1.42
% 8.20/1.42 The encoding turns the above axioms into the following unit equations and goals:
% 8.20/1.42
% 8.20/1.42 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 8.20/1.42 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 8.20/1.42 Axiom 3 (mv_1): is_a_theorem(implies(X, implies(Y, X))) = true.
% 8.20/1.42 Axiom 4 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 8.20/1.42 Axiom 5 (mv_5): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 8.20/1.42 Axiom 6 (mv_2): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 8.20/1.42 Axiom 7 (mv_3): is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) = true.
% 8.20/1.42
% 8.20/1.42 Lemma 8: fresh2(is_a_theorem(X), true, implies(Y, X)) = is_a_theorem(implies(Y, X)).
% 8.20/1.42 Proof:
% 8.20/1.42 fresh2(is_a_theorem(X), true, implies(Y, X))
% 8.20/1.42 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.42 fresh(is_a_theorem(implies(X, implies(Y, X))), true, X, implies(Y, X))
% 8.20/1.42 = { by axiom 3 (mv_1) }
% 8.20/1.42 fresh(true, true, X, implies(Y, X))
% 8.20/1.42 = { by axiom 2 (condensed_detachment) }
% 8.20/1.42 is_a_theorem(implies(Y, X))
% 8.20/1.42
% 8.20/1.42 Lemma 9: fresh2(is_a_theorem(implies(implies(X, Y), Y)), true, implies(implies(Y, X), X)) = is_a_theorem(implies(implies(Y, X), X)).
% 8.20/1.42 Proof:
% 8.20/1.42 fresh2(is_a_theorem(implies(implies(X, Y), Y)), true, implies(implies(Y, X), X))
% 8.20/1.42 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.42 fresh(is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))), true, implies(implies(X, Y), Y), implies(implies(Y, X), X))
% 8.20/1.42 = { by axiom 7 (mv_3) }
% 8.20/1.42 fresh(true, true, implies(implies(X, Y), Y), implies(implies(Y, X), X))
% 8.20/1.42 = { by axiom 2 (condensed_detachment) }
% 8.20/1.42 is_a_theorem(implies(implies(Y, X), X))
% 8.20/1.42
% 8.20/1.42 Lemma 10: is_a_theorem(implies(implies(implies(X, implies(Y, X)), Z), Z)) = true.
% 8.20/1.42 Proof:
% 8.20/1.42 is_a_theorem(implies(implies(implies(X, implies(Y, X)), Z), Z))
% 8.20/1.42 = { by lemma 9 R->L }
% 8.20/1.42 fresh2(is_a_theorem(implies(implies(Z, implies(X, implies(Y, X))), implies(X, implies(Y, X)))), true, implies(implies(implies(X, implies(Y, X)), Z), Z))
% 8.20/1.42 = { by lemma 8 R->L }
% 8.20/1.42 fresh2(fresh2(is_a_theorem(implies(X, implies(Y, X))), true, implies(implies(Z, implies(X, implies(Y, X))), implies(X, implies(Y, X)))), true, implies(implies(implies(X, implies(Y, X)), Z), Z))
% 8.20/1.42 = { by axiom 3 (mv_1) }
% 8.20/1.42 fresh2(fresh2(true, true, implies(implies(Z, implies(X, implies(Y, X))), implies(X, implies(Y, X)))), true, implies(implies(implies(X, implies(Y, X)), Z), Z))
% 8.20/1.42 = { by axiom 1 (condensed_detachment) }
% 8.20/1.42 fresh2(true, true, implies(implies(implies(X, implies(Y, X)), Z), Z))
% 8.20/1.42 = { by axiom 1 (condensed_detachment) }
% 8.20/1.42 true
% 8.20/1.42
% 8.20/1.42 Lemma 11: fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(Y, Z)) = is_a_theorem(implies(Y, Z)).
% 8.20/1.42 Proof:
% 8.20/1.42 fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(Y, Z))
% 8.20/1.42 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.42 fresh(is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))), true, implies(implies(X, Y), Z), implies(Y, Z))
% 8.20/1.42 = { by axiom 2 (condensed_detachment) R->L }
% 8.20/1.42 fresh(fresh(true, true, implies(implies(Y, implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(X, Y), Z), implies(Y, Z))), true, implies(implies(X, Y), Z), implies(Y, Z))
% 8.20/1.42 = { by lemma 10 R->L }
% 8.20/1.42 fresh(fresh(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(Y, implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z))), implies(implies(implies(X, Y), Z), implies(Y, Z))), true, implies(implies(X, Y), Z), implies(Y, Z))
% 8.20/1.42 = { by axiom 4 (condensed_detachment) }
% 8.20/1.43 fresh(fresh2(is_a_theorem(implies(implies(Y, implies(X, Y)), implies(implies(implies(X, Y), Z), implies(Y, Z)))), true, implies(implies(implies(X, Y), Z), implies(Y, Z))), true, implies(implies(X, Y), Z), implies(Y, Z))
% 8.20/1.43 = { by axiom 6 (mv_2) }
% 8.20/1.43 fresh(fresh2(true, true, implies(implies(implies(X, Y), Z), implies(Y, Z))), true, implies(implies(X, Y), Z), implies(Y, Z))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) }
% 8.20/1.43 fresh(true, true, implies(implies(X, Y), Z), implies(Y, Z))
% 8.20/1.43 = { by axiom 2 (condensed_detachment) }
% 8.20/1.43 is_a_theorem(implies(Y, Z))
% 8.20/1.43
% 8.20/1.43 Lemma 12: is_a_theorem(implies(X, implies(implies(X, Y), Y))) = true.
% 8.20/1.43 Proof:
% 8.20/1.43 is_a_theorem(implies(X, implies(implies(X, Y), Y)))
% 8.20/1.43 = { by lemma 11 R->L }
% 8.20/1.43 fresh2(is_a_theorem(implies(implies(implies(Y, X), X), implies(implies(X, Y), Y))), true, implies(X, implies(implies(X, Y), Y)))
% 8.20/1.43 = { by axiom 7 (mv_3) }
% 8.20/1.43 fresh2(true, true, implies(X, implies(implies(X, Y), Y)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) }
% 8.20/1.43 true
% 8.20/1.43
% 8.20/1.43 Lemma 13: fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z))) = is_a_theorem(implies(implies(Y, Z), implies(X, Z))).
% 8.20/1.43 Proof:
% 8.20/1.43 fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z)))
% 8.20/1.43 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.43 fresh(is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))), true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 8.20/1.43 = { by axiom 6 (mv_2) }
% 8.20/1.43 fresh(true, true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 8.20/1.43 = { by axiom 2 (condensed_detachment) }
% 8.20/1.43 is_a_theorem(implies(implies(Y, Z), implies(X, Z)))
% 8.20/1.43
% 8.20/1.43 Lemma 14: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))) = true.
% 8.20/1.43 Proof:
% 8.20/1.43 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 8.20/1.43 = { by lemma 13 R->L }
% 8.20/1.43 fresh2(is_a_theorem(implies(implies(Z, X), implies(implies(X, Y), implies(Z, Y)))), true, implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 8.20/1.43 = { by axiom 6 (mv_2) }
% 8.20/1.43 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) }
% 8.20/1.43 true
% 8.20/1.43
% 8.20/1.43 Goal 1 (prove_mv_33): is_a_theorem(implies(implies(not(a), b), implies(not(b), a))) = true.
% 8.20/1.43 Proof:
% 8.20/1.43 is_a_theorem(implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 2 (condensed_detachment) R->L }
% 8.20/1.43 fresh(true, true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.43 fresh(fresh2(true, true, implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.43 fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.43 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(not(a), b), implies(not(b), a)), implies(implies(not(a), not(not(b))), implies(not(b), a))), implies(implies(not(a), not(not(b))), implies(not(b), a)))), true, implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 5 (mv_5) R->L }
% 8.20/1.43 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(a), not(not(b))), implies(not(b), a))), true, implies(implies(implies(implies(not(a), b), implies(not(b), a)), implies(implies(not(a), not(not(b))), implies(not(b), a))), implies(implies(not(a), not(not(b))), implies(not(b), a)))), true, implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by lemma 8 }
% 8.20/1.43 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), a)), implies(implies(not(a), not(not(b))), implies(not(b), a))), implies(implies(not(a), not(not(b))), implies(not(b), a)))), true, implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by lemma 9 }
% 8.20/1.43 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.43 fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a))), implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a))))), true, implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a))), implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by lemma 14 }
% 8.20/1.43 fresh(fresh(true, true, implies(implies(implies(implies(not(a), not(not(b))), implies(not(b), a)), implies(implies(not(a), b), implies(not(b), a))), implies(implies(not(a), b), implies(not(b), a))), implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 2 (condensed_detachment) }
% 8.20/1.43 fresh(is_a_theorem(implies(implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))), true, implies(implies(not(a), b), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 4 (condensed_detachment) }
% 8.20/1.43 fresh2(is_a_theorem(implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 2 (condensed_detachment) R->L }
% 8.20/1.43 fresh2(fresh(true, true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.43 fresh2(fresh(fresh2(true, true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.43 fresh2(fresh(fresh2(fresh2(true, true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.43 fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.43 fresh2(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b))), true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by lemma 10 R->L }
% 8.20/1.43 fresh2(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(X, implies(Y, X)), not(b)), not(b))), true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b))), true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.43 fresh2(fresh(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)))), true, implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b))), true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by lemma 13 R->L }
% 8.20/1.43 fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(b)))), true, implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)))), true, implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b))), true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 5 (mv_5) }
% 8.20/1.43 fresh2(fresh(fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)))), true, implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b))), true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.43 = { by axiom 1 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(implies(X, implies(Y, X)), not(b)), not(b)), implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b))), true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 2 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b))), true, implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b)))), true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by lemma 13 R->L }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(not(not(not(b))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true, implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b)))), true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by lemma 11 R->L }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(b)))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true, implies(not(not(not(b))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true, implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b)))), true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 5 (mv_5) }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(not(not(not(b))), implies(not(not(b)), not(implies(X, implies(Y, X)))))), true, implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b)))), true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 1 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b)))), true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 1 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(fresh(true, true, implies(implies(not(not(b)), not(implies(X, implies(Y, X)))), not(b)), implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 2 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(not(not(not(b))), not(b))), true, implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.44 fresh2(fresh(fresh2(fresh(is_a_theorem(implies(implies(not(not(not(b))), not(b)), implies(b, not(not(b))))), true, implies(not(not(not(b))), not(b)), implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 5 (mv_5) }
% 8.20/1.44 fresh2(fresh(fresh2(fresh(true, true, implies(not(not(not(b))), not(b)), implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 2 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh(fresh2(is_a_theorem(implies(b, not(not(b)))), true, implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 4 (condensed_detachment) R->L }
% 8.20/1.44 fresh2(fresh(fresh(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))))), true, implies(b, not(not(b))), implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by lemma 12 }
% 8.20/1.44 fresh2(fresh(fresh(true, true, implies(b, not(not(b))), implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 2 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh(is_a_theorem(implies(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 4 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh2(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 2 (condensed_detachment) R->L }
% 8.20/1.44 fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 1 (condensed_detachment) R->L }
% 8.20/1.44 fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))))), true, implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by lemma 12 R->L }
% 8.20/1.44 fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(b, not(not(b))), implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))))), true, implies(implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))))), true, implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by lemma 13 }
% 8.20/1.44 fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b))))))), true, implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b))))), implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 4 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(b, not(not(b))), implies(not(a), not(not(b)))), implies(not(a), not(not(b)))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by lemma 14 }
% 8.20/1.44 fresh2(fresh2(fresh2(true, true, implies(implies(b, not(not(b))), implies(implies(not(a), b), implies(not(a), not(not(b)))))), true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 1 (condensed_detachment) }
% 8.20/1.44 fresh2(fresh2(true, true, implies(implies(not(a), b), implies(not(a), not(not(b))))), true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 1 (condensed_detachment) }
% 8.20/1.44 fresh2(true, true, implies(implies(not(a), b), implies(not(b), a)))
% 8.20/1.44 = { by axiom 1 (condensed_detachment) }
% 8.20/1.44 true
% 8.20/1.44 % SZS output end Proof
% 8.20/1.44
% 8.20/1.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------