TSTP Solution File: LCL065-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL065-1 : 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 : n018.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 08:17:15 EDT 2023
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL065-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n018.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 03:22:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.53 Command-line arguments: --no-flatten-goal
% 0.19/0.53
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53
% 0.19/0.55 % SZS output start Proof
% 0.19/0.55 Take the following subset of the input axioms:
% 0.19/0.55 fof(cn_18, axiom, ![X, Y]: is_a_theorem(implies(X, implies(Y, X)))).
% 0.19/0.55 fof(cn_35, axiom, ![Z, X2, Y2]: is_a_theorem(implies(implies(X2, implies(Y2, Z)), implies(implies(X2, Y2), implies(X2, Z))))).
% 0.19/0.55 fof(cn_49, axiom, ![X2, Y2]: is_a_theorem(implies(implies(not(X2), not(Y2)), implies(Y2, X2)))).
% 0.19/0.55 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 0.19/0.55 fof(prove_cn_2, negated_conjecture, ~is_a_theorem(implies(implies(not(a), a), a))).
% 0.19/0.55
% 0.19/0.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.55 fresh(y, y, x1...xn) = u
% 0.19/0.55 C => fresh(s, t, x1...xn) = v
% 0.19/0.55 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.55 variables of u and v.
% 0.19/0.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.55 input problem has no model of domain size 1).
% 0.19/0.55
% 0.19/0.55 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.55
% 0.19/0.55 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.19/0.55 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.19/0.55 Axiom 3 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 0.19/0.55 Axiom 4 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.19/0.55 Axiom 5 (cn_49): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 0.19/0.55 Axiom 6 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 0.19/0.55
% 0.19/0.55 Lemma 7: fresh2(is_a_theorem(implies(X, implies(Y, Z))), true, implies(implies(X, Y), implies(X, Z))) = is_a_theorem(implies(implies(X, Y), implies(X, Z))).
% 0.19/0.55 Proof:
% 0.19/0.55 fresh2(is_a_theorem(implies(X, implies(Y, Z))), true, implies(implies(X, Y), implies(X, Z)))
% 0.19/0.55 = { by axiom 4 (condensed_detachment) R->L }
% 0.19/0.55 fresh(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))), true, implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))
% 0.19/0.55 = { by axiom 6 (cn_35) }
% 0.19/0.55 fresh(true, true, implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))
% 0.19/0.55 = { by axiom 2 (condensed_detachment) }
% 0.19/0.55 is_a_theorem(implies(implies(X, Y), implies(X, Z)))
% 0.19/0.55
% 0.19/0.55 Lemma 8: is_a_theorem(implies(X, X)) = true.
% 0.19/0.55 Proof:
% 0.19/0.55 is_a_theorem(implies(X, X))
% 0.19/0.55 = { by axiom 2 (condensed_detachment) R->L }
% 0.19/0.55 fresh(true, true, implies(X, implies(Y, X)), implies(X, X))
% 0.19/0.55 = { by axiom 1 (condensed_detachment) R->L }
% 0.19/0.55 fresh(fresh2(true, true, implies(implies(X, implies(Y, X)), implies(X, X))), true, implies(X, implies(Y, X)), implies(X, X))
% 0.19/0.55 = { by axiom 3 (cn_18) R->L }
% 0.19/0.55 fresh(fresh2(is_a_theorem(implies(X, implies(implies(Y, X), X))), true, implies(implies(X, implies(Y, X)), implies(X, X))), true, implies(X, implies(Y, X)), implies(X, X))
% 0.19/0.55 = { by lemma 7 }
% 0.19/0.55 fresh(is_a_theorem(implies(implies(X, implies(Y, X)), implies(X, X))), true, implies(X, implies(Y, X)), implies(X, X))
% 0.19/0.55 = { by axiom 4 (condensed_detachment) }
% 0.19/0.55 fresh2(is_a_theorem(implies(X, implies(Y, X))), true, implies(X, X))
% 0.19/0.55 = { by axiom 3 (cn_18) }
% 0.19/0.55 fresh2(true, true, implies(X, X))
% 0.19/0.55 = { by axiom 1 (condensed_detachment) }
% 0.19/0.55 true
% 0.19/0.55
% 0.19/0.55 Lemma 9: fresh2(is_a_theorem(X), true, implies(Y, X)) = is_a_theorem(implies(Y, X)).
% 0.19/0.55 Proof:
% 0.19/0.55 fresh2(is_a_theorem(X), true, implies(Y, X))
% 0.19/0.55 = { by axiom 4 (condensed_detachment) R->L }
% 0.19/0.55 fresh(is_a_theorem(implies(X, implies(Y, X))), true, X, implies(Y, X))
% 0.19/0.55 = { by axiom 3 (cn_18) }
% 0.19/0.55 fresh(true, true, X, implies(Y, X))
% 0.19/0.55 = { by axiom 2 (condensed_detachment) }
% 0.19/0.55 is_a_theorem(implies(Y, X))
% 0.19/0.55
% 0.19/0.55 Lemma 10: fresh2(is_a_theorem(implies(implies(X, Y), X)), true, implies(implies(X, Y), Y)) = is_a_theorem(implies(implies(X, Y), Y)).
% 0.19/0.55 Proof:
% 0.19/0.55 fresh2(is_a_theorem(implies(implies(X, Y), X)), true, implies(implies(X, Y), Y))
% 0.19/0.55 = { by axiom 4 (condensed_detachment) R->L }
% 0.19/0.55 fresh(is_a_theorem(implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 0.19/0.55 = { by lemma 7 R->L }
% 0.19/0.55 fresh(fresh2(is_a_theorem(implies(implies(X, Y), implies(X, Y))), true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 0.19/0.55 = { by lemma 8 }
% 0.19/0.55 fresh(fresh2(true, true, implies(implies(implies(X, Y), X), implies(implies(X, Y), Y))), true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 0.19/0.55 = { by axiom 1 (condensed_detachment) }
% 0.19/0.55 fresh(true, true, implies(implies(X, Y), X), implies(implies(X, Y), Y))
% 0.19/0.55 = { by axiom 2 (condensed_detachment) }
% 0.19/0.55 is_a_theorem(implies(implies(X, Y), Y))
% 0.19/0.55
% 0.19/0.55 Lemma 11: is_a_theorem(implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y)))) = true.
% 0.19/0.55 Proof:
% 0.19/0.55 is_a_theorem(implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y))))
% 0.19/0.55 = { by lemma 7 R->L }
% 0.19/0.55 fresh2(is_a_theorem(implies(X, implies(implies(not(Y), not(Z)), implies(Z, Y)))), true, implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y))))
% 0.19/0.55 = { by lemma 9 R->L }
% 0.19/0.55 fresh2(fresh2(is_a_theorem(implies(implies(not(Y), not(Z)), implies(Z, Y))), true, implies(X, implies(implies(not(Y), not(Z)), implies(Z, Y)))), true, implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y))))
% 0.19/0.55 = { by axiom 5 (cn_49) }
% 0.19/0.55 fresh2(fresh2(true, true, implies(X, implies(implies(not(Y), not(Z)), implies(Z, Y)))), true, implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y))))
% 0.19/0.55 = { by axiom 1 (condensed_detachment) }
% 0.19/0.55 fresh2(true, true, implies(implies(X, implies(not(Y), not(Z))), implies(X, implies(Z, Y))))
% 0.19/0.55 = { by axiom 1 (condensed_detachment) }
% 0.19/0.55 true
% 0.19/0.55
% 0.19/0.55 Goal 1 (prove_cn_2): is_a_theorem(implies(implies(not(a), a), a)) = true.
% 0.19/0.55 Proof:
% 0.19/0.55 is_a_theorem(implies(implies(not(a), a), a))
% 0.19/0.55 = { by axiom 2 (condensed_detachment) R->L }
% 0.19/0.55 fresh(true, true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.55 = { by axiom 1 (condensed_detachment) R->L }
% 0.19/0.55 fresh(fresh2(true, true, implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.55 = { by axiom 1 (condensed_detachment) R->L }
% 0.19/0.55 fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.55 = { by axiom 6 (cn_35) R->L }
% 0.19/0.55 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(implies(not(a), a), implies(not(a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.55 = { by lemma 7 }
% 0.19/0.55 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.55 = { by axiom 4 (condensed_detachment) R->L }
% 0.19/0.55 fresh(fresh(is_a_theorem(implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.55 = { by lemma 10 R->L }
% 0.19/0.55 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.55 = { by lemma 9 R->L }
% 0.19/0.56 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.56 = { by lemma 9 R->L }
% 0.19/0.56 fresh(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(a), a), implies(not(a), a))), true, implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.56 = { by lemma 8 }
% 0.19/0.56 fresh(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) }
% 0.19/0.56 fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) }
% 0.19/0.56 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) }
% 0.19/0.56 fresh(fresh(true, true, implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 2 (condensed_detachment) }
% 0.19/0.56 fresh(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 4 (condensed_detachment) }
% 0.19/0.56 fresh2(is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 2 (condensed_detachment) R->L }
% 0.19/0.56 fresh2(fresh(true, true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by lemma 11 R->L }
% 0.19/0.56 fresh2(fresh(is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 4 (condensed_detachment) }
% 0.19/0.56 fresh2(fresh2(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by lemma 7 R->L }
% 0.19/0.56 fresh2(fresh2(fresh2(is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 2 (condensed_detachment) R->L }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh(true, true, implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) R->L }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) R->L }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(not(not(implies(not(a), a))), not(a))))), true, implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 3 (cn_18) R->L }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(not(a), implies(not(not(implies(not(a), a))), not(a)))), true, implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(not(not(implies(not(a), a))), not(a))))), true, implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by lemma 9 }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(not(not(implies(not(a), a))), not(a))))), true, implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by lemma 10 }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))), implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 4 (condensed_detachment) }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by lemma 11 }
% 0.19/0.56 fresh2(fresh2(fresh2(fresh2(true, true, implies(not(a), implies(a, not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) }
% 0.19/0.56 fresh2(fresh2(fresh2(true, true, implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) }
% 0.19/0.56 fresh2(fresh2(true, true, implies(implies(not(a), a), implies(implies(not(a), a), a))), true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) }
% 0.19/0.56 fresh2(true, true, implies(implies(not(a), a), a))
% 0.19/0.56 = { by axiom 1 (condensed_detachment) }
% 0.19/0.56 true
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56
% 0.19/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------