TSTP Solution File: LCL048-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL048-1 : 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 : n032.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 08:17:10 EDT 2023
% Result : Unsatisfiable 0.12s 0.50s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : LCL048-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.07 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Fri Aug 25 05:20:57 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.12/0.50 Command-line arguments: --no-flatten-goal
% 0.12/0.50
% 0.12/0.50 % SZS status Unsatisfiable
% 0.12/0.50
% 0.12/0.52 % SZS output start Proof
% 0.12/0.52 Take the following subset of the input axioms:
% 0.12/0.52 fof(cn_1, axiom, ![X, Y, Z]: is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))).
% 0.12/0.52 fof(cn_2, axiom, ![X2]: is_a_theorem(implies(implies(not(X2), X2), X2))).
% 0.12/0.52 fof(cn_3, axiom, ![X2, Y2]: is_a_theorem(implies(X2, implies(not(X2), Y2)))).
% 0.12/0.52 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 0.12/0.52 fof(prove_cn_19, negated_conjecture, ~is_a_theorem(implies(implies(implies(a, b), c), implies(b, c)))).
% 0.12/0.52
% 0.12/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.52 fresh(y, y, x1...xn) = u
% 0.12/0.52 C => fresh(s, t, x1...xn) = v
% 0.12/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.52 variables of u and v.
% 0.12/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.52 input problem has no model of domain size 1).
% 0.12/0.52
% 0.12/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.52
% 0.12/0.52 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.12/0.52 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.12/0.52 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 0.12/0.52 Axiom 4 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 0.12/0.52 Axiom 5 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.12/0.52 Axiom 6 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 0.12/0.52
% 0.12/0.52 Lemma 7: 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))).
% 0.12/0.52 Proof:
% 0.12/0.52 fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z)))
% 0.12/0.52 = { by axiom 5 (condensed_detachment) R->L }
% 0.12/0.52 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)))
% 0.12/0.52 = { by axiom 6 (cn_1) }
% 0.12/0.52 fresh(true, true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 0.12/0.52 = { by axiom 2 (condensed_detachment) }
% 0.12/0.52 is_a_theorem(implies(implies(Y, Z), implies(X, Z)))
% 0.12/0.52
% 0.12/0.52 Lemma 8: is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))) = true.
% 0.12/0.52 Proof:
% 0.12/0.52 is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 0.12/0.52 = { by lemma 7 R->L }
% 0.12/0.52 fresh2(is_a_theorem(implies(X, implies(not(X), Y))), true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 0.12/0.52 = { by axiom 3 (cn_3) }
% 0.12/0.52 fresh2(true, true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 0.12/0.52 = { by axiom 1 (condensed_detachment) }
% 0.12/0.52 true
% 0.12/0.52
% 0.12/0.52 Lemma 9: fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z)) = is_a_theorem(implies(X, Z)).
% 0.12/0.52 Proof:
% 0.12/0.52 fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z))
% 0.12/0.52 = { by axiom 5 (condensed_detachment) R->L }
% 0.12/0.53 fresh(is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))), true, implies(implies(not(X), Y), Z), implies(X, Z))
% 0.12/0.53 = { by lemma 8 }
% 0.12/0.53 fresh(true, true, implies(implies(not(X), Y), Z), implies(X, Z))
% 0.12/0.53 = { by axiom 2 (condensed_detachment) }
% 0.12/0.53 is_a_theorem(implies(X, Z))
% 0.12/0.53
% 0.12/0.53 Lemma 10: fresh2(is_a_theorem(implies(implies(implies(not(X), X), Y), Z)), true, implies(implies(X, Y), Z)) = is_a_theorem(implies(implies(X, Y), Z)).
% 0.12/0.53 Proof:
% 0.12/0.53 fresh2(is_a_theorem(implies(implies(implies(not(X), X), Y), Z)), true, implies(implies(X, Y), Z))
% 0.12/0.53 = { by axiom 5 (condensed_detachment) R->L }
% 0.12/0.53 fresh(is_a_theorem(implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 0.12/0.53 = { by lemma 7 R->L }
% 0.12/0.53 fresh(fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 0.12/0.53 = { by lemma 7 R->L }
% 0.12/0.53 fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 0.12/0.53 = { by axiom 4 (cn_2) }
% 0.12/0.53 fresh(fresh2(fresh2(true, true, implies(implies(X, Y), implies(implies(not(X), X), Y))), true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 0.12/0.53 = { by axiom 1 (condensed_detachment) }
% 0.12/0.53 fresh(fresh2(true, true, implies(implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))), true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 0.12/0.53 = { by axiom 1 (condensed_detachment) }
% 0.12/0.53 fresh(true, true, implies(implies(implies(not(X), X), Y), Z), implies(implies(X, Y), Z))
% 0.12/0.53 = { by axiom 2 (condensed_detachment) }
% 0.12/0.53 is_a_theorem(implies(implies(X, Y), Z))
% 0.12/0.53
% 0.12/0.53 Lemma 11: fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W)) = is_a_theorem(implies(implies(Z, X), W)).
% 0.12/0.53 Proof:
% 0.12/0.53 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W))
% 0.12/0.53 = { by axiom 5 (condensed_detachment) R->L }
% 0.12/0.53 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 0.12/0.53 = { by lemma 7 R->L }
% 0.12/0.53 fresh(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))), true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 0.12/0.53 = { by axiom 6 (cn_1) }
% 0.12/0.53 fresh(fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))), true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 0.12/0.53 = { by axiom 1 (condensed_detachment) }
% 0.12/0.53 fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 0.12/0.53 = { by axiom 2 (condensed_detachment) }
% 0.12/0.53 is_a_theorem(implies(implies(Z, X), W))
% 0.12/0.53
% 0.12/0.53 Goal 1 (prove_cn_19): is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))) = true.
% 0.12/0.53 Proof:
% 0.12/0.53 is_a_theorem(implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by lemma 10 R->L }
% 0.12/0.53 fresh2(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by lemma 7 R->L }
% 0.12/0.53 fresh2(fresh2(is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by axiom 2 (condensed_detachment) R->L }
% 0.12/0.53 fresh2(fresh2(fresh(true, true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by axiom 1 (condensed_detachment) R->L }
% 0.12/0.53 fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by axiom 1 (condensed_detachment) R->L }
% 0.12/0.53 fresh2(fresh2(fresh(fresh2(fresh2(true, true, implies(b, implies(a, implies(not(b), b)))), true, implies(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by axiom 1 (condensed_detachment) R->L }
% 0.12/0.53 fresh2(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(not(b), not(a)), implies(a, implies(not(b), b)))), true, implies(b, implies(a, implies(not(b), b)))), true, implies(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by lemma 8 R->L }
% 0.12/0.53 fresh2(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b)))), true, implies(implies(not(b), not(a)), implies(a, implies(not(b), b)))), true, implies(b, implies(a, implies(not(b), b)))), true, implies(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by lemma 11 }
% 0.12/0.53 fresh2(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(b), not(a)), implies(a, implies(not(b), b)))), true, implies(b, implies(a, implies(not(b), b)))), true, implies(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by lemma 9 }
% 0.12/0.53 fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true, implies(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by lemma 7 }
% 0.12/0.53 fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.53 = { by axiom 5 (condensed_detachment) }
% 0.12/0.54 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by lemma 11 R->L }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by lemma 10 R->L }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by lemma 7 R->L }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by lemma 9 R->L }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(implies(not(b), b), b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by lemma 7 R->L }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(not(b), b), b)), not(not(implies(a, b))))), true, implies(implies(not(not(implies(a, b))), implies(implies(not(b), b), b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by axiom 2 (condensed_detachment) R->L }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(not(b), b), b), implies(not(implies(implies(not(b), b), b)), not(not(implies(a, b))))), true, implies(implies(not(not(implies(a, b))), implies(implies(not(b), b), b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by axiom 3 (cn_3) R->L }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(b), b), b), implies(not(implies(implies(not(b), b), b)), not(not(implies(a, b)))))), true, implies(implies(not(b), b), b), implies(not(implies(implies(not(b), b), b)), not(not(implies(a, b))))), true, implies(implies(not(not(implies(a, b))), implies(implies(not(b), b), b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.54 = { by axiom 5 (condensed_detachment) }
% 0.12/0.54 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(b), b), b)), true, implies(not(implies(implies(not(b), b), b)), not(not(implies(a, b))))), true, implies(implies(not(not(implies(a, b))), implies(implies(not(b), b), b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 4 (cn_2) }
% 0.12/0.55 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(not(b), b), b)), not(not(implies(a, b))))), true, implies(implies(not(not(implies(a, b))), implies(implies(not(b), b), b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(implies(a, b))), implies(implies(not(b), b), b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(a, b)), implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)))), true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(implies(not(b), b), b)), implies(implies(not(b), b), b)), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(a, implies(not(b), b)), implies(not(implies(a, b)), implies(a, b)))), true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(fresh2(fresh2(true, true, implies(b, implies(not(implies(a, b)), implies(a, b)))), true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(fresh2(true, true, implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 fresh2(true, true, implies(implies(implies(a, b), c), implies(b, c)))
% 0.12/0.55 = { by axiom 1 (condensed_detachment) }
% 0.12/0.55 true
% 0.12/0.55 % SZS output end Proof
% 0.12/0.55
% 0.12/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------