TSTP Solution File: LCL059-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL059-1 : 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 : n004.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 08:17:13 EDT 2023
% Result : Unsatisfiable 13.75s 2.28s
% Output : Proof 13.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL059-1 : 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
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 20:40:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 13.75/2.28 Command-line arguments: --no-flatten-goal
% 13.75/2.28
% 13.75/2.28 % SZS status Unsatisfiable
% 13.75/2.28
% 13.75/2.30 % SZS output start Proof
% 13.75/2.30 Take the following subset of the input axioms:
% 13.75/2.30 fof(cn_1, axiom, ![X, Y, Z]: is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))).
% 13.75/2.30 fof(cn_2, axiom, ![X2]: is_a_theorem(implies(implies(not(X2), X2), X2))).
% 13.75/2.30 fof(cn_3, axiom, ![X2, Y2]: is_a_theorem(implies(X2, implies(not(X2), Y2)))).
% 13.75/2.30 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 13.75/2.30 fof(prove_cn_49, negated_conjecture, ~is_a_theorem(implies(implies(not(a), not(b)), implies(b, a)))).
% 13.75/2.30
% 13.75/2.30 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.75/2.30 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.75/2.30 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.75/2.30 fresh(y, y, x1...xn) = u
% 13.75/2.30 C => fresh(s, t, x1...xn) = v
% 13.75/2.30 where fresh is a fresh function symbol and x1..xn are the free
% 13.75/2.30 variables of u and v.
% 13.75/2.30 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.75/2.30 input problem has no model of domain size 1).
% 13.75/2.30
% 13.75/2.30 The encoding turns the above axioms into the following unit equations and goals:
% 13.75/2.30
% 13.75/2.30 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 13.75/2.30 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 13.75/2.30 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 13.75/2.30 Axiom 4 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 13.75/2.30 Axiom 5 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 13.75/2.30 Axiom 6 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 13.75/2.30
% 13.75/2.30 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))).
% 13.75/2.30 Proof:
% 13.75/2.30 fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z)))
% 13.75/2.30 = { by axiom 5 (condensed_detachment) R->L }
% 13.75/2.30 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)))
% 13.75/2.30 = { by axiom 6 (cn_1) }
% 13.75/2.30 fresh(true, true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 13.75/2.30 = { by axiom 2 (condensed_detachment) }
% 13.75/2.30 is_a_theorem(implies(implies(Y, Z), implies(X, Z)))
% 13.75/2.30
% 13.75/2.30 Lemma 8: is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))) = true.
% 13.75/2.30 Proof:
% 13.75/2.30 is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 13.75/2.30 = { by lemma 7 R->L }
% 13.75/2.30 fresh2(is_a_theorem(implies(X, implies(not(X), Y))), true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 13.75/2.30 = { by axiom 3 (cn_3) }
% 13.75/2.30 fresh2(true, true, implies(implies(implies(not(X), Y), Z), implies(X, Z)))
% 13.75/2.30 = { by axiom 1 (condensed_detachment) }
% 13.75/2.30 true
% 13.75/2.30
% 13.75/2.30 Lemma 9: 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)).
% 13.75/2.30 Proof:
% 13.75/2.30 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W))
% 13.75/2.30 = { by axiom 5 (condensed_detachment) R->L }
% 13.75/2.30 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))
% 13.75/2.30 = { by lemma 7 R->L }
% 13.75/2.30 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))
% 13.75/2.30 = { by axiom 6 (cn_1) }
% 13.75/2.30 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))
% 13.75/2.30 = { by axiom 1 (condensed_detachment) }
% 13.75/2.30 fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 13.75/2.30 = { by axiom 2 (condensed_detachment) }
% 13.75/2.30 is_a_theorem(implies(implies(Z, X), W))
% 13.75/2.30
% 13.75/2.30 Lemma 10: is_a_theorem(implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y))) = true.
% 13.75/2.30 Proof:
% 13.75/2.30 is_a_theorem(implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by axiom 2 (condensed_detachment) R->L }
% 13.75/2.30 fresh(true, true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by axiom 1 (condensed_detachment) R->L }
% 13.75/2.30 fresh(fresh2(true, true, implies(implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by axiom 1 (condensed_detachment) R->L }
% 13.75/2.30 fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(not(X), X), X), Y), implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y))), true, implies(implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by axiom 4 (cn_2) R->L }
% 13.75/2.30 fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), implies(implies(not(X), X), X))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y))), true, implies(implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by lemma 7 }
% 13.75/2.30 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(not(X), X), X), Y), implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y))), true, implies(implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by lemma 7 }
% 13.75/2.30 fresh(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y)), implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by axiom 5 (condensed_detachment) }
% 13.75/2.30 fresh2(is_a_theorem(implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by lemma 7 R->L }
% 13.75/2.30 fresh2(fresh2(is_a_theorem(implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.30 = { by axiom 2 (condensed_detachment) R->L }
% 13.75/2.30 fresh2(fresh2(fresh(true, true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X))), implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by lemma 8 R->L }
% 13.75/2.31 fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X))), implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X))))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X))), implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 5 (condensed_detachment) }
% 13.75/2.31 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by lemma 7 R->L }
% 13.75/2.31 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 2 (condensed_detachment) R->L }
% 13.75/2.31 fresh2(fresh2(fresh2(fresh2(fresh(true, true, implies(implies(not(X), X), X), implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 3 (cn_3) R->L }
% 13.75/2.31 fresh2(fresh2(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(not(X), X), X), implies(not(implies(implies(not(X), X), X)), not(Z)))), true, implies(implies(not(X), X), X), implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 5 (condensed_detachment) }
% 13.75/2.31 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(X), X), X)), true, implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 4 (cn_2) }
% 13.75/2.31 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(not(X), X), X)), not(Z))), true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) }
% 13.75/2.31 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(Z), implies(implies(not(X), X), X)), implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) }
% 13.75/2.31 fresh2(fresh2(fresh2(true, true, implies(Z, implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)))), true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) }
% 13.75/2.31 fresh2(fresh2(true, true, implies(implies(implies(not(implies(implies(not(X), X), X)), implies(implies(not(X), X), X)), Y), implies(Z, Y))), true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) }
% 13.75/2.31 fresh2(true, true, implies(implies(implies(implies(not(X), X), X), Y), implies(Z, Y)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) }
% 13.75/2.31 true
% 13.75/2.31
% 13.75/2.31 Lemma 11: is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))) = true.
% 13.75/2.31 Proof:
% 13.75/2.31 is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 13.75/2.31 = { by lemma 9 R->L }
% 13.75/2.31 fresh2(is_a_theorem(implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 13.75/2.31 = { by lemma 10 }
% 13.75/2.31 fresh2(true, true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y))))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) }
% 13.75/2.31 true
% 13.75/2.31
% 13.75/2.31 Goal 1 (prove_cn_49): is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))) = true.
% 13.75/2.31 Proof:
% 13.75/2.31 is_a_theorem(implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by axiom 2 (condensed_detachment) R->L }
% 13.75/2.31 fresh(true, true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) R->L }
% 13.75/2.31 fresh(fresh2(true, true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) R->L }
% 13.75/2.31 fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by axiom 1 (condensed_detachment) R->L }
% 13.75/2.31 fresh(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a))))), true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by lemma 10 R->L }
% 13.75/2.31 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(not(implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a))))), true, implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a))))), true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by axiom 5 (condensed_detachment) R->L }
% 13.75/2.31 fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(not(implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))))), true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(not(implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a))))), true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by lemma 11 }
% 13.75/2.31 fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(not(implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a))))), true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.31 = { by axiom 2 (condensed_detachment) }
% 13.75/2.32 fresh(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a))))), true, implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 5 (condensed_detachment) R->L }
% 13.75/2.32 fresh(fresh2(fresh(is_a_theorem(implies(implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a))))), true, implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 4 (cn_2) }
% 13.75/2.32 fresh(fresh2(fresh(true, true, implies(not(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 2 (condensed_detachment) }
% 13.75/2.32 fresh(fresh2(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by lemma 9 }
% 13.75/2.32 fresh(is_a_theorem(implies(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a))), implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 5 (condensed_detachment) }
% 13.75/2.32 fresh2(is_a_theorem(implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by lemma 9 R->L }
% 13.75/2.32 fresh2(fresh2(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 2 (condensed_detachment) R->L }
% 13.75/2.32 fresh2(fresh2(fresh(true, true, implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 1 (condensed_detachment) R->L }
% 13.75/2.32 fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))))), true, implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by lemma 8 R->L }
% 13.75/2.32 fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, implies(implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))))), true, implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by lemma 7 }
% 13.75/2.32 fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))))), true, implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 5 (condensed_detachment) }
% 13.75/2.32 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by lemma 11 }
% 13.75/2.32 fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 1 (condensed_detachment) }
% 13.75/2.32 fresh2(fresh2(true, true, implies(implies(not(a), not(b)), implies(not(implies(b, a)), implies(b, a)))), true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 1 (condensed_detachment) }
% 13.75/2.32 fresh2(true, true, implies(implies(not(a), not(b)), implies(b, a)))
% 13.75/2.32 = { by axiom 1 (condensed_detachment) }
% 13.75/2.32 true
% 13.75/2.32 % SZS output end Proof
% 13.75/2.32
% 13.75/2.32 RESULT: Unsatisfiable (the axioms are contradictory).
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