TSTP Solution File: LCL071-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL071-1 : 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 : n019.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 08:17:16 EDT 2023
% Result : Unsatisfiable 75.86s 10.11s
% Output : Proof 75.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL071-1 : 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
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 17:41:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 75.86/10.11 Command-line arguments: --no-flatten-goal
% 75.86/10.11
% 75.86/10.11 % SZS status Unsatisfiable
% 75.86/10.11
% 75.86/10.13 % SZS output start Proof
% 75.86/10.13 Take the following subset of the input axioms:
% 75.86/10.13 fof(cn_19, axiom, ![X, Y, Z]: is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z)))).
% 75.86/10.13 fof(cn_37, axiom, ![X2, Y2, Z2]: is_a_theorem(implies(implies(implies(X2, Y2), Z2), implies(not(X2), Z2)))).
% 75.86/10.13 fof(cn_60, axiom, ![U, X2, Y2, Z2]: is_a_theorem(implies(implies(X2, implies(not(Y2), Z2)), implies(X2, implies(implies(U, Z2), implies(implies(Y2, U), Z2)))))).
% 75.86/10.13 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 75.86/10.13 fof(prove_cn_2, negated_conjecture, ~is_a_theorem(implies(implies(not(a), a), a))).
% 75.86/10.13
% 75.86/10.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 75.86/10.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 75.86/10.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 75.86/10.13 fresh(y, y, x1...xn) = u
% 75.86/10.13 C => fresh(s, t, x1...xn) = v
% 75.86/10.13 where fresh is a fresh function symbol and x1..xn are the free
% 75.86/10.13 variables of u and v.
% 75.86/10.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 75.86/10.13 input problem has no model of domain size 1).
% 75.86/10.13
% 75.86/10.13 The encoding turns the above axioms into the following unit equations and goals:
% 75.86/10.13
% 75.86/10.13 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 75.86/10.13 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 75.86/10.13 Axiom 3 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 75.86/10.13 Axiom 4 (cn_19): is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))) = true.
% 75.86/10.13 Axiom 5 (cn_37): is_a_theorem(implies(implies(implies(X, Y), Z), implies(not(X), Z))) = true.
% 75.86/10.13 Axiom 6 (cn_60): is_a_theorem(implies(implies(X, implies(not(Y), Z)), implies(X, implies(implies(W, Z), implies(implies(Y, W), Z))))) = true.
% 75.86/10.13
% 75.86/10.13 Lemma 7: fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(Y, Z)) = is_a_theorem(implies(Y, Z)).
% 75.86/10.13 Proof:
% 75.86/10.13 fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(Y, Z))
% 75.86/10.13 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.13 fresh(is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))), true, implies(implies(X, Y), Z), implies(Y, Z))
% 75.86/10.13 = { by axiom 4 (cn_19) }
% 75.86/10.13 fresh(true, true, implies(implies(X, Y), Z), implies(Y, Z))
% 75.86/10.13 = { by axiom 2 (condensed_detachment) }
% 75.86/10.13 is_a_theorem(implies(Y, Z))
% 75.86/10.13
% 75.86/10.13 Lemma 8: is_a_theorem(implies(X, implies(Y, X))) = true.
% 75.86/10.13 Proof:
% 75.86/10.13 is_a_theorem(implies(X, implies(Y, X)))
% 75.86/10.13 = { by lemma 7 R->L }
% 75.86/10.13 fresh2(is_a_theorem(implies(implies(implies(Z, Y), X), implies(Y, X))), true, implies(X, implies(Y, X)))
% 75.86/10.13 = { by axiom 4 (cn_19) }
% 75.86/10.13 fresh2(true, true, implies(X, implies(Y, X)))
% 75.86/10.13 = { by axiom 1 (condensed_detachment) }
% 75.86/10.13 true
% 75.86/10.13
% 75.86/10.13 Lemma 9: is_a_theorem(implies(X, implies(Y, implies(Z, X)))) = true.
% 75.86/10.13 Proof:
% 75.86/10.13 is_a_theorem(implies(X, implies(Y, implies(Z, X))))
% 75.86/10.13 = { by lemma 7 R->L }
% 75.86/10.13 fresh2(is_a_theorem(implies(implies(Z, X), implies(Y, implies(Z, X)))), true, implies(X, implies(Y, implies(Z, X))))
% 75.86/10.13 = { by lemma 8 }
% 75.86/10.13 fresh2(true, true, implies(X, implies(Y, implies(Z, X))))
% 75.86/10.13 = { by axiom 1 (condensed_detachment) }
% 75.86/10.13 true
% 75.86/10.13
% 75.86/10.13 Lemma 10: fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(implies(W, Z), implies(implies(X, W), Z))) = is_a_theorem(implies(implies(W, Z), implies(implies(X, W), Z))).
% 75.86/10.13 Proof:
% 75.86/10.13 fresh2(is_a_theorem(implies(implies(X, Y), Z)), true, implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.13 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.14 fresh(is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))), true, implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) R->L }
% 75.86/10.14 fresh(fresh(true, true, implies(implies(implies(X, Y), Z), implies(not(X), Z)), implies(implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))), true, implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.14 = { by axiom 6 (cn_60) R->L }
% 75.86/10.14 fresh(fresh(is_a_theorem(implies(implies(implies(implies(X, Y), Z), implies(not(X), Z)), implies(implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z))))), true, implies(implies(implies(X, Y), Z), implies(not(X), Z)), implies(implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))), true, implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.14 = { by axiom 3 (condensed_detachment) }
% 75.86/10.14 fresh(fresh2(is_a_theorem(implies(implies(implies(X, Y), Z), implies(not(X), Z))), true, implies(implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))), true, implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.14 = { by axiom 5 (cn_37) }
% 75.86/10.14 fresh(fresh2(true, true, implies(implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))), true, implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) }
% 75.86/10.14 fresh(true, true, implies(implies(X, Y), Z), implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) }
% 75.86/10.14 is_a_theorem(implies(implies(W, Z), implies(implies(X, W), Z)))
% 75.86/10.14
% 75.86/10.14 Lemma 11: fresh2(is_a_theorem(implies(X, implies(Y, Z))), true, implies(implies(implies(W, Y), X), implies(Y, Z))) = is_a_theorem(implies(implies(implies(W, Y), X), implies(Y, Z))).
% 75.86/10.14 Proof:
% 75.86/10.14 fresh2(is_a_theorem(implies(X, implies(Y, Z))), true, implies(implies(implies(W, Y), X), implies(Y, Z)))
% 75.86/10.14 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.14 fresh(is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(implies(W, Y), X), implies(Y, Z)))), true, implies(X, implies(Y, Z)), implies(implies(implies(W, Y), X), implies(Y, Z)))
% 75.86/10.14 = { by lemma 10 R->L }
% 75.86/10.14 fresh(fresh2(is_a_theorem(implies(implies(implies(W, Y), Z), implies(Y, Z))), true, implies(implies(X, implies(Y, Z)), implies(implies(implies(W, Y), X), implies(Y, Z)))), true, implies(X, implies(Y, Z)), implies(implies(implies(W, Y), X), implies(Y, Z)))
% 75.86/10.14 = { by axiom 4 (cn_19) }
% 75.86/10.14 fresh(fresh2(true, true, implies(implies(X, implies(Y, Z)), implies(implies(implies(W, Y), X), implies(Y, Z)))), true, implies(X, implies(Y, Z)), implies(implies(implies(W, Y), X), implies(Y, Z)))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) }
% 75.86/10.14 fresh(true, true, implies(X, implies(Y, Z)), implies(implies(implies(W, Y), X), implies(Y, Z)))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) }
% 75.86/10.14 is_a_theorem(implies(implies(implies(W, Y), X), implies(Y, Z)))
% 75.86/10.14
% 75.86/10.14 Lemma 12: fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(Z, Y), W))), true, implies(Y, W)) = is_a_theorem(implies(Y, W)).
% 75.86/10.14 Proof:
% 75.86/10.14 fresh2(is_a_theorem(implies(implies(X, Y), implies(implies(Z, Y), W))), true, implies(Y, W))
% 75.86/10.14 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.14 fresh(is_a_theorem(implies(implies(implies(X, Y), implies(implies(Z, Y), W)), implies(Y, W))), true, implies(implies(X, Y), implies(implies(Z, Y), W)), implies(Y, W))
% 75.86/10.14 = { by lemma 11 R->L }
% 75.86/10.14 fresh(fresh2(is_a_theorem(implies(implies(implies(Z, Y), W), implies(Y, W))), true, implies(implies(implies(X, Y), implies(implies(Z, Y), W)), implies(Y, W))), true, implies(implies(X, Y), implies(implies(Z, Y), W)), implies(Y, W))
% 75.86/10.14 = { by axiom 4 (cn_19) }
% 75.86/10.14 fresh(fresh2(true, true, implies(implies(implies(X, Y), implies(implies(Z, Y), W)), implies(Y, W))), true, implies(implies(X, Y), implies(implies(Z, Y), W)), implies(Y, W))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) }
% 75.86/10.14 fresh(true, true, implies(implies(X, Y), implies(implies(Z, Y), W)), implies(Y, W))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) }
% 75.86/10.14 is_a_theorem(implies(Y, W))
% 75.86/10.14
% 75.86/10.14 Lemma 13: fresh2(is_a_theorem(implies(X, implies(Y, implies(Z, W)))), true, implies(implies(Z, X), implies(Y, implies(Z, W)))) = is_a_theorem(implies(implies(Z, X), implies(Y, implies(Z, W)))).
% 75.86/10.14 Proof:
% 75.86/10.14 fresh2(is_a_theorem(implies(X, implies(Y, implies(Z, W)))), true, implies(implies(Z, X), implies(Y, implies(Z, W))))
% 75.86/10.14 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.14 fresh(is_a_theorem(implies(implies(X, implies(Y, implies(Z, W))), implies(implies(Z, X), implies(Y, implies(Z, W))))), true, implies(X, implies(Y, implies(Z, W))), implies(implies(Z, X), implies(Y, implies(Z, W))))
% 75.86/10.14 = { by lemma 10 R->L }
% 75.86/10.14 fresh(fresh2(is_a_theorem(implies(implies(Z, W), implies(Y, implies(Z, W)))), true, implies(implies(X, implies(Y, implies(Z, W))), implies(implies(Z, X), implies(Y, implies(Z, W))))), true, implies(X, implies(Y, implies(Z, W))), implies(implies(Z, X), implies(Y, implies(Z, W))))
% 75.86/10.14 = { by lemma 8 }
% 75.86/10.14 fresh(fresh2(true, true, implies(implies(X, implies(Y, implies(Z, W))), implies(implies(Z, X), implies(Y, implies(Z, W))))), true, implies(X, implies(Y, implies(Z, W))), implies(implies(Z, X), implies(Y, implies(Z, W))))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) }
% 75.86/10.14 fresh(true, true, implies(X, implies(Y, implies(Z, W))), implies(implies(Z, X), implies(Y, implies(Z, W))))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) }
% 75.86/10.14 is_a_theorem(implies(implies(Z, X), implies(Y, implies(Z, W))))
% 75.86/10.14
% 75.86/10.14 Lemma 14: is_a_theorem(implies(implies(X, implies(X, implies(X, Y))), implies(Z, implies(X, Y)))) = true.
% 75.86/10.14 Proof:
% 75.86/10.14 is_a_theorem(implies(implies(X, implies(X, implies(X, Y))), implies(Z, implies(X, Y))))
% 75.86/10.14 = { by lemma 13 R->L }
% 75.86/10.14 fresh2(is_a_theorem(implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(X, implies(X, Y))), implies(Z, implies(X, Y))))
% 75.86/10.14 = { by lemma 13 R->L }
% 75.86/10.14 fresh2(fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(X, implies(X, Y))), implies(Z, implies(X, Y))))
% 75.86/10.14 = { by lemma 8 }
% 75.86/10.14 fresh2(fresh2(true, true, implies(implies(X, implies(X, Y)), implies(Z, implies(X, Y)))), true, implies(implies(X, implies(X, implies(X, Y))), implies(Z, implies(X, Y))))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) }
% 75.86/10.14 fresh2(true, true, implies(implies(X, implies(X, implies(X, Y))), implies(Z, implies(X, Y))))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) }
% 75.86/10.14 true
% 75.86/10.14
% 75.86/10.14 Lemma 15: fresh2(is_a_theorem(implies(X, implies(X, Y))), true, implies(X, Y)) = is_a_theorem(implies(X, Y)).
% 75.86/10.14 Proof:
% 75.86/10.14 fresh2(is_a_theorem(implies(X, implies(X, Y))), true, implies(X, Y))
% 75.86/10.14 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.14 fresh(is_a_theorem(implies(implies(X, implies(X, Y)), implies(X, Y))), true, implies(X, implies(X, Y)), implies(X, Y))
% 75.86/10.14 = { by lemma 12 R->L }
% 75.86/10.14 fresh(fresh2(is_a_theorem(implies(implies(X, implies(X, implies(X, Y))), implies(implies(Z, implies(X, implies(X, Y))), implies(X, Y)))), true, implies(implies(X, implies(X, Y)), implies(X, Y))), true, implies(X, implies(X, Y)), implies(X, Y))
% 75.86/10.14 = { by lemma 14 }
% 75.86/10.14 fresh(fresh2(true, true, implies(implies(X, implies(X, Y)), implies(X, Y))), true, implies(X, implies(X, Y)), implies(X, Y))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) }
% 75.86/10.14 fresh(true, true, implies(X, implies(X, Y)), implies(X, Y))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) }
% 75.86/10.14 is_a_theorem(implies(X, Y))
% 75.86/10.14
% 75.86/10.14 Goal 1 (prove_cn_2): is_a_theorem(implies(implies(not(a), a), a)) = true.
% 75.86/10.14 Proof:
% 75.86/10.14 is_a_theorem(implies(implies(not(a), a), a))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) R->L }
% 75.86/10.14 fresh(true, true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) R->L }
% 75.86/10.14 fresh(fresh2(true, true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) R->L }
% 75.86/10.14 fresh(fresh2(fresh2(true, true, implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by axiom 1 (condensed_detachment) R->L }
% 75.86/10.14 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by axiom 6 (cn_60) R->L }
% 75.86/10.14 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(X, implies(not(a), a)), implies(not(a), a)), implies(implies(X, implies(not(a), a)), implies(implies(a, a), implies(implies(a, a), a))))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by lemma 12 }
% 75.86/10.14 fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.14 fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by lemma 15 R->L }
% 75.86/10.14 fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by lemma 13 R->L }
% 75.86/10.14 fresh(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.14 = { by axiom 2 (condensed_detachment) R->L }
% 75.86/10.14 fresh(fresh2(fresh(fresh2(fresh2(fresh(true, true, implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) R->L }
% 75.86/10.15 fresh(fresh2(fresh(fresh2(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))))), true, implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 9 R->L }
% 75.86/10.15 fresh(fresh2(fresh(fresh2(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))))), true, implies(implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))))), true, implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 11 }
% 75.86/10.15 fresh(fresh2(fresh(fresh2(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))))), true, implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 3 (condensed_detachment) }
% 75.86/10.15 fresh(fresh2(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 14 }
% 75.86/10.15 fresh(fresh2(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(a, a), implies(implies(a, a), a)), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))))), true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh(fresh2(fresh(true, true, implies(implies(not(a), a), implies(implies(a, a), implies(implies(a, a), a))), implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 2 (condensed_detachment) }
% 75.86/10.15 fresh(fresh2(is_a_theorem(implies(implies(not(a), a), implies(implies(a, a), a))), true, implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 3 (condensed_detachment) R->L }
% 75.86/10.15 fresh(fresh(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 13 R->L }
% 75.86/10.15 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 15 R->L }
% 75.86/10.15 fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 13 R->L }
% 75.86/10.15 fresh(fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(a, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 7 R->L }
% 75.86/10.15 fresh(fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(a, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 9 }
% 75.86/10.15 fresh(fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(a, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh(fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(a, a), a), implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(a, a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh(fresh(fresh2(true, true, implies(implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh(fresh(true, true, implies(implies(not(a), a), implies(implies(a, a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 2 (condensed_detachment) }
% 75.86/10.15 fresh(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, implies(a, a), implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 3 (condensed_detachment) }
% 75.86/10.15 fresh2(is_a_theorem(implies(a, a)), true, implies(implies(not(a), a), a))
% 75.86/10.15 = { by lemma 12 R->L }
% 75.86/10.15 fresh2(fresh2(is_a_theorem(implies(implies(implies(Y, implies(Z, a)), a), implies(implies(Z, a), a))), true, implies(a, a)), true, implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 4 (cn_19) }
% 75.86/10.15 fresh2(fresh2(true, true, implies(a, a)), true, implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 fresh2(true, true, implies(implies(not(a), a), a))
% 75.86/10.15 = { by axiom 1 (condensed_detachment) }
% 75.86/10.15 true
% 75.86/10.15 % SZS output end Proof
% 75.86/10.15
% 75.86/10.15 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------