TSTP Solution File: LCL399-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL399-1 : TPTP v8.1.2. Released v2.3.0.
% 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 : n010.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 08:18:46 EDT 2023
% Result : Unsatisfiable 0.22s 0.93s
% Output : Proof 3.92s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL399-1 : TPTP v8.1.2. Released v2.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 04:13:50 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.93 Command-line arguments: --no-flatten-goal
% 0.22/0.93
% 0.22/0.93 % SZS status Unsatisfiable
% 0.22/0.93
% 3.92/0.95 % SZS output start Proof
% 3.92/0.95 Take the following subset of the input axioms:
% 3.92/0.95 fof(cn_1, axiom, ![X, Y, Z]: is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))).
% 3.92/0.95 fof(cn_2, axiom, ![X2]: is_a_theorem(implies(implies(not(X2), X2), X2))).
% 3.92/0.95 fof(cn_3, axiom, ![X2, Y2]: is_a_theorem(implies(X2, implies(not(X2), Y2)))).
% 3.92/0.95 fof(condensed_detachment, axiom, ![X2, Y2]: (~is_a_theorem(implies(X2, Y2)) | (~is_a_theorem(X2) | is_a_theorem(Y2)))).
% 3.92/0.95 fof(prove_cn_65, negated_conjecture, ~is_a_theorem(implies(implies(not(x), not(implies(y, y))), x))).
% 3.92/0.95
% 3.92/0.95 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.92/0.95 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.92/0.95 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.92/0.95 fresh(y, y, x1...xn) = u
% 3.92/0.95 C => fresh(s, t, x1...xn) = v
% 3.92/0.95 where fresh is a fresh function symbol and x1..xn are the free
% 3.92/0.95 variables of u and v.
% 3.92/0.95 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.92/0.95 input problem has no model of domain size 1).
% 3.92/0.95
% 3.92/0.95 The encoding turns the above axioms into the following unit equations and goals:
% 3.92/0.95
% 3.92/0.95 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 3.92/0.95 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 3.92/0.95 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 3.92/0.95 Axiom 4 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 3.92/0.95 Axiom 5 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 3.92/0.95 Axiom 6 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 3.92/0.95
% 3.92/0.95 Lemma 7: fresh2(is_a_theorem(X), true, implies(not(X), Y)) = is_a_theorem(implies(not(X), Y)).
% 3.92/0.95 Proof:
% 3.92/0.95 fresh2(is_a_theorem(X), true, implies(not(X), Y))
% 3.92/0.95 = { by axiom 5 (condensed_detachment) R->L }
% 3.92/0.95 fresh(is_a_theorem(implies(X, implies(not(X), Y))), true, X, implies(not(X), Y))
% 3.92/0.95 = { by axiom 3 (cn_3) }
% 3.92/0.95 fresh(true, true, X, implies(not(X), Y))
% 3.92/0.95 = { by axiom 2 (condensed_detachment) }
% 3.92/0.95 is_a_theorem(implies(not(X), Y))
% 3.92/0.95
% 3.92/0.95 Lemma 8: fresh2(is_a_theorem(implies(not(X), X)), true, X) = is_a_theorem(X).
% 3.92/0.95 Proof:
% 3.92/0.95 fresh2(is_a_theorem(implies(not(X), X)), true, X)
% 3.92/0.95 = { by axiom 5 (condensed_detachment) R->L }
% 3.92/0.95 fresh(is_a_theorem(implies(implies(not(X), X), X)), true, implies(not(X), X), X)
% 3.92/0.95 = { by axiom 4 (cn_2) }
% 3.92/0.95 fresh(true, true, implies(not(X), X), X)
% 3.92/0.95 = { by axiom 2 (condensed_detachment) }
% 3.92/0.95 is_a_theorem(X)
% 3.92/0.95
% 3.92/0.95 Lemma 9: 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))).
% 3.92/0.95 Proof:
% 3.92/0.95 fresh2(is_a_theorem(implies(X, Y)), true, implies(implies(Y, Z), implies(X, Z)))
% 3.92/0.95 = { by axiom 5 (condensed_detachment) R->L }
% 3.92/0.95 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)))
% 3.92/0.95 = { by axiom 6 (cn_1) }
% 3.92/0.95 fresh(true, true, implies(X, Y), implies(implies(Y, Z), implies(X, Z)))
% 3.92/0.95 = { by axiom 2 (condensed_detachment) }
% 3.92/0.95 is_a_theorem(implies(implies(Y, Z), implies(X, Z)))
% 3.92/0.95
% 3.92/0.95 Lemma 10: fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z)) = is_a_theorem(implies(X, Z)).
% 3.92/0.95 Proof:
% 3.92/0.95 fresh2(is_a_theorem(implies(implies(not(X), Y), Z)), true, implies(X, Z))
% 3.92/0.95 = { by axiom 5 (condensed_detachment) R->L }
% 3.92/0.95 fresh(is_a_theorem(implies(implies(implies(not(X), Y), Z), implies(X, Z))), true, implies(implies(not(X), Y), Z), implies(X, Z))
% 3.92/0.95 = { by lemma 9 R->L }
% 3.92/0.95 fresh(fresh2(is_a_theorem(implies(X, implies(not(X), Y))), true, implies(implies(implies(not(X), Y), Z), implies(X, Z))), true, implies(implies(not(X), Y), Z), implies(X, Z))
% 3.92/0.95 = { by axiom 3 (cn_3) }
% 3.92/0.95 fresh(fresh2(true, true, implies(implies(implies(not(X), Y), Z), implies(X, Z))), true, implies(implies(not(X), Y), Z), implies(X, Z))
% 3.92/0.95 = { by axiom 1 (condensed_detachment) }
% 3.92/0.95 fresh(true, true, implies(implies(not(X), Y), Z), implies(X, Z))
% 3.92/0.95 = { by axiom 2 (condensed_detachment) }
% 3.92/0.95 is_a_theorem(implies(X, Z))
% 3.92/0.95
% 3.92/0.95 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)).
% 3.92/0.95 Proof:
% 3.92/0.95 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), W)), true, implies(implies(Z, X), W))
% 3.92/0.95 = { by axiom 5 (condensed_detachment) R->L }
% 3.92/0.95 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))
% 3.92/0.95 = { by lemma 9 R->L }
% 3.92/0.95 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))
% 3.92/0.95 = { by axiom 6 (cn_1) }
% 3.92/0.95 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))
% 3.92/0.95 = { by axiom 1 (condensed_detachment) }
% 3.92/0.95 fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), W), implies(implies(Z, X), W))
% 3.92/0.95 = { by axiom 2 (condensed_detachment) }
% 3.92/0.95 is_a_theorem(implies(implies(Z, X), W))
% 3.92/0.95
% 3.92/0.95 Lemma 12: fresh2(is_a_theorem(implies(X, implies(not(Y), Y))), true, implies(Z, implies(X, Y))) = is_a_theorem(implies(Z, implies(X, Y))).
% 3.92/0.95 Proof:
% 3.92/0.95 fresh2(is_a_theorem(implies(X, implies(not(Y), Y))), true, implies(Z, implies(X, Y)))
% 3.92/0.95 = { by axiom 5 (condensed_detachment) R->L }
% 3.92/0.95 fresh(is_a_theorem(implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.95 = { by lemma 11 R->L }
% 3.92/0.95 fresh(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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.95 = { by axiom 2 (condensed_detachment) R->L }
% 3.92/0.95 fresh(fresh2(fresh(true, true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.95 = { by axiom 1 (condensed_detachment) R->L }
% 3.92/0.95 fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.95 = { by axiom 1 (condensed_detachment) R->L }
% 3.92/0.95 fresh(fresh2(fresh(fresh2(fresh2(true, true, implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)))), true, implies(implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 4 (cn_2) R->L }
% 3.92/0.96 fresh(fresh2(fresh(fresh2(fresh2(is_a_theorem(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y))), true, implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)))), true, implies(implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by lemma 9 }
% 3.92/0.96 fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)))), true, implies(implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by lemma 9 }
% 3.92/0.96 fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), implies(implies(implies(implies(not(Y), Y), Y), implies(X, Y)), implies(Z, implies(X, Y))))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y))), 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 5 (condensed_detachment) }
% 3.92/0.96 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by lemma 9 R->L }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(is_a_theorem(implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by lemma 10 R->L }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by lemma 9 R->L }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(not(Y), Y), Y)), not(Z))), true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by lemma 7 R->L }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(Y), Y), Y)), true, implies(not(implies(implies(not(Y), Y), Y)), not(Z))), true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 4 (cn_2) }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(not(Y), Y), Y)), not(Z))), true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 1 (condensed_detachment) }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(Z), implies(implies(not(Y), Y), Y)), implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 1 (condensed_detachment) }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(fresh2(true, true, implies(Z, implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)))), true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 1 (condensed_detachment) }
% 3.92/0.96 fresh(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(implies(not(Y), Y), Y)), implies(implies(not(Y), Y), Y)), implies(X, Y)), implies(Z, implies(X, Y)))), true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 1 (condensed_detachment) }
% 3.92/0.96 fresh(fresh2(fresh2(true, true, 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)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 1 (condensed_detachment) }
% 3.92/0.96 fresh(fresh2(true, true, implies(implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))), true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 1 (condensed_detachment) }
% 3.92/0.96 fresh(true, true, implies(X, implies(not(Y), Y)), implies(Z, implies(X, Y)))
% 3.92/0.96 = { by axiom 2 (condensed_detachment) }
% 3.92/0.96 is_a_theorem(implies(Z, implies(X, Y)))
% 3.92/0.96
% 3.92/0.96 Goal 1 (prove_cn_65): is_a_theorem(implies(implies(not(x), not(implies(y, y))), x)) = true.
% 3.92/0.96 Proof:
% 3.92/0.96 is_a_theorem(implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.96 = { by lemma 8 R->L }
% 3.92/0.96 fresh2(is_a_theorem(implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.96 = { by lemma 12 R->L }
% 3.92/0.96 fresh2(fresh2(is_a_theorem(implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.96 = { by lemma 11 R->L }
% 3.92/0.96 fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.96 = { by lemma 8 R->L }
% 3.92/0.96 fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.96 = { by lemma 12 R->L }
% 3.92/0.96 fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.96 = { by lemma 9 R->L }
% 3.92/0.96 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.96 = { by lemma 10 R->L }
% 3.92/0.96 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by lemma 9 R->L }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by lemma 7 R->L }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(y, y)), true, implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by lemma 10 R->L }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(is_a_theorem(implies(implies(not(y), y), y)), true, implies(y, y)), true, implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 4 (cn_2) }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(y, y)), true, implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(y, y)), not(not(implies(not(x), x))))), true, implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(not(not(implies(not(x), x))), x), implies(not(implies(y, y)), x))), true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(not(x), x)), implies(not(implies(y, y)), x))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(implies(not(x), x)), implies(not(x), x)))), true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(fresh2(true, true, implies(not(implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x)))), true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(fresh2(fresh2(true, true, implies(implies(implies(not(implies(y, y)), x), implies(not(x), x)), implies(not(x), x))), true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(fresh2(true, true, implies(implies(not(x), not(implies(y, y))), implies(not(x), x))), true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(fresh2(true, true, implies(not(implies(implies(not(x), not(implies(y, y))), x)), implies(implies(not(x), not(implies(y, y))), x))), true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 fresh2(true, true, implies(implies(not(x), not(implies(y, y))), x))
% 3.92/0.97 = { by axiom 1 (condensed_detachment) }
% 3.92/0.97 true
% 3.92/0.97 % SZS output end Proof
% 3.92/0.97
% 3.92/0.97 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------