TSTP Solution File: LCL086-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL086-1 : 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 08:17:21 EDT 2023
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL086-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 18:17:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Command-line arguments: --no-flatten-goal
% 0.20/0.46
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 Take the following subset of the input axioms:
% 0.20/0.49 fof(condensed_detachment, axiom, ![X, Y]: (~is_a_theorem(implies(X, Y)) | (~is_a_theorem(X) | is_a_theorem(Y)))).
% 0.20/0.49 fof(ic_JLukasiewicz_4, axiom, ![P, Q, R, S, T]: is_a_theorem(implies(implies(implies(P, Q), implies(R, S)), implies(T, implies(implies(S, P), implies(R, P)))))).
% 0.20/0.49 fof(prove_ic_1, negated_conjecture, ~is_a_theorem(implies(a, a))).
% 0.20/0.49
% 0.20/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.49 fresh(y, y, x1...xn) = u
% 0.20/0.49 C => fresh(s, t, x1...xn) = v
% 0.20/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.49 variables of u and v.
% 0.20/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.49 input problem has no model of domain size 1).
% 0.20/0.49
% 0.20/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.49
% 0.20/0.49 Axiom 1 (condensed_detachment): fresh2(X, X, Y) = true.
% 0.20/0.49 Axiom 2 (condensed_detachment): fresh(X, X, Y, Z) = is_a_theorem(Z).
% 0.20/0.49 Axiom 3 (condensed_detachment): fresh(is_a_theorem(implies(X, Y)), true, X, Y) = fresh2(is_a_theorem(X), true, Y).
% 0.20/0.49 Axiom 4 (ic_JLukasiewicz_4): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))) = true.
% 0.20/0.49
% 0.20/0.49 Lemma 5: fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(V, implies(implies(W, X), implies(Z, X)))) = is_a_theorem(implies(V, implies(implies(W, X), implies(Z, X)))).
% 0.20/0.49 Proof:
% 0.20/0.49 fresh2(is_a_theorem(implies(implies(X, Y), implies(Z, W))), true, implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.49 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.49 fresh(is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))), true, implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.49 = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.49 fresh(true, true, implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.49 = { by axiom 2 (condensed_detachment) }
% 0.20/0.49 is_a_theorem(implies(V, implies(implies(W, X), implies(Z, X))))
% 0.20/0.49
% 0.20/0.49 Lemma 6: is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))) = true.
% 0.20/0.49 Proof:
% 0.20/0.49 is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.49 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.49 fresh(true, true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.49 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.49 fresh(fresh2(true, true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.49 = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.49 fresh(fresh2(is_a_theorem(implies(implies(implies(Y, W), implies(Z, X)), implies(V, implies(implies(X, Y), implies(Z, Y))))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.49 = { by lemma 5 }
% 0.20/0.49 fresh(is_a_theorem(implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.49 = { by axiom 3 (condensed_detachment) }
% 0.20/0.49 fresh2(is_a_theorem(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U))))), true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.49 = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.49 fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W))))
% 0.20/0.49 = { by axiom 1 (condensed_detachment) }
% 0.20/0.49 true
% 0.20/0.49
% 0.20/0.49 Lemma 7: fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W))), true, implies(V, implies(Y, W))) = is_a_theorem(implies(V, implies(Y, W))).
% 0.20/0.49 Proof:
% 0.20/0.49 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W))), true, implies(V, implies(Y, W)))
% 0.20/0.49 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.49 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))), true, implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))
% 0.20/0.49 = { by lemma 6 }
% 0.20/0.49 fresh(true, true, implies(implies(implies(X, Y), implies(Z, Y)), implies(Y, W)), implies(V, implies(Y, W)))
% 0.20/0.49 = { by axiom 2 (condensed_detachment) }
% 0.20/0.49 is_a_theorem(implies(V, implies(Y, W)))
% 0.20/0.49
% 0.20/0.49 Lemma 8: is_a_theorem(implies(implies(implies(X, Y), X), implies(Y, X))) = true.
% 0.20/0.49 Proof:
% 0.20/0.49 is_a_theorem(implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.49 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.49 fresh(true, true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.49 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.49 fresh(fresh2(true, true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.49 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.49 fresh(fresh2(fresh2(true, true, implies(implies(X, Y), implies(Y, implies(X, Y)))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.49 = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.50 fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S))))), true, implies(implies(X, Y), implies(Y, implies(X, Y)))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.50 fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S)))), implies(implies(X, Y), implies(Y, implies(X, Y)))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by lemma 7 R->L }
% 0.20/0.50 fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(V2, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S)))), implies(implies(X, Y), implies(Y, implies(X, Y)))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by lemma 6 }
% 0.20/0.50 fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S)))), implies(implies(X, Y), implies(Y, implies(X, Y)))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by axiom 1 (condensed_detachment) }
% 0.20/0.50 fresh(fresh2(fresh(true, true, implies(implies(implies(S, X2), implies(Y2, Z2)), implies(W2, implies(implies(Z2, S), implies(Y2, S)))), implies(implies(X, Y), implies(Y, implies(X, Y)))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by axiom 2 (condensed_detachment) }
% 0.20/0.50 fresh(fresh2(is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true, implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by lemma 5 }
% 0.20/0.50 fresh(is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))), true, implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by axiom 3 (condensed_detachment) }
% 0.20/0.50 fresh2(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.50 fresh2(true, true, implies(implies(implies(X, Y), X), implies(Y, X)))
% 0.20/0.50 = { by axiom 1 (condensed_detachment) }
% 0.20/0.50 true
% 0.20/0.50
% 0.20/0.50 Goal 1 (prove_ic_1): is_a_theorem(implies(a, a)) = true.
% 0.20/0.50 Proof:
% 0.20/0.50 is_a_theorem(implies(a, a))
% 0.20/0.50 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.50 fresh(true, true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.50 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.50 fresh(fresh2(true, true, implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.50 = { by lemma 8 R->L }
% 0.20/0.50 fresh(fresh2(is_a_theorem(implies(implies(implies(a, a), a), implies(a, a))), true, implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.50 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.50 fresh(fresh(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.50 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.50 fresh(fresh(fresh(true, true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.50 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.50 fresh(fresh(fresh(fresh2(true, true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.50 = { by axiom 1 (condensed_detachment) R->L }
% 0.20/0.50 fresh(fresh(fresh(fresh2(fresh2(true, true, implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 4 (ic_JLukasiewicz_4) R->L }
% 0.20/0.51 fresh(fresh(fresh(fresh2(fresh2(is_a_theorem(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2))))), true, implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 3 (condensed_detachment) R->L }
% 0.20/0.51 fresh(fresh(fresh(fresh2(fresh(is_a_theorem(implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2)))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2)))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by lemma 7 R->L }
% 0.20/0.51 fresh(fresh(fresh(fresh2(fresh(fresh2(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)), implies(implies(a, a), a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a))))), true, implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2)))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2)))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by lemma 8 }
% 0.20/0.51 fresh(fresh(fresh(fresh2(fresh(fresh2(true, true, implies(implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2)))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a))))), true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2)))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 1 (condensed_detachment) }
% 0.20/0.51 fresh(fresh(fresh(fresh2(fresh(true, true, implies(implies(implies(Z2, W2), implies(V2, U2)), implies(T2, implies(implies(U2, Z2), implies(V2, Z2)))), implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 2 (condensed_detachment) }
% 0.20/0.51 fresh(fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(implies(a, a), a)))), true, implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by lemma 5 }
% 0.20/0.51 fresh(fresh(fresh(is_a_theorem(implies(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))))), true, implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U)))), implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 3 (condensed_detachment) }
% 0.20/0.51 fresh(fresh(fresh2(is_a_theorem(implies(implies(implies(U, T), implies(S, X2)), implies(Y2, implies(implies(X2, U), implies(S, U))))), true, implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.51 fresh(fresh(fresh2(true, true, implies(implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a)))), true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 1 (condensed_detachment) }
% 0.20/0.51 fresh(fresh(true, true, implies(implies(implies(a, a), a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 2 (condensed_detachment) }
% 0.20/0.51 fresh(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))), true, implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X)))), implies(a, a))
% 0.20/0.51 = { by axiom 3 (condensed_detachment) }
% 0.20/0.51 fresh2(is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))), true, implies(a, a))
% 0.20/0.51 = { by axiom 4 (ic_JLukasiewicz_4) }
% 0.20/0.51 fresh2(true, true, implies(a, a))
% 0.20/0.51 = { by axiom 1 (condensed_detachment) }
% 0.20/0.51 true
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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