TSTP Solution File: LCL517+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL517+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n017.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 08:19:17 EDT 2023
% Result : Theorem 0.19s 0.74s
% Output : Proof 3.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL517+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 17:14:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.74 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.74
% 0.19/0.74 % SZS status Theorem
% 0.19/0.74
% 3.24/0.81 % SZS output start Proof
% 3.24/0.81 Take the following subset of the input axioms:
% 3.54/0.81 fof(and_1, axiom, and_1 <=> ![X, Y]: is_a_theorem(implies(and(X, Y), X))).
% 3.54/0.81 fof(cn3, axiom, cn3 <=> ![P]: is_a_theorem(implies(implies(not(P), P), P))).
% 3.54/0.81 fof(kn1, axiom, kn1 <=> ![P2]: is_a_theorem(implies(P2, and(P2, P2)))).
% 3.54/0.81 fof(kn2, axiom, kn2 <=> ![Q, P2]: is_a_theorem(implies(and(P2, Q), P2))).
% 3.54/0.81 fof(kn3, axiom, kn3 <=> ![R, P2, Q2]: is_a_theorem(implies(implies(P2, Q2), implies(not(and(Q2, R)), not(and(R, P2)))))).
% 3.54/0.81 fof(luka_cn3, conjecture, cn3).
% 3.54/0.81 fof(modus_ponens, axiom, modus_ponens <=> ![X2, Y2]: ((is_a_theorem(X2) & is_a_theorem(implies(X2, Y2))) => is_a_theorem(Y2))).
% 3.54/0.81 fof(op_equiv, axiom, op_equiv => ![X2, Y2]: equiv(X2, Y2)=and(implies(X2, Y2), implies(Y2, X2))).
% 3.54/0.81 fof(op_implies_and, axiom, op_implies_and => ![X2, Y2]: implies(X2, Y2)=not(and(X2, not(Y2)))).
% 3.54/0.81 fof(op_or, axiom, op_or => ![X2, Y2]: or(X2, Y2)=not(and(not(X2), not(Y2)))).
% 3.54/0.81 fof(rosser_kn1, axiom, kn1).
% 3.54/0.81 fof(rosser_kn2, axiom, kn2).
% 3.54/0.81 fof(rosser_kn3, axiom, kn3).
% 3.54/0.81 fof(rosser_modus_ponens, axiom, modus_ponens).
% 3.54/0.81 fof(rosser_op_equiv, axiom, op_equiv).
% 3.54/0.81 fof(rosser_op_implies_and, axiom, op_implies_and).
% 3.54/0.81 fof(rosser_op_or, axiom, op_or).
% 3.54/0.81
% 3.54/0.81 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.54/0.81 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.54/0.81 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.54/0.81 fresh(y, y, x1...xn) = u
% 3.54/0.81 C => fresh(s, t, x1...xn) = v
% 3.54/0.81 where fresh is a fresh function symbol and x1..xn are the free
% 3.54/0.81 variables of u and v.
% 3.54/0.81 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.54/0.81 input problem has no model of domain size 1).
% 3.54/0.81
% 3.54/0.81 The encoding turns the above axioms into the following unit equations and goals:
% 3.54/0.81
% 3.54/0.81 Axiom 1 (rosser_modus_ponens): modus_ponens = true.
% 3.54/0.81 Axiom 2 (rosser_kn1): kn1 = true.
% 3.54/0.81 Axiom 3 (rosser_kn2): kn2 = true.
% 3.54/0.81 Axiom 4 (rosser_kn3): kn3 = true.
% 3.54/0.81 Axiom 5 (rosser_op_or): op_or = true.
% 3.54/0.81 Axiom 6 (rosser_op_equiv): op_equiv = true.
% 3.54/0.81 Axiom 7 (rosser_op_implies_and): op_implies_and = true.
% 3.54/0.81 Axiom 8 (and_1): fresh57(X, X) = true.
% 3.54/0.81 Axiom 9 (cn3): fresh48(X, X) = true.
% 3.54/0.81 Axiom 10 (modus_ponens_2): fresh60(X, X, Y) = true.
% 3.54/0.81 Axiom 11 (kn1_1): fresh33(X, X, Y) = true.
% 3.54/0.81 Axiom 12 (modus_ponens_2): fresh28(X, X, Y) = is_a_theorem(Y).
% 3.54/0.81 Axiom 13 (kn1_1): fresh33(kn1, true, X) = is_a_theorem(implies(X, and(X, X))).
% 3.54/0.81 Axiom 14 (modus_ponens_2): fresh59(X, X, Y, Z) = fresh60(modus_ponens, true, Z).
% 3.54/0.81 Axiom 15 (and_1_1): fresh58(X, X, Y, Z) = true.
% 3.54/0.81 Axiom 16 (and_1_1): fresh58(and_1, true, X, Y) = is_a_theorem(implies(and(X, Y), X)).
% 3.54/0.81 Axiom 17 (kn2_1): fresh31(X, X, Y, Z) = true.
% 3.54/0.81 Axiom 18 (kn2_1): fresh31(kn2, true, X, Y) = is_a_theorem(implies(and(X, Y), X)).
% 3.54/0.81 Axiom 19 (op_equiv): fresh23(X, X, Y, Z) = equiv(Y, Z).
% 3.54/0.81 Axiom 20 (op_equiv): fresh23(op_equiv, true, X, Y) = and(implies(X, Y), implies(Y, X)).
% 3.54/0.81 Axiom 21 (op_implies_and): fresh22(X, X, Y, Z) = implies(Y, Z).
% 3.54/0.81 Axiom 22 (op_implies_and): fresh22(op_implies_and, true, X, Y) = not(and(X, not(Y))).
% 3.54/0.81 Axiom 23 (op_or): fresh20(X, X, Y, Z) = or(Y, Z).
% 3.54/0.81 Axiom 24 (op_or): fresh20(op_or, true, X, Y) = not(and(not(X), not(Y))).
% 3.54/0.81 Axiom 25 (and_1): fresh57(is_a_theorem(implies(and(x9, y9), x9)), true) = and_1.
% 3.54/0.81 Axiom 26 (kn3_1): fresh29(X, X, Y, Z, W) = true.
% 3.54/0.81 Axiom 27 (modus_ponens_2): fresh59(is_a_theorem(implies(X, Y)), true, X, Y) = fresh28(is_a_theorem(X), true, Y).
% 3.54/0.81 Axiom 28 (cn3): fresh48(is_a_theorem(implies(implies(not(p6), p6), p6)), true) = cn3.
% 3.54/0.81 Axiom 29 (kn3_1): fresh29(kn3, true, X, Y, Z) = is_a_theorem(implies(implies(X, Y), implies(not(and(Y, Z)), not(and(Z, X))))).
% 3.54/0.81
% 3.54/0.81 Lemma 30: and_1 = true.
% 3.54/0.81 Proof:
% 3.54/0.81 and_1
% 3.54/0.81 = { by axiom 25 (and_1) R->L }
% 3.54/0.81 fresh57(is_a_theorem(implies(and(x9, y9), x9)), true)
% 3.54/0.81 = { by axiom 18 (kn2_1) R->L }
% 3.54/0.81 fresh57(fresh31(kn2, true, x9, y9), true)
% 3.54/0.81 = { by axiom 3 (rosser_kn2) }
% 3.54/0.81 fresh57(fresh31(true, true, x9, y9), true)
% 3.54/0.81 = { by axiom 17 (kn2_1) }
% 3.54/0.81 fresh57(true, true)
% 3.54/0.81 = { by axiom 8 (and_1) }
% 3.54/0.81 true
% 3.54/0.81
% 3.54/0.81 Lemma 31: not(and(X, not(Y))) = implies(X, Y).
% 3.54/0.81 Proof:
% 3.54/0.81 not(and(X, not(Y)))
% 3.54/0.81 = { by axiom 22 (op_implies_and) R->L }
% 3.54/0.81 fresh22(op_implies_and, true, X, Y)
% 3.54/0.81 = { by axiom 7 (rosser_op_implies_and) }
% 3.54/0.81 fresh22(true, true, X, Y)
% 3.54/0.81 = { by axiom 21 (op_implies_and) }
% 3.54/0.81 implies(X, Y)
% 3.54/0.81
% 3.54/0.81 Lemma 32: implies(not(X), Y) = or(X, Y).
% 3.54/0.81 Proof:
% 3.54/0.81 implies(not(X), Y)
% 3.54/0.81 = { by lemma 31 R->L }
% 3.54/0.81 not(and(not(X), not(Y)))
% 3.54/0.81 = { by axiom 24 (op_or) R->L }
% 3.54/0.81 fresh20(op_or, true, X, Y)
% 3.54/0.81 = { by axiom 5 (rosser_op_or) }
% 3.54/0.81 fresh20(true, true, X, Y)
% 3.54/0.81 = { by axiom 23 (op_or) }
% 3.54/0.81 or(X, Y)
% 3.54/0.81
% 3.54/0.81 Lemma 33: fresh59(X, X, Y, Z) = true.
% 3.54/0.81 Proof:
% 3.54/0.81 fresh59(X, X, Y, Z)
% 3.54/0.81 = { by axiom 14 (modus_ponens_2) }
% 3.54/0.81 fresh60(modus_ponens, true, Z)
% 3.54/0.81 = { by axiom 1 (rosser_modus_ponens) }
% 3.54/0.81 fresh60(true, true, Z)
% 3.54/0.81 = { by axiom 10 (modus_ponens_2) }
% 3.54/0.81 true
% 3.54/0.82
% 3.54/0.82 Lemma 34: is_a_theorem(implies(X, and(X, X))) = true.
% 3.54/0.82 Proof:
% 3.54/0.82 is_a_theorem(implies(X, and(X, X)))
% 3.54/0.82 = { by axiom 13 (kn1_1) R->L }
% 3.54/0.82 fresh33(kn1, true, X)
% 3.54/0.82 = { by axiom 2 (rosser_kn1) }
% 3.54/0.82 fresh33(true, true, X)
% 3.54/0.82 = { by axiom 11 (kn1_1) }
% 3.54/0.82 true
% 3.54/0.82
% 3.54/0.82 Lemma 35: or(and(X, not(Y)), Z) = implies(implies(X, Y), Z).
% 3.54/0.82 Proof:
% 3.54/0.82 or(and(X, not(Y)), Z)
% 3.54/0.82 = { by lemma 32 R->L }
% 3.54/0.82 implies(not(and(X, not(Y))), Z)
% 3.54/0.82 = { by lemma 31 }
% 3.54/0.82 implies(implies(X, Y), Z)
% 3.54/0.82
% 3.54/0.82 Lemma 36: is_a_theorem(implies(implies(X, Y), or(and(Y, Z), not(and(Z, X))))) = true.
% 3.54/0.82 Proof:
% 3.54/0.82 is_a_theorem(implies(implies(X, Y), or(and(Y, Z), not(and(Z, X)))))
% 3.54/0.82 = { by lemma 32 R->L }
% 3.54/0.82 is_a_theorem(implies(implies(X, Y), implies(not(and(Y, Z)), not(and(Z, X)))))
% 3.54/0.82 = { by axiom 29 (kn3_1) R->L }
% 3.54/0.82 fresh29(kn3, true, X, Y, Z)
% 3.54/0.82 = { by axiom 4 (rosser_kn3) }
% 3.54/0.82 fresh29(true, true, X, Y, Z)
% 3.54/0.82 = { by axiom 26 (kn3_1) }
% 3.54/0.82 true
% 3.54/0.82
% 3.54/0.82 Lemma 37: is_a_theorem(implies(or(X, Y), or(and(Y, Z), implies(Z, X)))) = true.
% 3.54/0.82 Proof:
% 3.54/0.82 is_a_theorem(implies(or(X, Y), or(and(Y, Z), implies(Z, X))))
% 3.54/0.82 = { by lemma 32 R->L }
% 3.54/0.82 is_a_theorem(implies(implies(not(X), Y), or(and(Y, Z), implies(Z, X))))
% 3.54/0.82 = { by lemma 31 R->L }
% 3.54/0.82 is_a_theorem(implies(implies(not(X), Y), or(and(Y, Z), not(and(Z, not(X))))))
% 3.54/0.82 = { by lemma 36 }
% 3.54/0.82 true
% 3.54/0.82
% 3.54/0.82 Lemma 38: fresh28(is_a_theorem(or(X, Y)), true, implies(implies(Y, Z), or(Z, X))) = true.
% 3.54/0.82 Proof:
% 3.54/0.82 fresh28(is_a_theorem(or(X, Y)), true, implies(implies(Y, Z), or(Z, X)))
% 3.54/0.82 = { by axiom 27 (modus_ponens_2) R->L }
% 3.54/0.82 fresh59(is_a_theorem(implies(or(X, Y), implies(implies(Y, Z), or(Z, X)))), true, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 3.54/0.82 = { by lemma 35 R->L }
% 3.54/0.82 fresh59(is_a_theorem(implies(or(X, Y), or(and(Y, not(Z)), or(Z, X)))), true, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 3.54/0.82 = { by lemma 32 R->L }
% 3.54/0.82 fresh59(is_a_theorem(implies(or(X, Y), or(and(Y, not(Z)), implies(not(Z), X)))), true, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 3.54/0.82 = { by lemma 37 }
% 3.54/0.82 fresh59(true, true, or(X, Y), implies(implies(Y, Z), or(Z, X)))
% 3.54/0.82 = { by lemma 33 }
% 3.54/0.82 true
% 3.54/0.82
% 3.54/0.82 Lemma 39: fresh28(is_a_theorem(implies(X, Y)), true, or(Y, not(X))) = true.
% 3.54/0.82 Proof:
% 3.54/0.82 fresh28(is_a_theorem(implies(X, Y)), true, or(Y, not(X)))
% 3.54/0.82 = { by axiom 27 (modus_ponens_2) R->L }
% 3.54/0.82 fresh59(is_a_theorem(implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by axiom 12 (modus_ponens_2) R->L }
% 3.54/0.82 fresh59(fresh28(true, true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 33 R->L }
% 3.54/0.82 fresh59(fresh28(fresh59(true, true, implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 33 R->L }
% 3.54/0.82 fresh59(fresh28(fresh59(fresh59(true, true, implies(not(X), and(not(X), not(X))), implies(implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X))))), true, implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 36 R->L }
% 3.54/0.82 fresh59(fresh28(fresh59(fresh59(is_a_theorem(implies(implies(not(X), and(not(X), not(X))), or(and(and(not(X), not(X)), not(not(X))), not(and(not(not(X)), not(X)))))), true, implies(not(X), and(not(X), not(X))), implies(implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X))))), true, implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 35 }
% 3.54/0.82 fresh59(fresh28(fresh59(fresh59(is_a_theorem(implies(implies(not(X), and(not(X), not(X))), implies(implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))))), true, implies(not(X), and(not(X), not(X))), implies(implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X))))), true, implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by axiom 27 (modus_ponens_2) }
% 3.54/0.82 fresh59(fresh28(fresh59(fresh28(is_a_theorem(implies(not(X), and(not(X), not(X)))), true, implies(implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X))))), true, implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 34 }
% 3.54/0.82 fresh59(fresh28(fresh59(fresh28(true, true, implies(implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X))))), true, implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by axiom 12 (modus_ponens_2) }
% 3.54/0.82 fresh59(fresh28(fresh59(is_a_theorem(implies(implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X))))), true, implies(and(not(X), not(X)), not(X)), not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by axiom 27 (modus_ponens_2) }
% 3.54/0.82 fresh59(fresh28(fresh28(is_a_theorem(implies(and(not(X), not(X)), not(X))), true, not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by axiom 16 (and_1_1) R->L }
% 3.54/0.82 fresh59(fresh28(fresh28(fresh58(and_1, true, not(X), not(X)), true, not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 30 }
% 3.54/0.82 fresh59(fresh28(fresh28(fresh58(true, true, not(X), not(X)), true, not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by axiom 15 (and_1_1) }
% 3.54/0.82 fresh59(fresh28(fresh28(true, true, not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by axiom 12 (modus_ponens_2) }
% 3.54/0.82 fresh59(fresh28(is_a_theorem(not(and(not(not(X)), not(X)))), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 31 }
% 3.54/0.82 fresh59(fresh28(is_a_theorem(implies(not(not(X)), X)), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 32 }
% 3.54/0.82 fresh59(fresh28(is_a_theorem(or(not(X), X)), true, implies(implies(X, Y), or(Y, not(X)))), true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 38 }
% 3.54/0.82 fresh59(true, true, implies(X, Y), or(Y, not(X)))
% 3.54/0.82 = { by lemma 33 }
% 3.54/0.82 true
% 3.54/0.82
% 3.54/0.82 Lemma 40: is_a_theorem(or(X, not(and(X, Y)))) = true.
% 3.54/0.82 Proof:
% 3.54/0.83 is_a_theorem(or(X, not(and(X, Y))))
% 3.54/0.83 = { by axiom 12 (modus_ponens_2) R->L }
% 3.54/0.83 fresh28(true, true, or(X, not(and(X, Y))))
% 3.54/0.83 = { by axiom 15 (and_1_1) R->L }
% 3.54/0.83 fresh28(fresh58(true, true, X, Y), true, or(X, not(and(X, Y))))
% 3.54/0.83 = { by lemma 30 R->L }
% 3.54/0.83 fresh28(fresh58(and_1, true, X, Y), true, or(X, not(and(X, Y))))
% 3.54/0.83 = { by axiom 16 (and_1_1) }
% 3.54/0.83 fresh28(is_a_theorem(implies(and(X, Y), X)), true, or(X, not(and(X, Y))))
% 3.54/0.83 = { by lemma 39 }
% 3.54/0.83 true
% 3.54/0.83
% 3.54/0.83 Lemma 41: and(implies(X, Y), implies(Y, X)) = equiv(X, Y).
% 3.54/0.83 Proof:
% 3.54/0.83 and(implies(X, Y), implies(Y, X))
% 3.54/0.83 = { by axiom 20 (op_equiv) R->L }
% 3.54/0.83 fresh23(op_equiv, true, X, Y)
% 3.54/0.83 = { by axiom 6 (rosser_op_equiv) }
% 3.54/0.83 fresh23(true, true, X, Y)
% 3.54/0.83 = { by axiom 19 (op_equiv) }
% 3.54/0.83 equiv(X, Y)
% 3.54/0.83
% 3.54/0.83 Lemma 42: is_a_theorem(or(X, and(not(X), not(X)))) = true.
% 3.54/0.83 Proof:
% 3.54/0.83 is_a_theorem(or(X, and(not(X), not(X))))
% 3.54/0.83 = { by lemma 32 R->L }
% 3.54/0.83 is_a_theorem(implies(not(X), and(not(X), not(X))))
% 3.54/0.83 = { by lemma 34 }
% 3.54/0.83 true
% 3.54/0.83
% 3.54/0.83 Goal 1 (luka_cn3): cn3 = true.
% 3.54/0.83 Proof:
% 3.54/0.83 cn3
% 3.54/0.83 = { by axiom 28 (cn3) R->L }
% 3.54/0.83 fresh48(is_a_theorem(implies(implies(not(p6), p6), p6)), true)
% 3.54/0.83 = { by lemma 35 R->L }
% 3.54/0.83 fresh48(is_a_theorem(or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 12 (modus_ponens_2) R->L }
% 3.54/0.83 fresh48(fresh28(true, true, or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 42 R->L }
% 3.54/0.83 fresh48(fresh28(is_a_theorem(or(p6, and(not(p6), not(p6)))), true, or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 27 (modus_ponens_2) R->L }
% 3.54/0.83 fresh48(fresh59(is_a_theorem(implies(or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 32 R->L }
% 3.54/0.83 fresh48(fresh59(is_a_theorem(implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 12 (modus_ponens_2) R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(true, true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 33 R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh59(true, true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), implies(not(p6), not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 15 (and_1_1) R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh59(fresh58(true, true, implies(not(p6), not(p6)), implies(not(p6), not(p6))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), implies(not(p6), not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 30 R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh59(fresh58(and_1, true, implies(not(p6), not(p6)), implies(not(p6), not(p6))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), implies(not(p6), not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 16 (and_1_1) }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh59(is_a_theorem(implies(and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), implies(not(p6), not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 27 (modus_ponens_2) }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(is_a_theorem(and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, implies(not(p6), not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 41 }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(is_a_theorem(equiv(not(p6), not(p6))), true, implies(not(p6), not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 32 }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(is_a_theorem(equiv(not(p6), not(p6))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 41 R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(is_a_theorem(and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 12 (modus_ponens_2) R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(true, true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 33 R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh59(true, true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 38 R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh59(fresh28(is_a_theorem(or(implies(not(p6), not(p6)), not(and(implies(not(p6), not(p6)), not(p6))))), true, implies(implies(not(and(implies(not(p6), not(p6)), not(p6))), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 40 }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh59(fresh28(true, true, implies(implies(not(and(implies(not(p6), not(p6)), not(p6))), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 12 (modus_ponens_2) }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh59(is_a_theorem(implies(implies(not(and(implies(not(p6), not(p6)), not(p6))), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 32 }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh59(is_a_theorem(implies(or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6))), or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 27 (modus_ponens_2) }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh28(is_a_theorem(or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6)))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 12 (modus_ponens_2) R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(true, true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6)))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 40 R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(or(not(p6), not(and(not(p6), not(not(p6)))))), true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6)))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by lemma 31 }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh28(fresh28(is_a_theorem(or(not(p6), implies(not(p6), not(p6)))), true, or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6)))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.83 = { by axiom 27 (modus_ponens_2) R->L }
% 3.54/0.83 fresh48(fresh59(fresh28(fresh28(fresh28(fresh28(fresh59(is_a_theorem(implies(or(not(p6), implies(not(p6), not(p6))), or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6))))), true, or(not(p6), implies(not(p6), not(p6))), or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6)))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by lemma 37 }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh28(fresh28(fresh59(true, true, or(not(p6), implies(not(p6), not(p6))), or(and(implies(not(p6), not(p6)), not(p6)), implies(not(p6), not(p6)))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by lemma 33 }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh28(fresh28(true, true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by axiom 12 (modus_ponens_2) }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh28(is_a_theorem(or(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by axiom 27 (modus_ponens_2) R->L }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(is_a_theorem(implies(or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by lemma 32 R->L }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(is_a_theorem(implies(implies(not(implies(not(p6), not(p6))), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by lemma 35 R->L }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(is_a_theorem(or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by axiom 12 (modus_ponens_2) R->L }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh28(true, true, or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by lemma 42 R->L }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh28(is_a_theorem(or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))))), true, or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by axiom 27 (modus_ponens_2) R->L }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh59(is_a_theorem(implies(or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))))), true, or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by lemma 32 R->L }
% 3.54/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh59(is_a_theorem(implies(implies(not(implies(not(p6), not(p6))), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))))), true, or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.54/0.84 = { by axiom 12 (modus_ponens_2) R->L }
% 3.72/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh59(fresh28(true, true, implies(implies(not(implies(not(p6), not(p6))), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))))), true, or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by lemma 39 R->L }
% 3.72/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh59(fresh28(fresh28(is_a_theorem(implies(implies(not(p6), not(p6)), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), true, implies(implies(not(implies(not(p6), not(p6))), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))))), true, or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by lemma 34 }
% 3.72/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh59(fresh28(fresh28(true, true, or(and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), true, implies(implies(not(implies(not(p6), not(p6))), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))))), true, or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by axiom 12 (modus_ponens_2) }
% 3.72/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh59(fresh28(is_a_theorem(or(and(implies(not(p6), not(p6)), implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), true, implies(implies(not(implies(not(p6), not(p6))), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))))), true, or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by lemma 38 }
% 3.72/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(fresh59(true, true, or(implies(not(p6), not(p6)), and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6))))), or(and(not(implies(not(p6), not(p6))), not(implies(not(p6), not(p6)))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6))))), true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by lemma 33 }
% 3.72/0.84 fresh48(fresh59(fresh28(fresh28(fresh59(true, true, or(implies(not(p6), not(p6)), implies(not(p6), not(p6))), and(implies(not(p6), not(p6)), implies(not(p6), not(p6)))), true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by lemma 33 }
% 3.72/0.84 fresh48(fresh59(fresh28(fresh28(true, true, or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by axiom 12 (modus_ponens_2) }
% 3.72/0.84 fresh48(fresh59(fresh28(is_a_theorem(or(p6, not(p6))), true, implies(implies(not(p6), and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6))), true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by lemma 38 }
% 3.72/0.84 fresh48(fresh59(true, true, or(p6, and(not(p6), not(p6))), or(and(not(p6), not(p6)), p6)), true)
% 3.72/0.84 = { by lemma 33 }
% 3.72/0.84 fresh48(true, true)
% 3.72/0.84 = { by axiom 9 (cn3) }
% 3.72/0.84 true
% 3.72/0.84 % SZS output end Proof
% 3.72/0.84
% 3.72/0.84 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------