%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL265-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:31 AM UTC 2026
% Result : Unsatisfiable 28.76s 4.14s
% Output : Proof 34.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL265-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:34:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.76/4.14 Command-line arguments: --flatten-regeneralise
% 28.76/4.14
% 28.76/4.14 % SZS status Unsatisfiable
% 28.76/4.14
% 33.05/4.61 % SZS output start Proof
% 33.05/4.61 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 33.05/4.61 Axiom 2 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 33.05/4.61 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 33.05/4.61 Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 33.05/4.61 Axiom 5 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 33.05/4.61 Axiom 6 (equivalent_defn): equivalent(X, Y) = and(implies(X, Y), implies(Y, X)).
% 33.05/4.61 Axiom 7 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 33.05/4.61 Axiom 8 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 33.05/4.61 Axiom 9 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 33.05/4.61 Axiom 10 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 33.05/4.63 Axiom 11 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 33.05/4.63
% 33.05/4.63 Goal 1 (prove_this): theorem(equivalent(p, not(not(p)))) = true.
% 33.05/4.63 Proof:
% 33.05/4.63 theorem(equivalent(p, not(not(p))))
% 33.05/4.63 = { by axiom 3 (ifeq_axiom) R->L }
% 33.05/4.63 ifeq(true, true, theorem(equivalent(p, not(not(p)))), true)
% 33.05/4.63 = { by axiom 3 (ifeq_axiom) R->L }
% 33.05/4.63 ifeq(true, true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 11 (rule_2) R->L }
% 33.05/4.63 ifeq(ifeq(theorem(implies(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p))), or(not(implies(not(not(p)), p)), equivalent(p, not(not(p)))))), true, ifeq(theorem(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 3 (ifeq_axiom) R->L }
% 33.05/4.63 ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p))), or(not(implies(not(not(p)), p)), equivalent(p, not(not(p)))))), true), true, ifeq(theorem(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 8 (axiom_1_4) R->L }
% 33.05/4.63 ifeq(ifeq(ifeq(axiom(implies(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p))), or(not(implies(not(not(p)), p)), equivalent(p, not(not(p)))))), true, theorem(implies(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p))), or(not(implies(not(not(p)), p)), equivalent(p, not(not(p)))))), true), true, ifeq(theorem(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 7 (rule_1) }
% 33.05/4.63 ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 3 (ifeq_axiom) }
% 33.05/4.63 ifeq(ifeq(theorem(or(equivalent(p, not(not(p))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 6 (equivalent_defn) }
% 33.05/4.63 ifeq(ifeq(theorem(or(and(implies(p, not(not(p))), implies(not(not(p)), p)), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 2 (and_defn) }
% 33.05/4.63 ifeq(ifeq(theorem(or(not(or(not(implies(p, not(not(p)))), not(implies(not(not(p)), p)))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 1 (implies_definition) R->L }
% 33.05/4.63 ifeq(ifeq(theorem(or(not(implies(implies(p, not(not(p))), not(implies(not(not(p)), p)))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.63 = { by axiom 1 (implies_definition) R->L }
% 33.05/4.63 ifeq(ifeq(theorem(implies(implies(implies(p, not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.64 = { by axiom 1 (implies_definition) }
% 33.05/4.64 ifeq(ifeq(theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.64 = { by axiom 3 (ifeq_axiom) R->L }
% 33.05/4.64 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.64 = { by axiom 11 (rule_2) R->L }
% 33.05/4.64 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.65 = { by axiom 3 (ifeq_axiom) R->L }
% 33.05/4.65 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(true, true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.65 = { by axiom 11 (rule_2) R->L }
% 33.05/4.65 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, ifeq(theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.66 = { by axiom 3 (ifeq_axiom) R->L }
% 33.05/4.66 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, ifeq(ifeq(true, true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.66 = { by axiom 4 (axiom_1_3) R->L }
% 33.05/4.66 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, ifeq(ifeq(axiom(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.67 = { by axiom 7 (rule_1) }
% 33.05/4.67 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, ifeq(true, true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.68 = { by axiom 3 (ifeq_axiom) }
% 33.05/4.68 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.69 = { by axiom 3 (ifeq_axiom) R->L }
% 33.05/4.69 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.69 = { by axiom 10 (axiom_1_5) R->L }
% 33.05/4.69 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), or(not(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.69 = { by axiom 1 (implies_definition) R->L }
% 33.05/4.70 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), or(not(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.05/4.70 = { by axiom 1 (implies_definition) R->L }
% 33.05/4.70 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))))), true), true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.70 = { by axiom 7 (rule_1) }
% 33.83/4.70 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.71 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.71 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.71 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.71 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.71 = { by axiom 7 (rule_1) R->L }
% 33.83/4.72 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(axiom(implies(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(implies(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, ifeq(theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.72 = { by axiom 5 (axiom_1_2) }
% 33.83/4.72 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true), true, ifeq(theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.72 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.72 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(ifeq(theorem(implies(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, ifeq(theorem(or(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.73 = { by axiom 11 (rule_2) }
% 33.83/4.73 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, ifeq(true, true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.73 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.73 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.73 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.73 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.73 = { by axiom 10 (axiom_1_5) R->L }
% 33.83/4.73 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), or(not(or(not(p), not(not(p)))), not(implies(not(not(p)), p)))), or(not(or(not(p), not(not(p)))), or(not(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.73 = { by axiom 1 (implies_definition) R->L }
% 33.83/4.73 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(not(or(not(p), not(not(p)))), not(implies(not(not(p)), p)))), or(not(or(not(p), not(not(p)))), or(not(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 1 (implies_definition) R->L }
% 33.83/4.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), or(not(or(not(p), not(not(p)))), not(implies(not(not(p)), p)))), or(not(or(not(p), not(not(p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 1 (implies_definition) R->L }
% 33.83/4.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), or(not(or(not(p), not(not(p)))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 1 (implies_definition) R->L }
% 33.83/4.74 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true, theorem(implies(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), implies(or(not(p), not(not(p))), not(implies(not(not(p)), p)))), implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))))), true), true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 7 (rule_1) }
% 33.83/4.74 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.74 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.74 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(true, true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 11 (rule_2) R->L }
% 33.83/4.74 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(theorem(implies(implies(not(p), not(p)), or(not(p), not(not(p))))), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 1 (implies_definition) }
% 33.83/4.74 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.74 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 8 (axiom_1_4) R->L }
% 33.83/4.74 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true, theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.74 = { by axiom 7 (rule_1) }
% 33.83/4.74 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.75 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.75 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.75 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.75 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.75 = { by axiom 11 (rule_2) R->L }
% 33.83/4.75 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(theorem(implies(not(p), or(implies(not(p), not(p)), not(p)))), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.75 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.75 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(ifeq(true, true, theorem(implies(not(p), or(implies(not(p), not(p)), not(p)))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.75 = { by axiom 4 (axiom_1_3) R->L }
% 33.83/4.75 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(ifeq(axiom(implies(not(p), or(implies(not(p), not(p)), not(p)))), true, theorem(implies(not(p), or(implies(not(p), not(p)), not(p)))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.75 = { by axiom 7 (rule_1) }
% 33.83/4.75 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(true, true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.75 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.75 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 10 (axiom_1_5) R->L }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(p)), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), or(not(not(p)), not(p))))), true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 1 (implies_definition) R->L }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), or(not(not(p)), not(p))))), true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 1 (implies_definition) R->L }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 7 (rule_1) }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.76 = { by axiom 7 (rule_1) R->L }
% 33.83/4.76 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true, theorem(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true), true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 5 (axiom_1_2) }
% 33.83/4.77 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true), true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.77 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 11 (rule_2) }
% 33.83/4.77 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(ifeq(true, true, theorem(or(not(p), not(not(p)))), true), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.77 ifeq(ifeq(ifeq(theorem(implies(or(not(p), not(not(p))), implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p))))), true, ifeq(theorem(or(not(p), not(not(p)))), true, theorem(implies(implies(or(not(p), not(not(p))), not(implies(not(not(p)), p))), not(implies(not(not(p)), p)))), true), true), true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 11 (rule_2) }
% 33.83/4.77 ifeq(ifeq(true, true, theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.77 ifeq(theorem(or(not(implies(not(not(p)), p)), equivalent(p, not(not(p))))), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 1 (implies_definition) R->L }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(true, true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 11 (rule_2) R->L }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(theorem(implies(or(p, not(not(not(p)))), or(not(not(not(p))), p))), true, ifeq(theorem(or(p, not(not(not(p))))), true, theorem(or(not(not(not(p))), p)), true), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, not(not(not(p)))), or(not(not(not(p))), p))), true), true, ifeq(theorem(or(p, not(not(not(p))))), true, theorem(or(not(not(not(p))), p)), true), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 8 (axiom_1_4) R->L }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(axiom(implies(or(p, not(not(not(p)))), or(not(not(not(p))), p))), true, theorem(implies(or(p, not(not(not(p)))), or(not(not(not(p))), p))), true), true, ifeq(theorem(or(p, not(not(not(p))))), true, theorem(or(not(not(not(p))), p)), true), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 7 (rule_1) }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(p, not(not(not(p))))), true, theorem(or(not(not(not(p))), p)), true), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(theorem(or(p, not(not(not(p))))), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 11 (rule_2) R->L }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(theorem(implies(not(p), not(not(not(p))))), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 1 (implies_definition) }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(theorem(or(not(not(p)), not(not(not(p))))), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.77 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.77 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(true, true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.78 = { by axiom 11 (rule_2) R->L }
% 33.83/4.78 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))), implies(not(not(p)), not(not(p))))), true, ifeq(theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true, theorem(implies(not(not(p)), not(not(p)))), true), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.78 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.78 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))), implies(not(not(p)), not(not(p))))), true), true, ifeq(theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true, theorem(implies(not(not(p)), not(not(p)))), true), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.78 = { by axiom 5 (axiom_1_2) R->L }
% 33.83/4.78 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))), implies(not(not(p)), not(not(p))))), true, theorem(implies(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))), implies(not(not(p)), not(not(p))))), true), true, ifeq(theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true, theorem(implies(not(not(p)), not(not(p)))), true), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.78 = { by axiom 7 (rule_1) }
% 33.83/4.78 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true, theorem(implies(not(not(p)), not(not(p)))), true), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.78 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.78 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.78 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.78 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.78 = { by axiom 7 (rule_1) R->L }
% 33.83/4.79 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true, theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.79 = { by axiom 1 (implies_definition) }
% 33.83/4.79 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), or(not(not(not(p))), not(not(p)))))), true, theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.79 = { by axiom 1 (implies_definition) }
% 33.83/4.79 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(not(p))), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), or(not(not(not(p))), not(not(p)))))), true, theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.79 = { by axiom 10 (axiom_1_5) }
% 33.83/4.79 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.79 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.79 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.79 = { by axiom 3 (ifeq_axiom) R->L }
% 33.83/4.79 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true, ifeq(true, true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.80 = { by axiom 7 (rule_1) R->L }
% 33.83/4.80 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true, ifeq(ifeq(axiom(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p))))), true, theorem(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p))))), true), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.80 = { by axiom 4 (axiom_1_3) }
% 33.83/4.80 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true, ifeq(ifeq(true, true, theorem(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p))))), true), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.80 = { by axiom 3 (ifeq_axiom) }
% 33.83/4.80 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p)))), or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p)))))), true, ifeq(theorem(implies(not(not(p)), or(implies(not(not(p)), not(not(p))), not(not(p))))), true, theorem(or(implies(not(not(p)), not(not(p))), implies(not(not(p)), not(not(p))))), true), true), true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.80 = { by axiom 11 (rule_2) }
% 33.83/4.80 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(not(not(p)), not(not(p)))), true), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 33.83/4.80 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.80 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(theorem(implies(not(not(p)), not(not(p)))), true, theorem(or(not(not(p)), not(not(not(p))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.80 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.80 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(not(not(p)), not(not(p)))), true, theorem(or(not(not(p)), not(not(not(p))))), true), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.80 = { by axiom 7 (rule_1) R->L }
% 34.62/4.80 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(not(not(p))), not(not(p))), or(not(not(p)), not(not(not(p)))))), true, theorem(implies(or(not(not(not(p))), not(not(p))), or(not(not(p)), not(not(not(p)))))), true), true, ifeq(theorem(implies(not(not(p)), not(not(p)))), true, theorem(or(not(not(p)), not(not(not(p))))), true), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.80 = { by axiom 8 (axiom_1_4) }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(not(p))), not(not(p))), or(not(not(p)), not(not(not(p)))))), true), true, ifeq(theorem(implies(not(not(p)), not(not(p)))), true, theorem(or(not(not(p)), not(not(not(p))))), true), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(theorem(implies(or(not(not(not(p))), not(not(p))), or(not(not(p)), not(not(not(p)))))), true, ifeq(theorem(implies(not(not(p)), not(not(p)))), true, theorem(or(not(not(p)), not(not(not(p))))), true), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 1 (implies_definition) R->L }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(ifeq(theorem(implies(implies(not(not(p)), not(not(p))), or(not(not(p)), not(not(not(p)))))), true, ifeq(theorem(implies(not(not(p)), not(not(p)))), true, theorem(or(not(not(p)), not(not(not(p))))), true), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 11 (rule_2) }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, ifeq(true, true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 9 (axiom_1_6) R->L }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true, theorem(implies(implies(not(p), not(not(not(p)))), implies(or(p, not(p)), or(p, not(not(not(p))))))), true), true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 7 (rule_1) }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, theorem(or(p, not(not(not(p))))), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(true, true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 11 (rule_2) R->L }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(theorem(implies(implies(p, p), or(p, not(p)))), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 1 (implies_definition) }
% 34.62/4.81 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(theorem(implies(or(not(p), p), or(p, not(p)))), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.81 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(p), p), or(p, not(p)))), true), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 8 (axiom_1_4) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(p), p), or(p, not(p)))), true, theorem(implies(or(not(p), p), or(p, not(p)))), true), true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 7 (rule_1) }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(theorem(implies(p, p)), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 11 (rule_2) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(theorem(implies(p, or(implies(p, p), p))), true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(ifeq(true, true, theorem(implies(p, or(implies(p, p), p))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 4 (axiom_1_3) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(ifeq(axiom(implies(p, or(implies(p, p), p))), true, theorem(implies(p, or(implies(p, p), p))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 7 (rule_1) }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, ifeq(true, true, theorem(or(implies(p, p), implies(p, p))), true), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 10 (axiom_1_5) R->L }
% 34.62/4.82 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(p), or(implies(p, p), p)), or(implies(p, p), or(not(p), p)))), true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.82 = { by axiom 1 (implies_definition) R->L }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), or(not(p), p)))), true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 1 (implies_definition) R->L }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true, theorem(implies(implies(p, or(implies(p, p), p)), or(implies(p, p), implies(p, p)))), true), true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 7 (rule_1) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(p, p), implies(p, p))), true), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 3 (ifeq_axiom) R->L }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 7 (rule_1) R->L }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true, theorem(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true), true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 5 (axiom_1_2) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true), true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(p, p), implies(p, p)), implies(p, p))), true, ifeq(theorem(or(implies(p, p), implies(p, p))), true, theorem(implies(p, p)), true), true), true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 11 (rule_2) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(ifeq(true, true, theorem(or(p, not(p))), true), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(p, not(p)), or(p, not(not(not(p)))))), true, ifeq(theorem(or(p, not(p))), true, theorem(or(p, not(not(not(p))))), true), true), true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 11 (rule_2) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(ifeq(true, true, theorem(or(not(not(not(p))), p)), true), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 3 (ifeq_axiom) }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(theorem(or(not(not(not(p))), p)), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 1 (implies_definition) R->L }
% 34.62/4.83 ifeq(theorem(implies(implies(not(not(p)), p), equivalent(p, not(not(p))))), true, ifeq(theorem(implies(not(not(p)), p)), true, theorem(equivalent(p, not(not(p)))), true), true)
% 34.62/4.83 = { by axiom 11 (rule_2) }
% 34.62/4.83 true
% 34.62/4.83 % SZS output end Proof
% 34.62/4.83
% 34.62/4.83 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------