Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL269-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n012.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 85.89s 11.16s
% Output   : Proof 88.78s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : LCL269-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30  % Computer : n012.cluster.edu
% 0.03/0.30  % Model    : x86_64 x86_64
% 0.03/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30  % Memory   : 8046.5625MB
% 0.03/0.30  % OS       : Linux 6.8.0-71-generic
% 0.03/0.30  % CPULimit : 300
% 0.03/0.30  % WCLimit  : 300
% 0.03/0.30  % DateTime : Sun Sep 27 15:31:34 UTC 2026
% 0.03/0.30  % CPUTime  : 
% 0.03/0.30  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 85.89/11.16  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 85.89/11.16  
% 85.89/11.16  % SZS status Unsatisfiable
% 85.89/11.16  
% 87.99/11.45  % SZS output start Proof
% 87.99/11.45  Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 87.99/11.45  Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 87.99/11.45  Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 87.99/11.45  Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 87.99/11.45  Axiom 5 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 87.99/11.45  Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 87.99/11.45  Axiom 7 (equivalent_defn): equivalent(X, Y) = and(implies(X, Y), implies(Y, X)).
% 87.99/11.45  Axiom 8 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 87.99/11.45  Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 87.99/11.45  Axiom 10 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 87.99/11.45  Axiom 11 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 87.99/11.45  
% 87.99/11.45  Lemma 12: implies(implies(X, not(Y)), Z) = or(and(X, Y), Z).
% 87.99/11.45  Proof:
% 87.99/11.45    implies(implies(X, not(Y)), Z)
% 87.99/11.45  = { by axiom 1 (implies_definition) }
% 87.99/11.45    or(not(implies(X, not(Y))), Z)
% 87.99/11.45  = { by axiom 1 (implies_definition) }
% 87.99/11.45    or(not(or(not(X), not(Y))), Z)
% 87.99/11.45  = { by axiom 5 (and_defn) R->L }
% 87.99/11.46    or(and(X, Y), Z)
% 87.99/11.46  
% 87.99/11.46  Goal 1 (prove_this): theorem(equivalent(equivalent(p, q), equivalent(q, p))) = true.
% 87.99/11.46  Proof:
% 87.99/11.46    theorem(equivalent(equivalent(p, q), equivalent(q, p)))
% 87.99/11.46  = { by axiom 2 (ifeq_axiom) R->L }
% 87.99/11.46    ifeq(true, true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.46  = { by axiom 9 (rule_2) R->L }
% 87.99/11.46    ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(p, q))), or(not(equivalent(p, q)), equivalent(q, p)))), true, ifeq(theorem(or(equivalent(q, p), not(equivalent(p, q)))), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.46  = { by axiom 2 (ifeq_axiom) R->L }
% 87.99/11.46    ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(q, p), not(equivalent(p, q))), or(not(equivalent(p, q)), equivalent(q, p)))), true), true, ifeq(theorem(or(equivalent(q, p), not(equivalent(p, q)))), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.46  = { by axiom 8 (axiom_1_4) R->L }
% 87.99/11.46    ifeq(ifeq(ifeq(axiom(implies(or(equivalent(q, p), not(equivalent(p, q))), or(not(equivalent(p, q)), equivalent(q, p)))), true, theorem(implies(or(equivalent(q, p), not(equivalent(p, q))), or(not(equivalent(p, q)), equivalent(q, p)))), true), true, ifeq(theorem(or(equivalent(q, p), not(equivalent(p, q)))), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.46  = { by axiom 6 (rule_1) }
% 87.99/11.46    ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(q, p), not(equivalent(p, q)))), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.46  = { by axiom 2 (ifeq_axiom) }
% 87.99/11.46    ifeq(ifeq(theorem(or(equivalent(q, p), not(equivalent(p, q)))), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.46  = { by axiom 2 (ifeq_axiom) R->L }
% 87.99/11.46    ifeq(ifeq(ifeq(true, true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.46  = { by axiom 9 (rule_2) R->L }
% 87.99/11.46    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, ifeq(theorem(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by lemma 12 R->L }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, ifeq(theorem(implies(implies(implies(q, p), not(implies(p, q))), implies(implies(p, q), not(implies(q, p))))), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by axiom 1 (implies_definition) }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, ifeq(theorem(implies(implies(implies(q, p), not(implies(p, q))), or(not(implies(p, q)), not(implies(q, p))))), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by axiom 1 (implies_definition) }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, ifeq(theorem(implies(or(not(implies(q, p)), not(implies(p, q))), or(not(implies(p, q)), not(implies(q, p))))), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by axiom 2 (ifeq_axiom) R->L }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(implies(q, p)), not(implies(p, q))), or(not(implies(p, q)), not(implies(q, p))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by axiom 8 (axiom_1_4) R->L }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, ifeq(ifeq(axiom(implies(or(not(implies(q, p)), not(implies(p, q))), or(not(implies(p, q)), not(implies(q, p))))), true, theorem(implies(or(not(implies(q, p)), not(implies(p, q))), or(not(implies(p, q)), not(implies(q, p))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by axiom 6 (rule_1) }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, ifeq(true, true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by axiom 2 (ifeq_axiom) }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.47  = { by axiom 2 (ifeq_axiom) R->L }
% 87.99/11.47    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.48  = { by axiom 6 (rule_1) R->L }
% 87.99/11.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.48  = { by axiom 1 (implies_definition) }
% 87.99/11.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), or(not(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.48  = { by axiom 1 (implies_definition) }
% 87.99/11.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(not(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), or(not(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.48  = { by axiom 1 (implies_definition) }
% 87.99/11.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(not(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), or(not(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), or(not(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.48  = { by axiom 1 (implies_definition) }
% 87.99/11.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q)))), or(not(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), or(not(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p))))), or(not(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.49  = { by axiom 11 (axiom_1_5) }
% 87.99/11.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.49  = { by axiom 2 (ifeq_axiom) }
% 87.99/11.49    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.49  = { by axiom 2 (ifeq_axiom) R->L }
% 87.99/11.49    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, ifeq(true, true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.49  = { by axiom 6 (rule_1) R->L }
% 87.99/11.49    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.49  = { by axiom 10 (axiom_1_6) }
% 87.99/11.49    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 87.99/11.50  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.50    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))))), true, ifeq(theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true, theorem(implies(or(and(implies(q, p), implies(p, q)), implies(implies(p, q), not(implies(q, p)))), implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q)))))), true), true), true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 9 (rule_2) }
% 88.78/11.50    ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), not(implies(q, p))), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by lemma 12 }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 7 (equivalent_defn) R->L }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(and(implies(q, p), implies(p, q)), not(equivalent(p, q))))), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 7 (equivalent_defn) R->L }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(true, true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 9 (rule_2) R->L }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(theorem(implies(implies(equivalent(p, q), equivalent(p, q)), or(equivalent(p, q), not(equivalent(p, q))))), true, ifeq(theorem(implies(equivalent(p, q), equivalent(p, q))), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 1 (implies_definition) }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(theorem(implies(or(not(equivalent(p, q)), equivalent(p, q)), or(equivalent(p, q), not(equivalent(p, q))))), true, ifeq(theorem(implies(equivalent(p, q), equivalent(p, q))), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(equivalent(p, q)), equivalent(p, q)), or(equivalent(p, q), not(equivalent(p, q))))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(p, q))), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 8 (axiom_1_4) R->L }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(equivalent(p, q)), equivalent(p, q)), or(equivalent(p, q), not(equivalent(p, q))))), true, theorem(implies(or(not(equivalent(p, q)), equivalent(p, q)), or(equivalent(p, q), not(equivalent(p, q))))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(p, q))), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 6 (rule_1) }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(equivalent(p, q), equivalent(p, q))), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(theorem(implies(equivalent(p, q), equivalent(p, q))), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.50    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.50  = { by axiom 9 (rule_2) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true, ifeq(theorem(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q)))), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true, ifeq(ifeq(true, true, theorem(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q)))), true), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 3 (axiom_1_3) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true, ifeq(ifeq(axiom(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q)))), true, theorem(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q)))), true), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 6 (rule_1) }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true, ifeq(true, true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 11 (axiom_1_5) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(equivalent(p, q)), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), or(not(equivalent(p, q)), equivalent(p, q))))), true, theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), or(not(equivalent(p, q)), equivalent(p, q))))), true, theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true, theorem(implies(implies(equivalent(p, q), or(implies(equivalent(p, q), equivalent(p, q)), equivalent(p, q))), or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))))), true), true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 6 (rule_1) }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 6 (rule_1) R->L }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))), implies(equivalent(p, q), equivalent(p, q)))), true, theorem(implies(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))), implies(equivalent(p, q), equivalent(p, q)))), true), true, ifeq(theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 4 (axiom_1_2) }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))), implies(equivalent(p, q), equivalent(p, q)))), true), true, ifeq(theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q))), implies(equivalent(p, q), equivalent(p, q)))), true, ifeq(theorem(or(implies(equivalent(p, q), equivalent(p, q)), implies(equivalent(p, q), equivalent(p, q)))), true, theorem(implies(equivalent(p, q), equivalent(p, q))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 9 (rule_2) }
% 88.78/11.51    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(ifeq(true, true, theorem(or(equivalent(p, q), not(equivalent(p, q)))), true), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.51  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.52    ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(p, q))), or(equivalent(q, p), not(equivalent(p, q))))), true, ifeq(theorem(or(equivalent(p, q), not(equivalent(p, q)))), true, theorem(or(equivalent(q, p), not(equivalent(p, q)))), true), true), true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.52  = { by axiom 9 (rule_2) }
% 88.78/11.52    ifeq(ifeq(true, true, theorem(or(not(equivalent(p, q)), equivalent(q, p))), true), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.52    ifeq(theorem(or(not(equivalent(p, q)), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.52  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.52    ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.52    ifeq(true, true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 9 (rule_2) R->L }
% 88.78/11.52    ifeq(ifeq(theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))), or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p))))), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))), or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p))))), true), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 8 (axiom_1_4) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(axiom(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))), or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p))))), true, theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))), or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p))))), true), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 6 (rule_1) }
% 88.78/11.52    ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.52    ifeq(ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(true, true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 9 (rule_2) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(p, q), not(equivalent(q, p))), or(not(equivalent(q, p)), equivalent(p, q)))), true, ifeq(theorem(or(equivalent(p, q), not(equivalent(q, p)))), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(p, q), not(equivalent(q, p))), or(not(equivalent(q, p)), equivalent(p, q)))), true), true, ifeq(theorem(or(equivalent(p, q), not(equivalent(q, p)))), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 8 (axiom_1_4) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(p, q), not(equivalent(q, p))), or(not(equivalent(q, p)), equivalent(p, q)))), true, theorem(implies(or(equivalent(p, q), not(equivalent(q, p))), or(not(equivalent(q, p)), equivalent(p, q)))), true), true, ifeq(theorem(or(equivalent(p, q), not(equivalent(q, p)))), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 6 (rule_1) }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(p, q), not(equivalent(q, p)))), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(theorem(or(equivalent(p, q), not(equivalent(q, p)))), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 9 (rule_2) R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, ifeq(theorem(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by lemma 12 R->L }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, ifeq(theorem(implies(implies(implies(p, q), not(implies(q, p))), implies(implies(q, p), not(implies(p, q))))), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.52  = { by axiom 1 (implies_definition) }
% 88.78/11.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, ifeq(theorem(implies(implies(implies(p, q), not(implies(q, p))), or(not(implies(q, p)), not(implies(p, q))))), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.53  = { by axiom 1 (implies_definition) }
% 88.78/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, ifeq(theorem(implies(or(not(implies(p, q)), not(implies(q, p))), or(not(implies(q, p)), not(implies(p, q))))), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.53  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(implies(p, q)), not(implies(q, p))), or(not(implies(q, p)), not(implies(p, q))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.53  = { by axiom 8 (axiom_1_4) R->L }
% 88.78/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, ifeq(ifeq(axiom(implies(or(not(implies(p, q)), not(implies(q, p))), or(not(implies(q, p)), not(implies(p, q))))), true, theorem(implies(or(not(implies(p, q)), not(implies(q, p))), or(not(implies(q, p)), not(implies(p, q))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.53  = { by axiom 6 (rule_1) }
% 88.78/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, ifeq(true, true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.53  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.53  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.53  = { by axiom 6 (rule_1) R->L }
% 88.78/11.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.54  = { by axiom 1 (implies_definition) }
% 88.78/11.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), or(not(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.54  = { by axiom 1 (implies_definition) }
% 88.78/11.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(not(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), or(not(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.54  = { by axiom 1 (implies_definition) }
% 88.78/11.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(not(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), or(not(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), or(not(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.54  = { by axiom 1 (implies_definition) }
% 88.78/11.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p)))), or(not(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), or(not(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q))))), or(not(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.54  = { by axiom 11 (axiom_1_5) }
% 88.78/11.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, ifeq(true, true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by axiom 6 (rule_1) R->L }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, ifeq(ifeq(axiom(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by axiom 10 (axiom_1_6) }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))))), true, ifeq(theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true, theorem(implies(or(and(implies(p, q), implies(q, p)), implies(implies(q, p), not(implies(p, q)))), implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p)))))), true), true), true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by axiom 9 (rule_2) }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(q, p), not(implies(p, q))), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.55  = { by lemma 12 }
% 88.78/11.55    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(implies(q, p), implies(p, q)), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 7 (equivalent_defn) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(and(implies(p, q), implies(q, p)), not(equivalent(q, p))))), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 7 (equivalent_defn) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(true, true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 9 (rule_2) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(theorem(implies(implies(equivalent(q, p), equivalent(q, p)), or(equivalent(q, p), not(equivalent(q, p))))), true, ifeq(theorem(implies(equivalent(q, p), equivalent(q, p))), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 1 (implies_definition) }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(theorem(implies(or(not(equivalent(q, p)), equivalent(q, p)), or(equivalent(q, p), not(equivalent(q, p))))), true, ifeq(theorem(implies(equivalent(q, p), equivalent(q, p))), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(equivalent(q, p)), equivalent(q, p)), or(equivalent(q, p), not(equivalent(q, p))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(q, p))), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 8 (axiom_1_4) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(axiom(implies(or(not(equivalent(q, p)), equivalent(q, p)), or(equivalent(q, p), not(equivalent(q, p))))), true, theorem(implies(or(not(equivalent(q, p)), equivalent(q, p)), or(equivalent(q, p), not(equivalent(q, p))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(q, p))), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 6 (rule_1) }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(equivalent(q, p), equivalent(q, p))), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(theorem(implies(equivalent(q, p), equivalent(q, p))), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.56  = { by axiom 9 (rule_2) R->L }
% 88.78/11.56    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true, ifeq(theorem(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p)))), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.57  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true, ifeq(ifeq(true, true, theorem(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p)))), true), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.57  = { by axiom 3 (axiom_1_3) R->L }
% 88.78/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true, ifeq(ifeq(axiom(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p)))), true, theorem(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p)))), true), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.57  = { by axiom 6 (rule_1) }
% 88.78/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true, ifeq(true, true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.57  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.57  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.57  = { by axiom 11 (axiom_1_5) R->L }
% 88.78/11.57    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(equivalent(q, p)), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), or(not(equivalent(q, p)), equivalent(q, p))))), true, theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), or(not(equivalent(q, p)), equivalent(q, p))))), true, theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true, theorem(implies(implies(equivalent(q, p), or(implies(equivalent(q, p), equivalent(q, p)), equivalent(q, p))), or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))))), true), true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 6 (rule_1) }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 6 (rule_1) R->L }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))), implies(equivalent(q, p), equivalent(q, p)))), true, theorem(implies(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))), implies(equivalent(q, p), equivalent(q, p)))), true), true, ifeq(theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 4 (axiom_1_2) }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))), implies(equivalent(q, p), equivalent(q, p)))), true), true, ifeq(theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(ifeq(theorem(implies(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p))), implies(equivalent(q, p), equivalent(q, p)))), true, ifeq(theorem(or(implies(equivalent(q, p), equivalent(q, p)), implies(equivalent(q, p), equivalent(q, p)))), true, theorem(implies(equivalent(q, p), equivalent(q, p))), true), true), true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 9 (rule_2) }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(ifeq(true, true, theorem(or(equivalent(q, p), not(equivalent(q, p)))), true), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(q, p), not(equivalent(q, p))), or(equivalent(p, q), not(equivalent(q, p))))), true, ifeq(theorem(or(equivalent(q, p), not(equivalent(q, p)))), true, theorem(or(equivalent(p, q), not(equivalent(q, p)))), true), true), true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 9 (rule_2) }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(equivalent(q, p)), equivalent(p, q))), true), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.58    ifeq(ifeq(ifeq(theorem(or(not(equivalent(q, p)), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.58    ifeq(ifeq(ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.58    ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.58  = { by axiom 9 (rule_2) R->L }
% 88.78/11.58    ifeq(ifeq(ifeq(ifeq(theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p))))), implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p))))), implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 11 (axiom_1_5) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), or(not(implies(equivalent(q, p), equivalent(p, q))), not(implies(equivalent(p, q), equivalent(q, p))))), or(not(implies(equivalent(q, p), equivalent(p, q))), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true, theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p))))), implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p))))), or(not(implies(equivalent(q, p), equivalent(p, q))), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true, theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p))))), implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p))))), implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true, theorem(implies(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p))))), implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))))), true), true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 6 (rule_1) }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 2 (ifeq_axiom) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 8 (axiom_1_4) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(equivalent(p, q), equivalent(q, p))), not(implies(equivalent(q, p), equivalent(p, q)))), or(not(implies(equivalent(q, p), equivalent(p, q))), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(q, p), equivalent(p, q)))), or(not(implies(equivalent(q, p), equivalent(p, q))), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by lemma 12 }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(and(implies(equivalent(p, q), equivalent(q, p)), implies(equivalent(q, p), equivalent(p, q))), or(not(implies(equivalent(q, p), equivalent(p, q))), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(and(implies(equivalent(p, q), equivalent(q, p)), implies(equivalent(q, p), equivalent(p, q))), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 7 (equivalent_defn) R->L }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), implies(implies(equivalent(q, p), equivalent(p, q)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 6 (rule_1) }
% 88.78/11.59    ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.59    ifeq(ifeq(ifeq(theorem(implies(implies(equivalent(q, p), equivalent(p, q)), or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p)))))), true, ifeq(theorem(implies(equivalent(q, p), equivalent(p, q))), true, theorem(or(equivalent(equivalent(p, q), equivalent(q, p)), not(implies(equivalent(p, q), equivalent(q, p))))), true), true), true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 9 (rule_2) }
% 88.78/11.59    ifeq(ifeq(true, true, theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 2 (ifeq_axiom) }
% 88.78/11.59    ifeq(theorem(or(not(implies(equivalent(p, q), equivalent(q, p))), equivalent(equivalent(p, q), equivalent(q, p)))), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 1 (implies_definition) R->L }
% 88.78/11.59    ifeq(theorem(implies(implies(equivalent(p, q), equivalent(q, p)), equivalent(equivalent(p, q), equivalent(q, p)))), true, ifeq(theorem(implies(equivalent(p, q), equivalent(q, p))), true, theorem(equivalent(equivalent(p, q), equivalent(q, p))), true), true)
% 88.78/11.59  = { by axiom 9 (rule_2) }
% 88.78/11.59    true
% 88.78/11.59  % SZS output end Proof
% 88.78/11.59  
% 88.78/11.59  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------