Twee---2.7.UNS-Prf.s

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% File     : Twee---2.7
% Problem  : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n005.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 11:49:06 AM UTC 2026

% Result   : Unsatisfiable 0.19s 0.56s
% Output   : Proof 5.03s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL120-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36  % Computer : n005.cluster.edu
% 0.11/0.36  % Model    : x86_64 x86_64
% 0.11/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36  % Memory   : 8046.5625MB
% 0.11/0.36  % OS       : Linux 6.8.0-71-generic
% 0.11/0.36  % CPULimit : 300
% 0.11/0.36  % WCLimit  : 300
% 0.11/0.36  % DateTime : Sun Sep 27 15:22:46 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.37  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.56  Command-line arguments: --no-flatten-goal
% 0.19/0.56  
% 0.19/0.56  % SZS status Unsatisfiable
% 0.19/0.56  
% 2.03/0.77  % SZS output start Proof
% 2.03/0.77  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.03/0.77  Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 2.03/0.79  Axiom 3 (qyf): is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Z, Y))) = true.
% 2.03/0.79  
% 2.03/0.79  Goal 1 (prove_xgj): is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))) = true.
% 2.03/0.79  Proof:
% 2.03/0.79    is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))
% 2.03/0.79  = { by axiom 1 (ifeq_axiom) R->L }
% 2.03/0.79    ifeq(true, true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.03/0.79  = { by axiom 2 (condensed_detachment) R->L }
% 2.03/0.79    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.03/0.79  = { by axiom 3 (qyf) }
% 2.03/0.79    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.03/0.80  = { by axiom 1 (ifeq_axiom) }
% 2.03/0.80    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.81  = { by axiom 1 (ifeq_axiom) R->L }
% 2.69/0.81    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.81  = { by axiom 2 (condensed_detachment) R->L }
% 2.69/0.82    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.82  = { by axiom 1 (ifeq_axiom) R->L }
% 2.69/0.83    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.83  = { by axiom 2 (condensed_detachment) R->L }
% 2.69/0.83    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.84  = { by axiom 3 (qyf) }
% 2.69/0.84    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.84  = { by axiom 1 (ifeq_axiom) }
% 2.69/0.85    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.85  = { by axiom 3 (qyf) }
% 2.69/0.85    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.86  = { by axiom 1 (ifeq_axiom) }
% 2.69/0.86    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.87  = { by axiom 1 (ifeq_axiom) R->L }
% 2.69/0.87    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 2.69/0.88  = { by axiom 2 (condensed_detachment) R->L }
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% 3.29/0.91  = { by axiom 3 (qyf) }
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% 3.29/0.94  = { by axiom 1 (ifeq_axiom) }
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% 3.29/0.95  = { by axiom 1 (ifeq_axiom) R->L }
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% 3.29/0.97  = { by axiom 3 (qyf) R->L }
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% 3.29/0.98  = { by axiom 1 (ifeq_axiom) R->L }
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% 3.29/1.00  = { by axiom 3 (qyf) R->L }
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equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 3.29/1.05  = { by axiom 2 (condensed_detachment) }
% 3.29/1.05    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 3.29/1.06  = { by axiom 1 (ifeq_axiom) }
% 3.29/1.06    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 3.29/1.06  = { by axiom 2 (condensed_detachment) }
% 3.29/1.07    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 3.29/1.07  = { by axiom 1 (ifeq_axiom) }
% 3.29/1.08    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 3.29/1.08  = { by axiom 1 (ifeq_axiom) R->L }
% 3.29/1.08    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.09  = { by axiom 3 (qyf) R->L }
% 5.03/1.10    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.11  = { by axiom 1 (ifeq_axiom) R->L }
% 5.03/1.11    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.11  = { by axiom 2 (condensed_detachment) R->L }
% 5.03/1.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, 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% 5.03/1.14  = { by axiom 3 (qyf) }
% 5.03/1.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, 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% 5.03/1.15  = { by axiom 1 (ifeq_axiom) }
% 5.03/1.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, 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equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.16  = { by axiom 3 (qyf) }
% 5.03/1.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.16  = { by axiom 1 (ifeq_axiom) }
% 5.03/1.17    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.17  = { by axiom 2 (condensed_detachment) }
% 5.03/1.17    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.17  = { by axiom 1 (ifeq_axiom) }
% 5.03/1.17    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.17  = { by axiom 1 (ifeq_axiom) R->L }
% 5.03/1.17    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.17  = { by axiom 3 (qyf) R->L }
% 5.03/1.18    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), equivalent(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)), equivalent(c, equivalent(c, a))), equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.18  = { by axiom 2 (condensed_detachment) }
% 5.03/1.18    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.18  = { by axiom 1 (ifeq_axiom) }
% 5.03/1.18    ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true)
% 5.03/1.18  = { by axiom 1 (ifeq_axiom) R->L }
% 5.03/1.18    ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true, ifeq(true, true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true), true)
% 5.03/1.18  = { by axiom 2 (condensed_detachment) R->L }
% 5.03/1.18    ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(c, equivalent(c, a))), equivalent(equivalent(c, a), a)), equivalent(a, equivalent(c, equivalent(c, a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(c, equivalent(c, a))), equivalent(equivalent(c, a), a))), true, is_a_theorem(equivalent(a, equivalent(c, equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true), true)
% 5.03/1.18  = { by axiom 3 (qyf) }
% 5.03/1.18    ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(c, equivalent(c, a))), equivalent(equivalent(c, a), a))), true, is_a_theorem(equivalent(a, equivalent(c, equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true), true)
% 5.03/1.18  = { by axiom 1 (ifeq_axiom) }
% 5.03/1.18    ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(c, equivalent(c, a))), equivalent(equivalent(c, a), a))), true, is_a_theorem(equivalent(a, equivalent(c, equivalent(c, a)))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true), true)
% 5.03/1.18  = { by axiom 3 (qyf) }
% 5.03/1.18    ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(a, equivalent(c, equivalent(c, a)))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true), true)
% 5.03/1.18  = { by axiom 1 (ifeq_axiom) }
% 5.03/1.18    ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(c, equivalent(c, a))), equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c))))), true, ifeq(is_a_theorem(equivalent(a, equivalent(c, equivalent(c, a)))), true, is_a_theorem(equivalent(a, equivalent(equivalent(b, equivalent(c, a)), equivalent(b, c)))), true), true)
% 5.03/1.18  = { by axiom 2 (condensed_detachment) }
% 5.03/1.18    true
% 5.03/1.18  % SZS output end Proof
% 5.03/1.18  
% 5.03/1.18  RESULT: Unsatisfiable (the axioms are contradictory).
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