Twee---2.7.UNS-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz
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% File     : Twee---2.7
% Problem  : LCL107-1 : 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 11:49:02 AM UTC 2026

% Result   : Unsatisfiable 0.25s 0.57s
% Output   : Proof 7.75s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LCL107-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43  % Computer : n005.cluster.edu
% 0.19/0.43  % Model    : x86_64 x86_64
% 0.19/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43  % Memory   : 8046.5625MB
% 0.19/0.43  % OS       : Linux 6.8.0-71-generic
% 0.19/0.43  % CPULimit : 300
% 0.19/0.43  % WCLimit  : 300
% 0.19/0.43  % DateTime : Sun Sep 27 15:21:46 UTC 2026
% 0.19/0.44  % CPUTime  : 
% 0.19/0.44  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.25/0.57  Command-line arguments: --no-flatten-goal
% 0.25/0.57  
% 0.25/0.57  % SZS status Unsatisfiable
% 0.25/0.57  
% 2.72/0.96  % SZS output start Proof
% 2.72/0.96  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.72/0.96  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.
% 2.72/0.97  Axiom 3 (lg_27_1690): is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), equivalent(equivalent(W, V), equivalent(equivalent(equivalent(U, V), equivalent(U, W)), T))), equivalent(Z, equivalent(equivalent(Y, X), T)))) = true.
% 2.72/0.97  
% 2.72/0.97  Goal 1 (prove_p_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) = true.
% 2.72/0.97  Proof:
% 2.72/0.97    is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 2.72/0.97  = { by axiom 1 (ifeq_axiom) R->L }
% 2.72/0.97    ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.72/0.97  = { by axiom 2 (condensed_detachment) R->L }
% 2.72/0.98    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.72/0.98  = { by axiom 3 (lg_27_1690) }
% 2.72/0.99    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.72/1.00  = { by axiom 1 (ifeq_axiom) }
% 2.72/1.00    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.72/1.00  = { by axiom 1 (ifeq_axiom) R->L }
% 2.72/1.00    ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.01  = { by axiom 2 (condensed_detachment) R->L }
% 3.45/1.03    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.04  = { by axiom 3 (lg_27_1690) }
% 3.45/1.05    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.06  = { by axiom 1 (ifeq_axiom) }
% 3.45/1.06    ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), 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% 3.45/1.08  = { by axiom 1 (ifeq_axiom) R->L }
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% 3.45/1.11  = { by axiom 3 (lg_27_1690) R->L }
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% 3.45/1.13  = { by axiom 1 (ifeq_axiom) R->L }
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% 3.45/1.15  = { by axiom 3 (lg_27_1690) R->L }
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% 3.45/1.18  = { by axiom 2 (condensed_detachment) }
% 3.45/1.18    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.18  = { by axiom 1 (ifeq_axiom) }
% 3.45/1.19    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.19  = { by axiom 1 (ifeq_axiom) R->L }
% 3.45/1.19    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c)))), equivalent(equivalent(b, e), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(X, equivalent(equivalent(a, e), equivalent(a, b))), equivalent(X, equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.19  = { by axiom 3 (lg_27_1690) R->L }
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% 3.45/1.20  = { by axiom 2 (condensed_detachment) }
% 3.45/1.20    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.20  = { by axiom 1 (ifeq_axiom) }
% 3.45/1.20    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 3.45/1.21  = { by axiom 1 (ifeq_axiom) R->L }
% 3.45/1.21    ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.45/1.21  = { by axiom 2 (condensed_detachment) R->L }
% 3.45/1.21    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 5.40/1.22  = { by axiom 3 (lg_27_1690) }
% 5.40/1.22    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 5.40/1.24  = { by axiom 1 (ifeq_axiom) }
% 5.40/1.24    ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 5.40/1.25  = { by axiom 1 (ifeq_axiom) R->L }
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% 5.40/1.27  = { by axiom 2 (condensed_detachment) R->L }
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% 5.40/1.31  = { by axiom 3 (lg_27_1690) }
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% 7.75/1.54  = { by axiom 1 (ifeq_axiom) }
% 7.75/1.55    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 7.75/1.55  = { by axiom 1 (ifeq_axiom) R->L }
% 7.75/1.56    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 7.75/1.56  = { by axiom 3 (lg_27_1690) R->L }
% 7.75/1.57    ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), 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equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), 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equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(c, equivalent(a, b)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(Y, equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(Y, equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 7.75/1.57  = { by axiom 2 (condensed_detachment) }
% 7.75/1.58    ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 7.75/1.58  = { by axiom 1 (ifeq_axiom) }
% 7.75/1.58    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 7.75/1.58  = { by axiom 2 (condensed_detachment) }
% 7.75/1.58    true
% 7.75/1.58  % SZS output end Proof
% 7.75/1.58  
% 7.75/1.58  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------