Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL075-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n003.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 11:48:58 AM UTC 2026

% Result   : Unsatisfiable 0.28s 1.08s
% Output   : Proof 10.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : LCL075-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45  % Computer : n003.cluster.edu
% 0.19/0.45  % Model    : x86_64 x86_64
% 0.19/0.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45  % Memory   : 8046.5625MB
% 0.19/0.45  % OS       : Linux 6.8.0-71-generic
% 0.19/0.45  % CPULimit : 300
% 0.19/0.45  % WCLimit  : 300
% 0.19/0.45  % DateTime : Sun Sep 27 15:22:10 UTC 2026
% 0.19/0.46  % CPUTime  : 
% 0.19/0.46  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.28/1.08  Command-line arguments: --no-flatten-goal
% 0.28/1.08  
% 0.28/1.08  % SZS status Unsatisfiable
% 0.28/1.08  
% 8.06/1.62  % SZS output start Proof
% 8.06/1.62  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 8.06/1.62  Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 8.06/1.64  Axiom 3 (cn_CAMeredith): is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(not(Z), not(W))), Z), V), implies(implies(V, X), implies(W, X)))) = true.
% 8.06/1.64  
% 8.06/1.64  Goal 1 (prove_cn_3): is_a_theorem(implies(a, implies(not(a), b))) = true.
% 8.06/1.64  Proof:
% 8.06/1.64    is_a_theorem(implies(a, implies(not(a), b)))
% 8.06/1.64  = { by axiom 1 (ifeq_axiom) R->L }
% 8.06/1.64    ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.64  = { by axiom 2 (condensed_detachment) R->L }
% 8.06/1.64    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b)), implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.65  = { by axiom 3 (cn_CAMeredith) }
% 8.06/1.65    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.65  = { by axiom 1 (ifeq_axiom) }
% 8.06/1.65    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.65  = { by axiom 1 (ifeq_axiom) R->L }
% 8.06/1.65    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.65  = { by axiom 2 (condensed_detachment) R->L }
% 8.06/1.65    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.65  = { by axiom 3 (cn_CAMeredith) }
% 8.06/1.65    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.66  = { by axiom 1 (ifeq_axiom) }
% 8.06/1.66    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.66  = { by axiom 1 (ifeq_axiom) R->L }
% 8.06/1.66    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.66  = { by axiom 2 (condensed_detachment) R->L }
% 8.06/1.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.67  = { by axiom 3 (cn_CAMeredith) }
% 8.06/1.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.68  = { by axiom 1 (ifeq_axiom) }
% 8.06/1.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.68  = { by axiom 1 (ifeq_axiom) R->L }
% 8.06/1.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.69  = { by axiom 2 (condensed_detachment) R->L }
% 8.06/1.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))))))), implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(implies(not(b), not(a)))), implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a))))))), implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))))))), implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(implies(not(b), not(a)))), implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.06/1.70  = { by axiom 3 (cn_CAMeredith) }
% 8.73/1.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))))))), implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(implies(not(b), not(a)))), implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.71  = { by axiom 1 (ifeq_axiom) }
% 8.73/1.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W))))))), implies(not(not(implies(not(b), not(a)))), not(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V)))), not(implies(not(b), not(a)))), implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.72  = { by axiom 3 (cn_CAMeredith) }
% 8.73/1.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.72  = { by axiom 1 (ifeq_axiom) }
% 8.73/1.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.73  = { by axiom 1 (ifeq_axiom) R->L }
% 8.73/1.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.74  = { by axiom 3 (cn_CAMeredith) R->L }
% 8.73/1.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W))))), implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(not(implies(not(b), not(a))))), implies(not(implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(not(implies(not(b), not(a)))))), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), V), implies(not(not(implies(not(b), not(a)))), not(implies(b, W)))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.74  = { by axiom 2 (condensed_detachment) }
% 8.73/1.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.75  = { by axiom 1 (ifeq_axiom) }
% 8.73/1.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.75  = { by axiom 1 (ifeq_axiom) R->L }
% 8.73/1.76    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.76  = { by axiom 2 (condensed_detachment) R->L }
% 8.73/1.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.77  = { by axiom 3 (cn_CAMeredith) }
% 8.73/1.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 8.73/1.79  = { by axiom 1 (ifeq_axiom) }
% 8.73/1.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.80  = { by axiom 1 (ifeq_axiom) R->L }
% 9.40/1.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.82  = { by axiom 2 (condensed_detachment) R->L }
% 9.40/1.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), not(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), not(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.84  = { by axiom 3 (cn_CAMeredith) }
% 9.40/1.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), not(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.86  = { by axiom 1 (ifeq_axiom) }
% 9.40/1.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), not(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.87  = { by axiom 3 (cn_CAMeredith) }
% 9.40/1.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.89  = { by axiom 1 (ifeq_axiom) }
% 9.40/1.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.90  = { by axiom 1 (ifeq_axiom) R->L }
% 9.40/1.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 9.40/1.90  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.12/1.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z))))), implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(not(implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), U), implies(not(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), not(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.91  = { by axiom 2 (condensed_detachment) }
% 10.12/1.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.91  = { by axiom 1 (ifeq_axiom) }
% 10.12/1.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))), implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(b), not(a))), not(implies(not(b), not(a)))), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), not(a)), Y), implies(not(Z), not(implies(implies(not(a), b), X)))), Z), implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.92  = { by axiom 2 (condensed_detachment) }
% 10.12/1.92    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.92  = { by axiom 1 (ifeq_axiom) }
% 10.12/1.92    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.92  = { by axiom 1 (ifeq_axiom) R->L }
% 10.12/1.92    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.92  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.12/1.93    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a)))), implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, W), implies(not(implies(not(b), not(a))), not(implies(not(b), not(a))))), implies(not(b), not(a))), implies(implies(implies(not(a), b), X), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), b), X), implies(not(b), not(a))), b), implies(implies(not(b), not(a)), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.93  = { by axiom 2 (condensed_detachment) }
% 10.12/1.93    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.93  = { by axiom 1 (ifeq_axiom) }
% 10.12/1.93    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, is_a_theorem(implies(a, implies(not(a), b))), true)
% 10.12/1.93  = { by axiom 1 (ifeq_axiom) R->L }
% 10.12/1.93    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.93  = { by axiom 2 (condensed_detachment) R->L }
% 10.12/1.93    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a))), implies(implies(implies(not(b), not(a)), b), implies(not(a), b)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.93  = { by axiom 3 (cn_CAMeredith) }
% 10.12/1.93    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.93  = { by axiom 1 (ifeq_axiom) }
% 10.12/1.93    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.94  = { by axiom 1 (ifeq_axiom) R->L }
% 10.12/1.94    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.94  = { by axiom 2 (condensed_detachment) R->L }
% 10.12/1.94    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.95  = { by axiom 1 (ifeq_axiom) R->L }
% 10.12/1.95    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.95  = { by axiom 2 (condensed_detachment) R->L }
% 10.12/1.96    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))))), implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.96  = { by axiom 3 (cn_CAMeredith) }
% 10.12/1.97    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.97  = { by axiom 1 (ifeq_axiom) }
% 10.12/1.97    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.98  = { by axiom 1 (ifeq_axiom) R->L }
% 10.12/1.98    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/1.99  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.12/1.99    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), not(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), implies(not(not(a)), not(not(a)))), implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.12/2.00  = { by axiom 1 (ifeq_axiom) R->L }
% 10.12/2.00    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), not(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), implies(not(not(a)), not(not(a)))), implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.00  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.82/2.01    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), not(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), implies(not(not(a)), not(not(a)))), implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a))))))), implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), not(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2))))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2)))), implies(not(not(a)), not(not(a)))), implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), not(implies(not(not(a)), not(not(a))))), implies(not(implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), not(implies(not(not(a)), not(not(a)))))), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.02  = { by axiom 2 (condensed_detachment) }
% 10.82/2.02    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.02  = { by axiom 1 (ifeq_axiom) }
% 10.82/2.02    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.02  = { by axiom 1 (ifeq_axiom) R->L }
% 10.82/2.03    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.03  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.82/2.03    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), Y2), implies(not(implies(not(not(a)), not(not(a)))), not(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2)))), implies(not(not(a)), not(not(a)))), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.03  = { by axiom 2 (condensed_detachment) }
% 10.82/2.03    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.04  = { by axiom 1 (ifeq_axiom) }
% 10.82/2.04    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.04  = { by axiom 1 (ifeq_axiom) R->L }
% 10.82/2.04    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.04  = { by axiom 2 (condensed_detachment) R->L }
% 10.82/2.05    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T))))), implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.05  = { by axiom 3 (cn_CAMeredith) }
% 10.82/2.05    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.05  = { by axiom 1 (ifeq_axiom) }
% 10.82/2.05    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.06  = { by axiom 1 (ifeq_axiom) R->L }
% 10.82/2.06    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.06  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.82/2.07    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(a))), not(implies(b, T))), implies(not(implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(implies(not(not(not(a))), not(implies(b, T))))))), implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(a))), implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.07  = { by axiom 1 (ifeq_axiom) R->L }
% 10.82/2.07    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(a))), not(implies(b, T))), implies(not(implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(implies(not(not(not(a))), not(implies(b, T))))))), implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(a))), implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.07  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.82/2.08    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(not(not(a))), not(implies(b, T))), implies(not(implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(implies(not(not(not(a))), not(implies(b, T))))))), implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(a))), implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a)))))), implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(a))), not(implies(b, T))), implies(not(implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(implies(not(not(not(a))), not(implies(b, T))))))), implies(not(not(not(a))), not(implies(implies(not(not(a)), not(not(a))), Z2)))), not(not(a))), implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(a)), not(not(not(a)))), implies(not(implies(not(not(not(a))), not(implies(b, T)))), not(not(not(a))))), implies(not(not(not(a))), not(implies(b, T)))), implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.08  = { by axiom 2 (condensed_detachment) }
% 10.82/2.08    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.09  = { by axiom 1 (ifeq_axiom) }
% 10.82/2.09    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.09  = { by axiom 1 (ifeq_axiom) R->L }
% 10.82/2.09    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.09  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.82/2.09    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(a)), not(not(a))), Z2), implies(not(not(not(a))), not(implies(b, T)))), not(not(a))), implies(not(not(a)), not(not(a))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.09  = { by axiom 2 (condensed_detachment) }
% 10.82/2.09    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.09  = { by axiom 1 (ifeq_axiom) }
% 10.82/2.09    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.09  = { by axiom 1 (ifeq_axiom) R->L }
% 10.82/2.09    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.09  = { by axiom 3 (cn_CAMeredith) R->L }
% 10.82/2.10    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), S), implies(not(X2), not(not(b)))), X2), implies(implies(b, T), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(b, T), implies(not(not(a)), not(not(a)))), not(a)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.10  = { by axiom 2 (condensed_detachment) }
% 10.82/2.10    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.10  = { by axiom 1 (ifeq_axiom) }
% 10.82/2.10    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), b), implies(not(a), b)), implies(a, implies(not(a), b)))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), not(a)), b), implies(not(a), b))), true, is_a_theorem(implies(a, implies(not(a), b))), true), true)
% 10.82/2.10  = { by axiom 2 (condensed_detachment) }
% 10.82/2.10    true
% 10.82/2.10  % SZS output end Proof
% 10.82/2.10  
% 10.82/2.10  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------