Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL080-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:48:59 AM UTC 2026

% Result   : Unsatisfiable 79.30s 10.34s
% Output   : Proof 81.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : LCL080-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30  % Computer : n012.cluster.edu
% 0.03/0.30  % Model    : x86_64 x86_64
% 0.03/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30  % Memory   : 8046.5625MB
% 0.03/0.30  % OS       : Linux 6.8.0-71-generic
% 0.03/0.30  % CPULimit : 300
% 0.03/0.30  % WCLimit  : 300
% 0.03/0.30  % DateTime : Sun Sep 27 15:20:49 UTC 2026
% 0.03/0.30  % CPUTime  : 
% 0.03/0.30  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 79.30/10.34  Command-line arguments: --no-flatten-goal
% 79.30/10.34  
% 79.30/10.34  % SZS status Unsatisfiable
% 79.30/10.34  
% 80.11/10.49  % SZS output start Proof
% 80.11/10.49  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 80.11/10.49  Axiom 2 (ic_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 80.11/10.49  Axiom 3 (ic_3): is_a_theorem(implies(implies(implies(X, Y), X), X)) = true.
% 80.11/10.49  Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 80.11/10.50  Axiom 5 (ic_4): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 80.11/10.50  
% 80.11/10.50  Goal 1 (prove_ic_JLukasiewicz): is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))) = true.
% 80.11/10.50  Proof:
% 80.11/10.50    is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a))))
% 80.11/10.50  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.50    ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.11/10.50  = { by axiom 4 (condensed_detachment) R->L }
% 80.11/10.50    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.50  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.50    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.50  = { by axiom 4 (condensed_detachment) R->L }
% 80.86/10.50    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), a)), true, is_a_theorem(implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.50  = { by axiom 3 (ic_3) }
% 80.86/10.50    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.50  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.50    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a))))), true, is_a_theorem(implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.50  = { by axiom 5 (ic_4) }
% 80.86/10.51    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.51    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.51    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 2 (ic_2) R->L }
% 80.86/10.51    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(e, a)), implies(implies(implies(a, b), a), implies(e, a)))), true, ifeq(is_a_theorem(implies(a, implies(e, a))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(e, a))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 4 (condensed_detachment) }
% 80.86/10.51    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.51    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.51    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 4 (condensed_detachment) R->L }
% 80.86/10.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 5 (ic_4) }
% 80.86/10.51    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.51    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 5 (ic_4) }
% 80.86/10.51    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.51    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.51  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.51    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.52  = { by axiom 4 (condensed_detachment) R->L }
% 80.86/10.52    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.52  = { by axiom 5 (ic_4) }
% 80.86/10.52    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.52  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.52    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.52  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.52    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.52  = { by axiom 4 (condensed_detachment) R->L }
% 80.86/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.53  = { by axiom 5 (ic_4) }
% 80.86/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.53  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.54  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.54  = { by axiom 5 (ic_4) R->L }
% 80.86/10.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.54  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.55  = { by axiom 4 (condensed_detachment) R->L }
% 80.86/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.55  = { by axiom 2 (ic_2) }
% 80.86/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.56  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.56  = { by axiom 5 (ic_4) }
% 80.86/10.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.56  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.57  = { by axiom 4 (condensed_detachment) }
% 80.86/10.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.57  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.57  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.58  = { by axiom 4 (condensed_detachment) R->L }
% 80.86/10.58    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.58  = { by axiom 3 (ic_3) }
% 80.86/10.58    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.58  = { by axiom 1 (ifeq_axiom) }
% 80.86/10.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.59  = { by axiom 1 (ifeq_axiom) R->L }
% 80.86/10.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 80.86/10.60  = { by axiom 5 (ic_4) R->L }
% 80.86/10.60    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.60  = { by axiom 1 (ifeq_axiom) R->L }
% 81.50/10.60    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.60  = { by axiom 5 (ic_4) R->L }
% 81.50/10.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.61  = { by axiom 4 (condensed_detachment) }
% 81.50/10.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.61  = { by axiom 1 (ifeq_axiom) }
% 81.50/10.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.61  = { by axiom 4 (condensed_detachment) }
% 81.50/10.61    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.61  = { by axiom 1 (ifeq_axiom) }
% 81.50/10.61    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(c, a), implies(e, a))), implies(implies(c, a), implies(e, a))), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(e, a)), implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))))), true), true), true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.61  = { by axiom 4 (condensed_detachment) }
% 81.50/10.61    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.61  = { by axiom 1 (ifeq_axiom) }
% 81.50/10.61    ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true)
% 81.50/10.61  = { by axiom 1 (ifeq_axiom) R->L }
% 81.50/10.61    ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true), true)
% 81.50/10.61  = { by axiom 4 (condensed_detachment) R->L }
% 81.50/10.61    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), c), implies(implies(c, a), implies(implies(a, b), a))), implies(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true), true)
% 81.50/10.61  = { by axiom 5 (ic_4) }
% 81.50/10.61    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true), true)
% 81.50/10.61  = { by axiom 1 (ifeq_axiom) }
% 81.50/10.61    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true), true)
% 81.50/10.61  = { by axiom 5 (ic_4) }
% 81.50/10.61    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true), true)
% 81.50/10.61  = { by axiom 1 (ifeq_axiom) }
% 81.50/10.61    ifeq(is_a_theorem(implies(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a))), implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a))))), true, ifeq(is_a_theorem(implies(implies(implies(c, a), implies(implies(a, b), a)), implies(implies(c, a), implies(e, a)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(c, a), implies(e, a)))), true), true)
% 81.50/10.61  = { by axiom 4 (condensed_detachment) }
% 81.50/10.61    true
% 81.50/10.61  % SZS output end Proof
% 81.50/10.61  
% 81.50/10.61  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------