%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL048-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 11:48:54 AM UTC 2026
% Result : Unsatisfiable 18.69s 2.86s
% Output : Proof 25.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL048-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 15:24:45 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.69/2.86 Command-line arguments: --no-flatten-goal
% 18.69/2.86
% 18.69/2.86 % SZS status Unsatisfiable
% 18.69/2.86
% 23.14/3.46 % SZS output start Proof
% 23.14/3.46 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 23.14/3.46 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 23.14/3.46 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 23.14/3.46 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.
% 23.14/3.48 Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 23.14/3.48
% 23.14/3.48 Goal 1 (prove_cn_19): is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))) = true.
% 23.14/3.48 Proof:
% 23.14/3.48 is_a_theorem(implies(implies(implies(a, b), c), implies(b, c)))
% 23.14/3.48 = { by axiom 1 (ifeq_axiom) R->L }
% 23.14/3.48 ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.48 = { by axiom 4 (condensed_detachment) R->L }
% 23.14/3.48 ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(implies(a, b)), implies(a, b))), implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)))), true, ifeq(is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.48 = { by axiom 5 (cn_1) }
% 23.14/3.48 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.48 = { by axiom 1 (ifeq_axiom) }
% 23.14/3.48 ifeq(ifeq(is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.48 = { by axiom 1 (ifeq_axiom) R->L }
% 23.14/3.48 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.48 = { by axiom 4 (condensed_detachment) R->L }
% 23.14/3.48 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.48 = { by axiom 1 (ifeq_axiom) R->L }
% 23.14/3.48 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.49 = { by axiom 5 (cn_1) R->L }
% 23.14/3.49 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.49 = { by axiom 1 (ifeq_axiom) R->L }
% 23.14/3.49 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.49 = { by axiom 5 (cn_1) R->L }
% 23.14/3.49 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(b, b)), implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b)))), implies(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))), implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.49 = { by axiom 4 (condensed_detachment) }
% 23.14/3.49 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.49 = { by axiom 1 (ifeq_axiom) }
% 23.14/3.49 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.49 = { by axiom 1 (ifeq_axiom) R->L }
% 23.14/3.49 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.50 = { by axiom 4 (condensed_detachment) R->L }
% 23.14/3.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.14/3.50 = { by axiom 1 (ifeq_axiom) R->L }
% 23.14/3.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.50 = { by axiom 4 (condensed_detachment) R->L }
% 23.89/3.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b)))), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.51 = { by axiom 1 (ifeq_axiom) R->L }
% 23.89/3.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.51 = { by axiom 5 (cn_1) R->L }
% 23.89/3.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))))), true, is_a_theorem(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.52 = { by axiom 1 (ifeq_axiom) R->L }
% 23.89/3.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.52 = { by axiom 2 (cn_3) R->L }
% 23.89/3.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), b)), implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))))), true, ifeq(is_a_theorem(implies(a, implies(not(a), b))), true, is_a_theorem(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.53 = { by axiom 4 (condensed_detachment) }
% 23.89/3.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true, ifeq(true, true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.53 = { by axiom 1 (ifeq_axiom) }
% 23.89/3.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.54 = { by axiom 1 (ifeq_axiom) R->L }
% 23.89/3.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.55 = { by axiom 4 (condensed_detachment) R->L }
% 23.89/3.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b))))), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.56 = { by axiom 1 (ifeq_axiom) R->L }
% 23.89/3.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.56 = { by axiom 5 (cn_1) R->L }
% 23.89/3.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(a))), implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b)))))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.56 = { by axiom 1 (ifeq_axiom) R->L }
% 23.89/3.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(a))), implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.57 = { by axiom 2 (cn_3) R->L }
% 23.89/3.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(a))), implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b)))))), true, ifeq(is_a_theorem(implies(b, implies(not(b), not(a)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b))), implies(b, implies(implies(not(a), b), implies(not(b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.57 = { by axiom 4 (condensed_detachment) }
% 23.89/3.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.58 = { by axiom 1 (ifeq_axiom) }
% 23.89/3.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.58 = { by axiom 5 (cn_1) }
% 23.89/3.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.58 = { by axiom 1 (ifeq_axiom) }
% 23.89/3.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.59 = { by axiom 1 (ifeq_axiom) R->L }
% 23.89/3.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.59 = { by axiom 5 (cn_1) R->L }
% 23.89/3.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(implies(not(a), b), implies(not(b), b))), implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b)))))), true, ifeq(is_a_theorem(implies(b, implies(implies(not(a), b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(a), b), implies(not(b), b)), implies(a, implies(not(b), b))), implies(b, implies(a, implies(not(b), b))))), true), true), true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.60 = { by axiom 4 (condensed_detachment) }
% 23.89/3.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.60 = { by axiom 1 (ifeq_axiom) }
% 23.89/3.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 23.89/3.60 = { by axiom 1 (ifeq_axiom) R->L }
% 23.89/3.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.60 = { by axiom 5 (cn_1) R->L }
% 24.68/3.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(a, implies(not(b), b))), implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(b, implies(a, implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))), implies(b, implies(implies(b, b), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.60 = { by axiom 4 (condensed_detachment) }
% 24.68/3.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.61 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.61 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.61 = { by axiom 4 (condensed_detachment) R->L }
% 24.68/3.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.61 = { by axiom 5 (cn_1) }
% 24.68/3.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.62 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.62 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.62 = { by axiom 5 (cn_1) R->L }
% 24.68/3.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.62 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, ifeq(true, true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.63 = { by axiom 3 (cn_2) R->L }
% 24.68/3.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, ifeq(is_a_theorem(implies(implies(not(b), b), b)), true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.63 = { by axiom 4 (condensed_detachment) }
% 24.68/3.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.63 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.63 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.64 = { by axiom 4 (condensed_detachment) R->L }
% 24.68/3.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(a, b))), implies(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b))), implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b))), implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.64 = { by axiom 5 (cn_1) }
% 24.68/3.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b))), implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.64 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b))), implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.64 = { by axiom 5 (cn_1) }
% 24.68/3.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b))), implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.65 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b))), implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(a, b)), implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(a, implies(not(b), b)), implies(implies(b, b), implies(a, b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.65 = { by axiom 4 (condensed_detachment) }
% 24.68/3.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.65 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.65 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.65 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.65 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.65 = { by axiom 5 (cn_1) R->L }
% 24.68/3.65 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(implies(b, b), implies(a, b))), implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b)))))), true, ifeq(is_a_theorem(implies(b, implies(implies(b, b), implies(a, b)))), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(a, b)), implies(not(implies(a, b)), implies(a, b))), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.65 = { by axiom 4 (condensed_detachment) }
% 24.68/3.65 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.65 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.65 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.66 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.66 = { by axiom 4 (condensed_detachment) R->L }
% 24.68/3.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true, ifeq(is_a_theorem(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b))), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.66 = { by axiom 3 (cn_2) }
% 24.68/3.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.66 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.66 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.66 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.66 = { by axiom 4 (condensed_detachment) R->L }
% 24.68/3.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.67 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.67 = { by axiom 5 (cn_1) R->L }
% 24.68/3.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(not(not(implies(a, b))), implies(b, b))), implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.67 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.67 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(not(not(implies(a, b))), implies(b, b))), implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.68 = { by axiom 2 (cn_3) R->L }
% 24.68/3.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(not(not(implies(a, b))), implies(b, b))), implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))))), true, ifeq(is_a_theorem(implies(not(implies(a, b)), implies(not(not(implies(a, b))), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.68 = { by axiom 4 (condensed_detachment) }
% 24.68/3.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.68 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.68 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.68 = { by axiom 4 (condensed_detachment) R->L }
% 24.68/3.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, b), implies(not(implies(b, b)), not(not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.68 = { by axiom 2 (cn_3) }
% 24.68/3.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 4 (condensed_detachment) R->L }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, ifeq(is_a_theorem(implies(b, implies(not(b), b))), true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 2 (cn_3) }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 5 (cn_1) }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.69 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, ifeq(true, true, is_a_theorem(implies(b, b)), true), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 3 (cn_2) R->L }
% 24.68/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, ifeq(is_a_theorem(implies(implies(not(b), b), b)), true, is_a_theorem(implies(b, b)), true), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 4 (condensed_detachment) }
% 24.68/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 1 (ifeq_axiom) R->L }
% 24.68/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 5 (cn_1) R->L }
% 24.68/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, b)), not(not(implies(a, b)))), implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(not(implies(b, b)), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(not(implies(a, b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 4 (condensed_detachment) }
% 24.68/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 1 (ifeq_axiom) }
% 24.68/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 24.68/3.70 = { by axiom 1 (ifeq_axiom) R->L }
% 25.50/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 25.50/3.70 = { by axiom 5 (cn_1) R->L }
% 25.50/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(not(implies(a, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(a, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 25.50/3.70 = { by axiom 4 (condensed_detachment) }
% 25.50/3.70 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 25.50/3.70 = { by axiom 1 (ifeq_axiom) }
% 25.50/3.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(b, b)), implies(b, implies(not(implies(a, b)), implies(a, b))))), true, ifeq(is_a_theorem(implies(not(implies(a, b)), implies(b, b))), true, is_a_theorem(implies(b, implies(not(implies(a, b)), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 25.50/3.71 = { by axiom 4 (condensed_detachment) }
% 25.50/3.71 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 25.50/3.71 = { by axiom 1 (ifeq_axiom) }
% 25.50/3.71 ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true)
% 25.50/3.71 = { by axiom 1 (ifeq_axiom) R->L }
% 25.50/3.71 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 4 (condensed_detachment) R->L }
% 25.50/3.71 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c)), implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 5 (cn_1) }
% 25.50/3.71 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 1 (ifeq_axiom) }
% 25.50/3.71 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 1 (ifeq_axiom) R->L }
% 25.50/3.71 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 5 (cn_1) R->L }
% 25.50/3.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c)))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 1 (ifeq_axiom) R->L }
% 25.50/3.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 3 (cn_2) R->L }
% 25.50/3.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b)), implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c)))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, b)), implies(a, b)), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(implies(not(implies(a, b)), implies(a, b)), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 4 (condensed_detachment) }
% 25.50/3.71 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 1 (ifeq_axiom) }
% 25.50/3.71 ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c)), implies(implies(implies(a, b), c), implies(b, c)))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(a, b)), c), implies(b, c))), true, is_a_theorem(implies(implies(implies(a, b), c), implies(b, c))), true), true)
% 25.50/3.71 = { by axiom 4 (condensed_detachment) }
% 25.50/3.71 true
% 25.50/3.71 % SZS output end Proof
% 25.50/3.71
% 25.50/3.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------