%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL365+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:40 AM UTC 2026
% Result : Theorem 181.71s 23.31s
% Output : Proof 184.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL365+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 27 15:36:44 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 181.71/23.31 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 181.71/23.31
% 181.71/23.31 % SZS status Theorem
% 181.71/23.31
% 183.29/23.51 % SZS output start Proof
% 183.29/23.51 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 183.29/23.51 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 183.29/23.51 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 183.29/23.51 Axiom 4 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 183.29/23.51 Axiom 5 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 183.29/23.51
% 183.29/23.51 Goal 1 (prove_cn_14): is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))) = true.
% 183.29/23.51 Proof:
% 183.29/23.51 is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u)))
% 183.29/23.52 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.52 ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.52 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.52 ifeq(ifeq(is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.52 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.52 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.52 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.52 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.52 = { by axiom 4 (cn_1) }
% 183.29/23.52 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.52 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.52 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.52 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.52 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.52 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.53 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.53 = { by axiom 4 (cn_1) R->L }
% 183.29/23.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.53 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.53 = { by axiom 4 (cn_1) R->L }
% 183.29/23.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z))), implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.53 = { by axiom 5 (condensed_detachment) }
% 183.29/23.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.53 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(implies(z, z), implies(implies(not(z), z), z)))), true, ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(implies(z, z), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 3 (cn_2) }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(implies(z, z), implies(implies(not(z), z), z)))), true, ifeq(true, true, is_a_theorem(implies(implies(z, z), implies(implies(not(z), z), z))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(implies(z, z), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(z, z), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 4 (cn_1) }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(z, z), implies(implies(not(z), z), z))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(not(z), z), z))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(z, z), implies(implies(not(z), z), z))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 4 (cn_1) R->L }
% 183.29/23.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(z, z), implies(implies(not(z), z), z)), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(z, z), implies(implies(not(z), z), z))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.54 = { by axiom 5 (condensed_detachment) }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z))), implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 4 (cn_1) }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 4 (cn_1) }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z))), implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(z, z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(implies(z, z), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 5 (condensed_detachment) }
% 183.29/23.55 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.55 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.55 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.56 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(z, z)), implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z)))), implies(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))))), true, ifeq(is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 4 (cn_1) }
% 183.29/23.56 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 4 (cn_1) }
% 183.29/23.56 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.56 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, z), implies(implies(y, z), z)), implies(x, implies(implies(y, z), z))), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(x, implies(z, z)), implies(implies(not(z), y), implies(x, implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 5 (condensed_detachment) }
% 183.29/23.56 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.56 ifeq(ifeq(is_a_theorem(implies(x, implies(z, z))), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.56 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 3 (cn_2) }
% 183.29/23.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.56 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.57 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.57 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.57 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.57 = { by axiom 4 (cn_1) R->L }
% 183.29/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(z, z), implies(not(implies(z, z)), not(x))), implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))))), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.57 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(z, z), implies(not(implies(z, z)), not(x))), implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.57 = { by axiom 2 (cn_3) R->L }
% 183.29/23.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(z, z), implies(not(implies(z, z)), not(x))), implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))))), true, ifeq(is_a_theorem(implies(implies(z, z), implies(not(implies(z, z)), not(x)))), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.58 = { by axiom 5 (condensed_detachment) }
% 183.29/23.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.58 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.58 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.58 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(z, z)), not(x)), implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z)))), implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true), true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.58 = { by axiom 4 (cn_1) }
% 183.29/23.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true), true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.59 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.59 = { by axiom 4 (cn_1) }
% 183.29/23.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true), true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.59 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.59 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.59 = { by axiom 4 (cn_1) R->L }
% 183.29/23.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(x), implies(z, z)), implies(not(implies(z, z)), implies(z, z))), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(not(implies(z, z)), not(x)), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true), true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 5 (condensed_detachment) }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 5 (condensed_detachment) R->L }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(z, z))), true, ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(z, z)), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 3 (cn_2) }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(z, z))), true, ifeq(true, true, is_a_theorem(implies(z, z)), true), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 1 (ifeq_axiom) }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(z, z))), true, is_a_theorem(implies(z, z)), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(z), z), z), implies(z, z))), true), true, is_a_theorem(implies(z, z)), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 4 (cn_1) R->L }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(z, z)))), true, is_a_theorem(implies(implies(implies(not(z), z), z), implies(z, z))), true), true, is_a_theorem(implies(z, z)), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 1 (ifeq_axiom) R->L }
% 183.29/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(z, z)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(z), z), z), implies(z, z))), true), true), true, is_a_theorem(implies(z, z)), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 183.29/23.60 = { by axiom 2 (cn_3) R->L }
% 184.08/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(z, z)))), true, ifeq(is_a_theorem(implies(z, implies(not(z), z))), true, is_a_theorem(implies(implies(implies(not(z), z), z), implies(z, z))), true), true), true, is_a_theorem(implies(z, z)), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.60 = { by axiom 5 (condensed_detachment) }
% 184.08/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(z, z)), true), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.60 = { by axiom 1 (ifeq_axiom) }
% 184.08/23.60 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, z), implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z))))), true, ifeq(is_a_theorem(implies(z, z)), true, is_a_theorem(implies(implies(implies(not(implies(z, z)), implies(z, z)), implies(z, z)), implies(implies(not(x), implies(z, z)), implies(z, z)))), true), true), true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.60 = { by axiom 5 (condensed_detachment) }
% 184.08/23.61 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 1 (ifeq_axiom) }
% 184.08/23.61 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(x, implies(z, z))), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 1 (ifeq_axiom) R->L }
% 184.08/23.61 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(x, implies(z, z))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 5 (condensed_detachment) R->L }
% 184.08/23.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), implies(z, z))), implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z))))), true, ifeq(is_a_theorem(implies(x, implies(not(x), implies(z, z)))), true, is_a_theorem(implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(x, implies(z, z))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 2 (cn_3) }
% 184.08/23.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), implies(z, z))), implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(x, implies(z, z))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 1 (ifeq_axiom) }
% 184.08/23.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), implies(z, z))), implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z))))), true, is_a_theorem(implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z)))), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(x, implies(z, z))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 4 (cn_1) }
% 184.08/23.61 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z)))), true), true, ifeq(is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(x, implies(z, z))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 1 (ifeq_axiom) }
% 184.08/23.61 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), implies(z, z)), implies(z, z)), implies(x, implies(z, z)))), true, ifeq(is_a_theorem(implies(implies(not(x), implies(z, z)), implies(z, z))), true, is_a_theorem(implies(x, implies(z, z))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 5 (condensed_detachment) }
% 184.08/23.61 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 1 (ifeq_axiom) }
% 184.08/23.61 ifeq(is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true)
% 184.08/23.61 = { by axiom 1 (ifeq_axiom) R->L }
% 184.08/23.61 ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true), true)
% 184.08/23.61 = { by axiom 4 (cn_1) R->L }
% 184.08/23.61 ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(x, implies(implies(y, z), z))), implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u)))), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(x, implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(x, implies(implies(y, z), z)), u), implies(implies(not(z), y), u))), true), true)
% 184.08/23.61 = { by axiom 5 (condensed_detachment) }
% 184.08/23.61 true
% 184.08/23.61 % SZS output end Proof
% 184.08/23.61
% 184.08/23.61 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------