%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL030-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 11:48:52 AM UTC 2026
% Result : Unsatisfiable 198.97s 25.56s
% Output : Proof 200.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL030-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 15:18:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 198.97/25.56 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
% 198.97/25.56
% 198.97/25.56 % SZS status Unsatisfiable
% 198.97/25.56
% 199.80/25.67 % SZS output start Proof
% 199.80/25.67 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 199.80/25.67 Axiom 2 (c0_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 199.80/25.67 Axiom 3 (c0_3): is_a_theorem(implies(implies(implies(X, Y), X), X)) = true.
% 199.80/25.67 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.
% 199.80/25.67 Axiom 5 (c0_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 199.80/25.67
% 199.80/25.67 Goal 1 (prove_c0_6): is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))) = true.
% 199.80/25.67 Proof:
% 199.80/25.67 is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))
% 199.80/25.67 = { by axiom 1 (ifeq_axiom) R->L }
% 199.80/25.67 ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true)
% 199.80/25.67 = { by axiom 1 (ifeq_axiom) R->L }
% 199.80/25.67 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.67 = { by axiom 4 (condensed_detachment) R->L }
% 199.80/25.68 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c)))), implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 5 (c0_1) }
% 199.80/25.68 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.68 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 1 (ifeq_axiom) R->L }
% 199.80/25.68 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 4 (condensed_detachment) R->L }
% 199.80/25.68 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 5 (c0_1) }
% 199.80/25.68 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.68 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 5 (c0_1) }
% 199.80/25.68 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 1 (ifeq_axiom) R->L }
% 199.80/25.68 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 4 (condensed_detachment) R->L }
% 199.80/25.68 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c)))), implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 5 (c0_1) }
% 199.80/25.68 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.68 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.68 = { by axiom 5 (c0_1) }
% 199.80/25.69 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.69 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.69 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c)))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(a, implies(a, c))), implies(implies(a, b), implies(a, implies(a, c))))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.69 = { by axiom 4 (condensed_detachment) }
% 199.80/25.69 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.69 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.69 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.69 = { by axiom 4 (condensed_detachment) R->L }
% 199.80/25.69 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.69 = { by axiom 1 (ifeq_axiom) R->L }
% 199.80/25.69 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.69 = { by axiom 5 (c0_1) R->L }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 1 (ifeq_axiom) R->L }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 5 (c0_1) R->L }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 4 (condensed_detachment) }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 1 (ifeq_axiom) R->L }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 4 (condensed_detachment) R->L }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 5 (c0_1) }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 1 (ifeq_axiom) }
% 199.80/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 199.80/25.70 = { by axiom 1 (ifeq_axiom) R->L }
% 200.59/25.70 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.70 = { by axiom 4 (condensed_detachment) R->L }
% 200.59/25.71 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c))), true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.71 = { by axiom 3 (c0_3) }
% 200.59/25.71 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.71 = { by axiom 1 (ifeq_axiom) }
% 200.59/25.71 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.71 = { by axiom 1 (ifeq_axiom) R->L }
% 200.59/25.71 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.71 = { by axiom 5 (c0_1) R->L }
% 200.59/25.71 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, c)), implies(implies(implies(a, c), c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.72 = { by axiom 1 (ifeq_axiom) R->L }
% 200.59/25.72 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(a, c)), implies(implies(implies(a, c), c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.72 = { by axiom 5 (c0_1) R->L }
% 200.59/25.72 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(a, c)), implies(implies(implies(a, c), c), implies(a, c))), implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(a, implies(a, c)), implies(implies(implies(a, c), c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, c), c), implies(a, c)), implies(a, c)), implies(implies(a, implies(a, c)), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.72 = { by axiom 4 (condensed_detachment) }
% 200.59/25.72 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.72 = { by axiom 1 (ifeq_axiom) }
% 200.59/25.72 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.72 = { by axiom 1 (ifeq_axiom) R->L }
% 200.59/25.72 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.72 = { by axiom 2 (c0_2) R->L }
% 200.59/25.72 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(a, implies(a, c)), implies(a, c))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(a, c)), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.72 = { by axiom 4 (condensed_detachment) }
% 200.59/25.72 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.73 = { by axiom 1 (ifeq_axiom) }
% 200.59/25.73 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.73 = { by axiom 1 (ifeq_axiom) R->L }
% 200.59/25.73 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.73 = { by axiom 4 (condensed_detachment) R->L }
% 200.59/25.74 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.74 = { by axiom 3 (c0_3) }
% 200.59/25.74 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.74 = { by axiom 1 (ifeq_axiom) }
% 200.59/25.74 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.75 = { by axiom 1 (ifeq_axiom) R->L }
% 200.59/25.75 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.75 = { by axiom 5 (c0_1) R->L }
% 200.59/25.75 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.75 = { by axiom 1 (ifeq_axiom) R->L }
% 200.59/25.75 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.76 = { by axiom 5 (c0_1) R->L }
% 200.59/25.76 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.76 = { by axiom 4 (condensed_detachment) }
% 200.59/25.76 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.76 = { by axiom 1 (ifeq_axiom) }
% 200.59/25.76 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, c)), implies(a, c)), implies(implies(a, b), implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.76 = { by axiom 4 (condensed_detachment) }
% 200.59/25.76 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.76 = { by axiom 1 (ifeq_axiom) }
% 200.59/25.76 ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c))), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, c))), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true), true)
% 200.59/25.76 = { by axiom 4 (condensed_detachment) }
% 200.59/25.76 true
% 200.59/25.76 % SZS output end Proof
% 200.59/25.76
% 200.59/25.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------