%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL064-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 11:48:56 AM UTC 2026
% Result : Unsatisfiable 0.62s 0.56s
% Output : Proof 2.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL064-2 : 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 : n020.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 15:21:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.56 Command-line arguments: --no-flatten-goal
% 0.62/0.56
% 0.62/0.56 % SZS status Unsatisfiable
% 0.62/0.56
% 1.91/0.70 % SZS output start Proof
% 1.91/0.70 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.91/0.70 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 1.91/0.70 Axiom 3 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 2.13/0.70 Axiom 4 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 2.13/0.70
% 2.13/0.70 Goal 1 (prove_cn_1): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 2.13/0.70 Proof:
% 2.13/0.70 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 2.13/0.70 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.70 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.70 = { by axiom 3 (condensed_detachment) R->L }
% 2.13/0.70 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(a, c))), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.70 = { by axiom 4 (cn_35) }
% 2.13/0.70 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.70 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.70 ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.70 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.70 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.70 = { by axiom 3 (condensed_detachment) R->L }
% 2.13/0.70 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))), implies(implies(b, 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, c)))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.70 = { by axiom 2 (cn_18) }
% 2.13/0.70 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.71 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.71 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.71 = { by axiom 4 (cn_35) }
% 2.13/0.71 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.71 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.71 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.71 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.71 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.71 = { by axiom 3 (condensed_detachment) R->L }
% 2.13/0.71 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.72 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.72 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.72 = { by axiom 2 (cn_18) R->L }
% 2.13/0.72 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(b, c), implies(a, implies(b, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.72 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.72 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, c), implies(a, implies(b, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.72 = { by axiom 2 (cn_18) R->L }
% 2.13/0.72 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(a, implies(b, c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.72 = { by axiom 3 (condensed_detachment) }
% 2.13/0.72 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.72 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.72 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.72 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.73 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 4 (cn_35) R->L }
% 2.13/0.73 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.73 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 4 (cn_35) R->L }
% 2.13/0.73 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(implies(b, c), implies(a, implies(b, c))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(a, implies(b, c)))), implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 3 (condensed_detachment) }
% 2.13/0.73 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.73 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, implies(b, c)), implies(implies(a, b), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 3 (condensed_detachment) }
% 2.13/0.73 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.73 ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 2.13/0.73 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.73 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.74 = { by axiom 3 (condensed_detachment) R->L }
% 2.13/0.74 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.74 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.74 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.74 = { by axiom 3 (condensed_detachment) R->L }
% 2.13/0.74 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.75 = { by axiom 4 (cn_35) }
% 2.13/0.75 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.75 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.75 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.76 = { by axiom 4 (cn_35) }
% 2.13/0.76 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.76 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.76 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.77 = { by axiom 3 (condensed_detachment) R->L }
% 2.13/0.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.78 = { by axiom 2 (cn_18) }
% 2.13/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.78 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.78 = { by axiom 2 (cn_18) }
% 2.13/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.78 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.79 = { by axiom 3 (condensed_detachment) }
% 2.13/0.79 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.79 = { by axiom 1 (ifeq_axiom) }
% 2.13/0.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.79 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.79 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.79 = { by axiom 3 (condensed_detachment) R->L }
% 2.13/0.79 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.80 = { by axiom 1 (ifeq_axiom) R->L }
% 2.13/0.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.80 = { by axiom 2 (cn_18) R->L }
% 2.13/0.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.13/0.80 = { by axiom 1 (ifeq_axiom) R->L }
% 2.84/0.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.80 = { by axiom 2 (cn_18) R->L }
% 2.84/0.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, b)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.81 = { by axiom 3 (condensed_detachment) }
% 2.84/0.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.81 = { by axiom 1 (ifeq_axiom) }
% 2.84/0.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.81 = { by axiom 1 (ifeq_axiom) R->L }
% 2.84/0.81 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.81 = { by axiom 4 (cn_35) R->L }
% 2.84/0.81 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.81 = { by axiom 1 (ifeq_axiom) R->L }
% 2.84/0.81 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.81 = { by axiom 4 (cn_35) R->L }
% 2.84/0.81 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, b))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, b)))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.82 = { by axiom 3 (condensed_detachment) }
% 2.84/0.82 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.82 = { by axiom 1 (ifeq_axiom) }
% 2.84/0.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.82 = { by axiom 1 (ifeq_axiom) R->L }
% 2.84/0.82 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.82 = { by axiom 2 (cn_18) R->L }
% 2.84/0.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.82 = { by axiom 3 (condensed_detachment) }
% 2.84/0.82 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.82 = { by axiom 1 (ifeq_axiom) }
% 2.84/0.82 ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, b)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 2.84/0.82 = { by axiom 3 (condensed_detachment) }
% 2.84/0.82 true
% 2.84/0.82 % SZS output end Proof
% 2.84/0.82
% 2.84/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------