%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL064-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 6.44s 1.39s
% Output : Proof 9.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL064-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n002.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 27 15:22:51 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.44/1.39 Command-line arguments: --no-flatten-goal
% 6.44/1.39
% 6.44/1.39 % SZS status Unsatisfiable
% 6.44/1.39
% 8.61/1.61 % SZS output start Proof
% 8.61/1.61 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 8.61/1.61 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 8.61/1.61 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.
% 8.61/1.62 Axiom 4 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 8.61/1.62
% 8.61/1.62 Goal 1 (prove_cn_1): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 8.61/1.62 Proof:
% 8.61/1.62 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 8.61/1.62 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.62 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 8.61/1.62 = { by axiom 3 (condensed_detachment) R->L }
% 8.61/1.62 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)
% 8.61/1.62 = { by axiom 4 (cn_35) }
% 8.61/1.62 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)
% 8.61/1.62 = { by axiom 1 (ifeq_axiom) }
% 8.61/1.62 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)
% 8.61/1.62 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.63 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)
% 8.61/1.63 = { by axiom 3 (condensed_detachment) R->L }
% 8.61/1.63 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)
% 8.61/1.63 = { by axiom 2 (cn_18) }
% 8.61/1.63 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)
% 8.61/1.63 = { by axiom 1 (ifeq_axiom) }
% 8.61/1.63 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)
% 8.61/1.63 = { by axiom 4 (cn_35) }
% 8.61/1.63 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)
% 8.61/1.63 = { by axiom 1 (ifeq_axiom) }
% 8.61/1.63 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)
% 8.61/1.63 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.63 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)
% 8.61/1.64 = { by axiom 3 (condensed_detachment) R->L }
% 8.61/1.64 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)
% 8.61/1.64 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.64 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)
% 8.61/1.65 = { by axiom 2 (cn_18) R->L }
% 8.61/1.65 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)
% 8.61/1.65 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.65 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)
% 8.61/1.65 = { by axiom 2 (cn_18) R->L }
% 8.61/1.66 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)
% 8.61/1.66 = { by axiom 3 (condensed_detachment) }
% 8.61/1.66 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)
% 8.61/1.66 = { by axiom 1 (ifeq_axiom) }
% 8.61/1.66 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)
% 8.61/1.66 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.66 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)
% 8.61/1.66 = { by axiom 4 (cn_35) R->L }
% 8.61/1.66 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)
% 8.61/1.66 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.67 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)
% 8.61/1.67 = { by axiom 4 (cn_35) R->L }
% 8.61/1.67 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)
% 8.61/1.67 = { by axiom 3 (condensed_detachment) }
% 8.61/1.67 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)
% 8.61/1.67 = { by axiom 1 (ifeq_axiom) }
% 8.61/1.67 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)
% 8.61/1.67 = { by axiom 3 (condensed_detachment) }
% 8.61/1.67 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)
% 8.61/1.67 = { by axiom 1 (ifeq_axiom) }
% 8.61/1.67 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)
% 8.61/1.67 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.67 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)
% 8.61/1.68 = { by axiom 3 (condensed_detachment) R->L }
% 8.61/1.68 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)
% 8.61/1.68 = { by axiom 1 (ifeq_axiom) R->L }
% 8.61/1.68 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)
% 8.61/1.69 = { by axiom 3 (condensed_detachment) R->L }
% 8.61/1.69 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)
% 8.61/1.69 = { by axiom 4 (cn_35) }
% 9.25/1.70 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)
% 9.25/1.71 = { by axiom 1 (ifeq_axiom) }
% 9.25/1.71 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)
% 9.25/1.71 = { by axiom 4 (cn_35) }
% 9.25/1.71 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)
% 9.25/1.72 = { by axiom 1 (ifeq_axiom) }
% 9.25/1.72 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)
% 9.25/1.73 = { by axiom 1 (ifeq_axiom) R->L }
% 9.25/1.74 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)
% 9.25/1.74 = { by axiom 3 (condensed_detachment) R->L }
% 9.25/1.74 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)
% 9.25/1.75 = { by axiom 2 (cn_18) }
% 9.25/1.75 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)
% 9.25/1.75 = { by axiom 1 (ifeq_axiom) }
% 9.25/1.76 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, 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)
% 9.25/1.76 = { by axiom 2 (cn_18) }
% 9.25/1.76 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, 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)
% 9.25/1.76 = { by axiom 1 (ifeq_axiom) }
% 9.25/1.76 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, 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)
% 9.25/1.77 = { by axiom 3 (condensed_detachment) }
% 9.25/1.77 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)
% 9.25/1.77 = { by axiom 1 (ifeq_axiom) }
% 9.25/1.77 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)
% 9.25/1.77 = { by axiom 1 (ifeq_axiom) R->L }
% 9.25/1.77 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)
% 9.25/1.77 = { by axiom 3 (condensed_detachment) R->L }
% 9.25/1.78 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)
% 9.25/1.78 = { by axiom 1 (ifeq_axiom) R->L }
% 9.25/1.78 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)
% 9.25/1.79 = { by axiom 2 (cn_18) R->L }
% 9.25/1.79 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(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)
% 9.25/1.79 = { by axiom 1 (ifeq_axiom) R->L }
% 9.25/1.79 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(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)
% 9.25/1.79 = { by axiom 2 (cn_18) R->L }
% 9.25/1.79 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(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)
% 9.25/1.79 = { by axiom 3 (condensed_detachment) }
% 9.25/1.80 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(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)
% 9.25/1.80 = { by axiom 1 (ifeq_axiom) }
% 9.25/1.80 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, 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)
% 9.25/1.80 = { by axiom 1 (ifeq_axiom) R->L }
% 9.96/1.80 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)
% 9.96/1.81 = { by axiom 4 (cn_35) R->L }
% 9.96/1.81 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)
% 9.96/1.81 = { by axiom 1 (ifeq_axiom) R->L }
% 9.96/1.81 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)
% 9.96/1.81 = { by axiom 4 (cn_35) R->L }
% 9.96/1.81 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)
% 9.96/1.81 = { by axiom 3 (condensed_detachment) }
% 9.96/1.81 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)
% 9.96/1.81 = { by axiom 1 (ifeq_axiom) }
% 9.96/1.81 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)
% 9.96/1.81 = { by axiom 1 (ifeq_axiom) R->L }
% 9.96/1.81 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)
% 9.96/1.81 = { by axiom 2 (cn_18) R->L }
% 9.96/1.82 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)
% 9.96/1.82 = { by axiom 3 (condensed_detachment) }
% 9.96/1.82 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)
% 9.96/1.82 = { by axiom 1 (ifeq_axiom) }
% 9.96/1.82 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)
% 9.96/1.82 = { by axiom 3 (condensed_detachment) }
% 9.96/1.82 true
% 9.96/1.82 % SZS output end Proof
% 9.96/1.82
% 9.96/1.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------