%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL067-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 11:48:57 AM UTC 2026
% Result : Unsatisfiable 10.75s 1.86s
% Output : Proof 12.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL067-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n008.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 15:21:24 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.75/1.86 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 10.75/1.86
% 10.75/1.86 % SZS status Unsatisfiable
% 10.75/1.86
% 11.50/1.99 % SZS output start Proof
% 11.50/1.99 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 11.50/1.99 Axiom 2 (cn_19): is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))) = true.
% 11.50/1.99 Axiom 3 (cn_37): is_a_theorem(implies(implies(implies(X, Y), Z), implies(not(X), Z))) = true.
% 11.50/1.99 Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 11.50/2.00 Axiom 5 (cn_59): is_a_theorem(implies(implies(not(X), Y), implies(implies(Z, Y), implies(implies(X, Z), Y)))) = true.
% 11.50/2.00
% 11.50/2.00 Goal 1 (prove_cn_1): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 11.50/2.00 Proof:
% 11.50/2.00 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 11.50/2.00 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.00 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 11.50/2.00 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.00 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.00 ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(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(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 5 (cn_59) }
% 11.50/2.00 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.00 ifeq(ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.00 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.00 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c))), implies(implies(a, c), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(X, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 2 (cn_19) }
% 11.50/2.00 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.00 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 2 (cn_19) }
% 11.50/2.00 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.00 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.00 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.00 = { by axiom 3 (cn_37) R->L }
% 11.50/2.01 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, c), implies(implies(b, c), implies(a, c))), implies(not(a), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.01 = { by axiom 4 (condensed_detachment) }
% 11.50/2.01 ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.01 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.01 ifeq(is_a_theorem(implies(implies(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(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 11.50/2.01 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.01 ifeq(is_a_theorem(implies(implies(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(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.01 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.01 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.01 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.02 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.02 = { by axiom 5 (cn_59) }
% 11.50/2.02 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.02 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.02 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.02 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.02 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.02 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.02 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.02 = { by axiom 2 (cn_19) }
% 11.50/2.02 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.03 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.03 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.03 = { by axiom 2 (cn_19) }
% 11.50/2.03 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.03 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.03 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.03 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.03 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.03 = { by axiom 3 (cn_37) R->L }
% 11.50/2.03 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c)))), implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(implies(b, c)), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.03 = { by axiom 4 (condensed_detachment) }
% 11.50/2.03 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 2 (cn_19) R->L }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c)))), implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(b, implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(b, implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 4 (condensed_detachment) }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(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(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(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(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 2 (cn_19) }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.04 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.04 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, implies(a, b)), implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(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(Z, 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(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 2 (cn_19) }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z, 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(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, 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(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 2 (cn_19) }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(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(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 2 (cn_19) R->L }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(a, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(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, c)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 4 (condensed_detachment) }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.05 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(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), true)
% 11.50/2.05 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 5 (cn_59) }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(implies(b, c), implies(a, c))), implies(implies(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(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 5 (cn_59) }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.06 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.06 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.07 = { by axiom 4 (condensed_detachment) R->L }
% 11.50/2.07 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c))), implies(implies(a, c), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(W, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.07 = { by axiom 2 (cn_19) }
% 11.50/2.07 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.07 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.07 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W, implies(b, c)), implies(a, c)), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.07 = { by axiom 2 (cn_19) }
% 11.50/2.07 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.07 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.07 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.07 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.07 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.07 = { by axiom 3 (cn_37) R->L }
% 11.50/2.08 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, c), implies(implies(b, c), implies(a, c))), implies(not(a), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(a, c), implies(implies(b, c), implies(a, c)))), true, is_a_theorem(implies(not(a), implies(implies(b, c), implies(a, c)))), true), true), true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.08 = { by axiom 4 (condensed_detachment) }
% 11.50/2.08 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(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(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.08 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.08 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.08 = { by axiom 1 (ifeq_axiom) R->L }
% 11.50/2.08 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.08 = { by axiom 3 (cn_37) R->L }
% 11.50/2.08 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(not(b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.08 = { by axiom 4 (condensed_detachment) }
% 11.50/2.08 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.08 = { by axiom 1 (ifeq_axiom) }
% 11.50/2.08 ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), implies(a, c))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(c, implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(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), true)
% 11.50/2.08 = { by axiom 4 (condensed_detachment) }
% 12.89/2.08 ifeq(is_a_theorem(implies(implies(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(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), true)
% 12.89/2.08 = { by axiom 1 (ifeq_axiom) }
% 12.89/2.08 ifeq(is_a_theorem(implies(implies(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(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)
% 12.89/2.09 = { by axiom 4 (condensed_detachment) }
% 12.89/2.09 true
% 12.89/2.09 % SZS output end Proof
% 12.89/2.09
% 12.89/2.09 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------