%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL115-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:05 AM UTC 2026
% Result : Unsatisfiable 29.08s 4.11s
% Output : Proof 32.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL115-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 15:28:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.08/4.11 Command-line arguments: --no-flatten-goal
% 29.08/4.11
% 29.08/4.11 % SZS status Unsatisfiable
% 29.08/4.11
% 31.54/4.44 % SZS output start Proof
% 31.54/4.44 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 31.54/4.44 Axiom 2 (mv_1): is_a_theorem(implies(X, implies(Y, X))) = true.
% 31.54/4.44 Axiom 3 (mv_5): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 31.54/4.44 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.
% 31.54/4.44 Axiom 5 (mv_2): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 31.54/4.46 Axiom 6 (mv_3): is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) = true.
% 31.54/4.46
% 31.54/4.46 Goal 1 (prove_mv_39): is_a_theorem(implies(not(implies(a, b)), not(b))) = true.
% 31.54/4.46 Proof:
% 31.54/4.46 is_a_theorem(implies(not(implies(a, b)), not(b)))
% 31.54/4.46 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.46 ifeq(true, true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 4 (condensed_detachment) R->L }
% 31.54/4.46 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), not(not(implies(a, b)))), implies(implies(not(b), not(a)), not(not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.46 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), not(not(implies(a, b)))), implies(implies(not(b), not(a)), not(not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 3 (mv_5) R->L }
% 31.54/4.46 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), not(not(implies(a, b)))), implies(implies(not(b), not(a)), not(not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.46 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), not(not(implies(a, b)))), implies(implies(not(b), not(a)), not(not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 5 (mv_2) R->L }
% 31.54/4.46 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), not(a)), implies(a, b)), implies(implies(implies(a, b), not(not(implies(a, b)))), implies(implies(not(b), not(a)), not(not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), not(not(implies(a, b)))), implies(implies(not(b), not(a)), not(not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 4 (condensed_detachment) }
% 31.54/4.46 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 1 (ifeq_axiom) }
% 31.54/4.46 ifeq(ifeq(is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.46 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.47 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.47 = { by axiom 4 (condensed_detachment) R->L }
% 31.54/4.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, ifeq(is_a_theorem(implies(X, implies(Y, X))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.47 = { by axiom 2 (mv_1) }
% 31.54/4.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.47 = { by axiom 1 (ifeq_axiom) }
% 31.54/4.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.47 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.48 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.48 = { by axiom 4 (condensed_detachment) R->L }
% 31.54/4.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.48 = { by axiom 5 (mv_2) }
% 31.54/4.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.48 = { by axiom 1 (ifeq_axiom) }
% 31.54/4.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.48 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.49 = { by axiom 3 (mv_5) R->L }
% 31.54/4.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.49 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.49 = { by axiom 4 (condensed_detachment) R->L }
% 31.54/4.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.50 = { by axiom 5 (mv_2) }
% 31.54/4.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.50 = { by axiom 1 (ifeq_axiom) }
% 31.54/4.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.51 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.52 = { by axiom 3 (mv_5) R->L }
% 31.54/4.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 31.54/4.53 = { by axiom 1 (ifeq_axiom) R->L }
% 31.54/4.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.53 = { by axiom 4 (condensed_detachment) R->L }
% 32.36/4.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(a, b)))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b)))))), implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.54 = { by axiom 2 (mv_1) }
% 32.36/4.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(a, b)))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b)))))), implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.55 = { by axiom 1 (ifeq_axiom) }
% 32.36/4.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(a, b)))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b)))))), implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.56 = { by axiom 5 (mv_2) }
% 32.36/4.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.56 = { by axiom 1 (ifeq_axiom) }
% 32.36/4.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))), implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(implies(a, b))))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.56 = { by axiom 4 (condensed_detachment) }
% 32.36/4.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.56 = { by axiom 1 (ifeq_axiom) }
% 32.36/4.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))), implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(a, b))), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true, is_a_theorem(implies(not(not(not(implies(a, b)))), implies(implies(X, implies(Y, X)), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.57 = { by axiom 4 (condensed_detachment) }
% 32.36/4.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.57 = { by axiom 1 (ifeq_axiom) }
% 32.36/4.57 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.57 = { by axiom 1 (ifeq_axiom) R->L }
% 32.36/4.58 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.58 = { by axiom 4 (condensed_detachment) R->L }
% 32.36/4.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.58 = { by axiom 5 (mv_2) }
% 32.36/4.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.58 = { by axiom 1 (ifeq_axiom) }
% 32.36/4.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.59 = { by axiom 1 (ifeq_axiom) R->L }
% 32.36/4.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.60 = { by axiom 6 (mv_3) R->L }
% 32.36/4.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.60 = { by axiom 1 (ifeq_axiom) R->L }
% 32.36/4.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.36/4.61 = { by axiom 4 (condensed_detachment) R->L }
% 32.96/4.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X)))), implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.62 = { by axiom 2 (mv_1) }
% 32.96/4.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X)))), implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.62 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X)))), implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.63 = { by axiom 5 (mv_2) }
% 32.96/4.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.63 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(a, b)), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.63 = { by axiom 4 (condensed_detachment) }
% 32.96/4.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.63 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b)))), implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(implies(a, b))), not(implies(a, b))), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(implies(a, b)))), not(implies(a, b))))), true), true), true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.63 = { by axiom 4 (condensed_detachment) }
% 32.96/4.63 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.64 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.64 ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.64 = { by axiom 1 (ifeq_axiom) R->L }
% 32.96/4.64 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.64 = { by axiom 3 (mv_5) R->L }
% 32.96/4.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(a, b)))), not(implies(a, b))), implies(implies(a, b), not(not(implies(a, b)))))), true, ifeq(is_a_theorem(implies(not(not(not(implies(a, b)))), not(implies(a, b)))), true, is_a_theorem(implies(implies(a, b), not(not(implies(a, b))))), true), true), true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.64 = { by axiom 4 (condensed_detachment) }
% 32.96/4.64 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.64 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.64 ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true)
% 32.96/4.64 = { by axiom 1 (ifeq_axiom) R->L }
% 32.96/4.64 ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.64 = { by axiom 4 (condensed_detachment) R->L }
% 32.96/4.64 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true, ifeq(is_a_theorem(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.64 = { by axiom 3 (mv_5) }
% 32.96/4.64 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.64 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.65 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.65 = { by axiom 1 (ifeq_axiom) R->L }
% 32.96/4.65 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.65 = { by axiom 4 (condensed_detachment) R->L }
% 32.96/4.65 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(b)), implies(not(b), not(a))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b))))))), true, ifeq(is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.65 = { by axiom 5 (mv_2) }
% 32.96/4.65 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.65 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.65 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.65 = { by axiom 1 (ifeq_axiom) R->L }
% 32.96/4.65 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.66 = { by axiom 3 (mv_5) R->L }
% 32.96/4.66 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a)))), true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.66 = { by axiom 1 (ifeq_axiom) R->L }
% 32.96/4.67 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a)))), true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.67 = { by axiom 4 (condensed_detachment) R->L }
% 32.96/4.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(b)), implies(not(not(a)), not(not(b)))), implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a)))))), true, ifeq(is_a_theorem(implies(not(not(b)), implies(not(not(a)), not(not(b))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a)))), true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.67 = { by axiom 2 (mv_1) }
% 32.96/4.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(b)), implies(not(not(a)), not(not(b)))), implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a)))), true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.67 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(b)), implies(not(not(a)), not(not(b)))), implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a)))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a)))), true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.67 = { by axiom 5 (mv_2) }
% 32.96/4.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a)))), true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.68 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a))), implies(not(not(b)), implies(not(b), not(a))))), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(b))), implies(not(b), not(a)))), true, is_a_theorem(implies(not(not(b)), implies(not(b), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 4 (condensed_detachment) }
% 32.96/4.68 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 1 (ifeq_axiom) R->L }
% 32.96/4.68 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 5 (mv_2) R->L }
% 32.96/4.68 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b))))), implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(not(b)), not(not(implies(a, b)))))), true, is_a_theorem(implies(implies(implies(not(not(b)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))), implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b))))), true), true), true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 4 (condensed_detachment) }
% 32.96/4.68 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 1 (ifeq_axiom) }
% 32.96/4.68 ifeq(is_a_theorem(implies(implies(implies(not(b), not(a)), not(not(implies(a, b)))), implies(not(implies(a, b)), not(b)))), true, ifeq(is_a_theorem(implies(implies(not(b), not(a)), not(not(implies(a, b))))), true, is_a_theorem(implies(not(implies(a, b)), not(b))), true), true)
% 32.96/4.68 = { by axiom 4 (condensed_detachment) }
% 32.96/4.68 true
% 32.96/4.68 % SZS output end Proof
% 32.96/4.68
% 32.96/4.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------