Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n003.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 11:48:59 AM UTC 2026

% Result   : Unsatisfiable 0.14s 0.47s
% Output   : Proof 2.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL081-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35  % Computer : n003.cluster.edu
% 0.09/0.35  % Model    : x86_64 x86_64
% 0.09/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35  % Memory   : 8046.5625MB
% 0.09/0.35  % OS       : Linux 6.8.0-71-generic
% 0.09/0.35  % CPULimit : 300
% 0.09/0.35  % WCLimit  : 300
% 0.09/0.35  % DateTime : Sun Sep 27 15:22:55 UTC 2026
% 0.09/0.35  % CPUTime  : 
% 0.09/0.35  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.47  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.47  
% 0.14/0.47  % SZS status Unsatisfiable
% 0.14/0.47  
% 1.82/0.68  % SZS output start Proof
% 1.82/0.68  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.82/0.68  Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 1.82/0.69  Axiom 3 (ic_JLukasiewicz): is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))) = true.
% 1.82/0.69  
% 1.82/0.69  Goal 1 (prove_ic_1): is_a_theorem(implies(a, a)) = true.
% 1.82/0.69  Proof:
% 1.82/0.69    is_a_theorem(implies(a, a))
% 1.82/0.69  = { by axiom 1 (ifeq_axiom) R->L }
% 1.82/0.69    ifeq(true, true, is_a_theorem(implies(a, a)), true)
% 1.82/0.70  = { by axiom 1 (ifeq_axiom) R->L }
% 1.82/0.70    ifeq(true, true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 1.82/0.70  = { by axiom 2 (condensed_detachment) R->L }
% 1.82/0.70    ifeq(ifeq(is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 1.82/0.70  = { by axiom 1 (ifeq_axiom) R->L }
% 1.82/0.70    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 1.82/0.70  = { by axiom 2 (condensed_detachment) R->L }
% 1.82/0.70    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(a, a)), implies(implies(implies(a, a), a), implies(X, a)))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 1.82/0.70  = { by axiom 3 (ic_JLukasiewicz) }
% 1.82/0.70    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 1.82/0.70  = { by axiom 1 (ifeq_axiom) }
% 1.82/0.70    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 1.82/0.70  = { by axiom 1 (ifeq_axiom) R->L }
% 1.82/0.70    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.70  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.70  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.71  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.71  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.71  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.71  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.72  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.72  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.72  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a))), implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), implies(a, a)), implies(implies(implies(W, a), implies(V, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))), implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.72  = { by axiom 2 (condensed_detachment) }
% 2.14/0.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.72  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.73  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.73  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), W), implies(implies(W, a), implies(V, a))), implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.73  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), W), implies(implies(W, a), implies(V, a))), implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.73  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), W), implies(implies(W, a), implies(V, a))), implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), W), implies(implies(W, a), implies(V, a)))), true, is_a_theorem(implies(implies(implies(implies(W, a), implies(V, a)), implies(a, a)), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.73  = { by axiom 2 (condensed_detachment) }
% 2.14/0.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.73  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.73    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U))), implies(implies(a, a), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(implies(U, T), S), implies(implies(S, U), implies(X2, U)))), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 2 (condensed_detachment) }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.74    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(X, a)), implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(X, a))), true, is_a_theorem(implies(implies(implies(X, a), implies(a, a)), implies(implies(Y, implies(Z, Z)), implies(a, a)))), true), true), true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 2 (condensed_detachment) }
% 2.14/0.74    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.74    ifeq(ifeq(is_a_theorem(implies(implies(X, a), implies(a, a))), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), X), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), X), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), X), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.74  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), X), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a))), implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, a), implies(a, a)), implies(a, a)), implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))), implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 2 (condensed_detachment) }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), Y2), implies(implies(Y2, a), implies(Z2, a))), implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), Y2), implies(implies(Y2, a), implies(Z2, a))), implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), Y2), implies(implies(Y2, a), implies(Z2, a))), implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), Y2), implies(implies(Y2, a), implies(Z2, a)))), true, is_a_theorem(implies(implies(implies(implies(Y2, a), implies(Z2, a)), implies(a, a)), implies(implies(X, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 2 (condensed_detachment) }
% 2.14/0.75    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.75    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.75    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2))), implies(implies(X, a), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(implies(W2, V2), U2), implies(implies(U2, W2), implies(T2, W2)))), true, is_a_theorem(implies(implies(X, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 2 (condensed_detachment) }
% 2.14/0.75    ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.75    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.75    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.75  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.75    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, Z), implies(Z, Z)), implies(implies(implies(Z, Z), Z), implies(S2, Z)))), true, ifeq(is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), Z), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, Z), Z), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.76  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.76    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), Z), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.77  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.77    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), Z), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z))))), true, is_a_theorem(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.77  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.77    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.77  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.77    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.77  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.77    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.77  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.77    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z))), implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))), implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.77  = { by axiom 2 (condensed_detachment) }
% 2.14/0.77    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.77  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.77    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), X3), implies(implies(X3, Z), implies(Y3, Z))), implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))))), true, is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), X3), implies(implies(X3, Z), implies(Y3, Z))), implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), X3), implies(implies(X3, Z), implies(Y3, Z))), implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, Z), X3), implies(implies(X3, Z), implies(Y3, Z)))), true, is_a_theorem(implies(implies(implies(implies(X3, Z), implies(Y3, Z)), implies(Z, Z)), implies(implies(Z, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 2 (condensed_detachment) }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true, ifeq(true, true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3))), implies(implies(Z, Z), implies(Z, Z)))), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), V3), implies(implies(V3, Z3), implies(U3, Z3)))), true, is_a_theorem(implies(implies(Z, Z), implies(Z, Z))), true), true), true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 2 (condensed_detachment) }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.78    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), Z), implies(S2, Z)), implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, Z), Z), implies(S2, Z))), true, is_a_theorem(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Y, implies(Z, Z)))), true), true), true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.78  = { by axiom 2 (condensed_detachment) }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 2 (condensed_detachment) R->L }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), S2), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, Z), S2), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), S2), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), S2), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z))))), true, is_a_theorem(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 3 (ic_JLukasiewicz) }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.14/0.79    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z))), implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S2, Z), implies(Z, Z)), implies(Z, Z)), implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))), implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.79  = { by axiom 2 (condensed_detachment) }
% 2.14/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.80  = { by axiom 1 (ifeq_axiom) }
% 2.14/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.80  = { by axiom 1 (ifeq_axiom) R->L }
% 2.14/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.14/0.80  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), T3), implies(implies(T3, Z), implies(S3, Z))), implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))))), true, is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 1 (ifeq_axiom) R->L }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), T3), implies(implies(T3, Z), implies(S3, Z))), implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Z), T3), implies(implies(T3, Z), implies(S3, Z))), implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, Z), T3), implies(implies(T3, Z), implies(S3, Z)))), true, is_a_theorem(implies(implies(implies(implies(T3, Z), implies(S3, Z)), implies(Z, Z)), implies(implies(S2, Z), implies(Z, Z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 2 (condensed_detachment) }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 1 (ifeq_axiom) }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 1 (ifeq_axiom) R->L }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true, ifeq(true, true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4))), implies(implies(S2, Z), implies(Z, Z)))), true, ifeq(is_a_theorem(implies(implies(implies(X4, Y4), Z4), implies(implies(Z4, X4), implies(W4, X4)))), true, is_a_theorem(implies(implies(S2, Z), implies(Z, Z))), true), true), true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 2 (condensed_detachment) }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(ifeq(true, true, is_a_theorem(implies(Y, implies(Z, Z))), true), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 1 (ifeq_axiom) }
% 2.76/0.80    ifeq(is_a_theorem(implies(implies(Y, implies(Z, Z)), implies(a, a))), true, ifeq(is_a_theorem(implies(Y, implies(Z, Z))), true, is_a_theorem(implies(a, a)), true), true)
% 2.76/0.80  = { by axiom 2 (condensed_detachment) }
% 2.76/0.80    true
% 2.76/0.80  % SZS output end Proof
% 2.76/0.80  
% 2.76/0.80  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------