%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL102-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:02 AM UTC 2026
% Result : Unsatisfiable 2.74s 0.81s
% Output : Proof 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL102-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:19:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.74/0.81 Command-line arguments: --no-flatten-goal
% 2.74/0.81
% 2.74/0.81 % SZS status Unsatisfiable
% 2.74/0.81
% 2.74/0.85 % SZS output start Proof
% 2.74/0.85 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.74/0.85 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 2.74/0.85 Axiom 3 (q_1): is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, Y), X)))) = true.
% 2.74/0.85 Axiom 4 (q_2): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, X), equivalent(Z, Y)))) = true.
% 2.74/0.85 Axiom 5 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 2.74/0.85
% 2.74/0.85 Goal 1 (prove_p_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) = true.
% 2.74/0.85 Proof:
% 2.74/0.85 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 2.74/0.85 = { by axiom 1 (ifeq_axiom) R->L }
% 2.74/0.85 ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.86 = { by axiom 2 (condensed_detachment) R->L }
% 2.74/0.86 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.86 = { by axiom 1 (ifeq_axiom) R->L }
% 2.74/0.86 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.86 = { by axiom 5 (lg_2) R->L }
% 2.74/0.86 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.86 = { by axiom 1 (ifeq_axiom) R->L }
% 2.74/0.86 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.86 = { by axiom 4 (q_2) R->L }
% 2.74/0.87 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.87 = { by axiom 2 (condensed_detachment) }
% 2.74/0.87 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.87 = { by axiom 1 (ifeq_axiom) }
% 2.74/0.87 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.87 = { by axiom 1 (ifeq_axiom) R->L }
% 2.74/0.87 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.87 = { by axiom 2 (condensed_detachment) R->L }
% 2.74/0.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.87 = { by axiom 4 (q_2) }
% 2.74/0.88 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.88 = { by axiom 1 (ifeq_axiom) }
% 2.74/0.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.88 = { by axiom 5 (lg_2) }
% 2.74/0.88 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.88 = { by axiom 1 (ifeq_axiom) }
% 2.74/0.88 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.88 = { by axiom 1 (ifeq_axiom) R->L }
% 2.74/0.88 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.88 = { by axiom 4 (q_2) R->L }
% 2.74/0.88 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(b, e)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), equivalent(a, e)), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.88 = { by axiom 2 (condensed_detachment) }
% 2.74/0.88 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.89 = { by axiom 1 (ifeq_axiom) }
% 2.74/0.89 ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 2.74/0.89 = { by axiom 1 (ifeq_axiom) R->L }
% 2.74/0.89 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 2.74/0.89 = { by axiom 2 (condensed_detachment) R->L }
% 2.74/0.90 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 2.74/0.90 = { by axiom 1 (ifeq_axiom) R->L }
% 2.74/0.90 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.90 = { by axiom 5 (lg_2) R->L }
% 3.53/0.90 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.91 = { by axiom 1 (ifeq_axiom) R->L }
% 3.53/0.91 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.91 = { by axiom 4 (q_2) R->L }
% 3.53/0.91 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.91 = { by axiom 2 (condensed_detachment) }
% 3.53/0.92 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.92 = { by axiom 1 (ifeq_axiom) }
% 3.53/0.92 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.92 = { by axiom 1 (ifeq_axiom) R->L }
% 3.53/0.92 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.92 = { by axiom 3 (q_1) R->L }
% 3.53/0.92 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.92 = { by axiom 1 (ifeq_axiom) R->L }
% 3.53/0.92 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.92 = { by axiom 4 (q_2) R->L }
% 3.53/0.92 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, e), c), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(b, e), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.92 = { by axiom 2 (condensed_detachment) }
% 3.53/0.92 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.92 = { by axiom 1 (ifeq_axiom) }
% 3.53/0.93 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, e), equivalent(equivalent(a, b), c)), equivalent(equivalent(a, e), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 3.53/0.93 = { by axiom 2 (condensed_detachment) }
% 3.53/0.93 true
% 3.53/0.93 % SZS output end Proof
% 3.53/0.93
% 3.53/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------