%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL362-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 11:49:39 AM UTC 2026
% Result : Unsatisfiable 1.31s 0.79s
% Output : Proof 2.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL362-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n010.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 15:36:31 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.31/0.79 Command-line arguments: --no-flatten-goal
% 1.31/0.79
% 1.31/0.79 % SZS status Unsatisfiable
% 1.31/0.79
% 2.29/0.93 % SZS output start Proof
% 2.29/0.93 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.29/0.93 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 2.29/0.93 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 2.29/0.93 Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 2.29/0.94 Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 2.29/0.94
% 2.29/0.94 Goal 1 (prove_cn_11): is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))) = true.
% 2.29/0.94 Proof:
% 2.29/0.94 is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))
% 2.29/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.94 ifeq(true, true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true)
% 2.29/0.94 = { by axiom 4 (condensed_detachment) R->L }
% 2.29/0.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(implies(y, y), implies(implies(not(y), y), y)))), true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true)
% 2.29/0.94 = { by axiom 3 (cn_2) }
% 2.29/0.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(implies(y, y), implies(implies(not(y), y), y)))), true, ifeq(true, true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true)
% 2.29/0.94 = { by axiom 1 (ifeq_axiom) }
% 2.29/0.94 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(implies(y, y), implies(implies(not(y), y), y)))), true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true)
% 2.29/0.94 = { by axiom 5 (cn_1) }
% 2.29/0.94 ifeq(ifeq(true, true, is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true)
% 2.29/0.94 = { by axiom 1 (ifeq_axiom) }
% 2.29/0.94 ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true)
% 2.29/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.94 ifeq(true, true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.94 = { by axiom 4 (condensed_detachment) R->L }
% 2.29/0.95 ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)), implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))))), true, ifeq(is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.95 = { by axiom 5 (cn_1) }
% 2.29/0.95 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.95 = { by axiom 1 (ifeq_axiom) }
% 2.29/0.95 ifeq(ifeq(is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.95 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.95 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.95 = { by axiom 4 (condensed_detachment) R->L }
% 2.29/0.95 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))))), true, ifeq(is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.95 = { by axiom 5 (cn_1) }
% 2.29/0.95 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.96 = { by axiom 1 (ifeq_axiom) }
% 2.29/0.96 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.96 = { by axiom 4 (condensed_detachment) R->L }
% 2.29/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y)))), implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))))), true, ifeq(is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.96 = { by axiom 5 (cn_1) }
% 2.29/0.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.97 = { by axiom 1 (ifeq_axiom) }
% 2.29/0.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.97 = { by axiom 4 (condensed_detachment) R->L }
% 2.29/0.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, ifeq(is_a_theorem(implies(implies(not(y), y), y)), true, is_a_theorem(implies(y, y)), true), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.97 = { by axiom 3 (cn_2) }
% 2.29/0.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, ifeq(true, true, is_a_theorem(implies(y, y)), true), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.98 = { by axiom 1 (ifeq_axiom) }
% 2.29/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.98 = { by axiom 5 (cn_1) R->L }
% 2.29/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.99 = { by axiom 2 (cn_3) R->L }
% 2.29/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, implies(not(y), y)), implies(implies(implies(not(y), y), y), implies(y, y)))), true, ifeq(is_a_theorem(implies(y, implies(not(y), y))), true, is_a_theorem(implies(implies(implies(not(y), y), y), implies(y, y))), true), true), true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.99 = { by axiom 4 (condensed_detachment) }
% 2.29/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(y, y)), true), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.99 = { by axiom 1 (ifeq_axiom) }
% 2.29/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.99 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/0.99 = { by axiom 2 (cn_3) R->L }
% 2.29/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(y, y), implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y)))))), true, ifeq(is_a_theorem(implies(y, y)), true, is_a_theorem(implies(not(implies(y, y)), not(implies(x, implies(implies(not(y), y), y))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.00 = { by axiom 4 (condensed_detachment) }
% 2.29/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.00 = { by axiom 1 (ifeq_axiom) }
% 2.29/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.00 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.01 = { by axiom 4 (condensed_detachment) R->L }
% 2.29/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y))), implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))))), true, ifeq(is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)))), true, is_a_theorem(implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.01 = { by axiom 2 (cn_3) }
% 2.29/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y))), implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.01 = { by axiom 1 (ifeq_axiom) }
% 2.29/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y))), implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))))), true, is_a_theorem(implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.01 = { by axiom 5 (cn_1) }
% 2.29/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.01 = { by axiom 1 (ifeq_axiom) }
% 2.29/1.02 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y))), implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, implies(implies(not(y), y), y))), implies(y, y)), implies(not(implies(y, y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(not(implies(y, y)), implies(y, y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.02 = { by axiom 4 (condensed_detachment) }
% 2.29/1.02 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.02 = { by axiom 1 (ifeq_axiom) }
% 2.29/1.02 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.02 = { by axiom 1 (ifeq_axiom) R->L }
% 2.29/1.02 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true, ifeq(true, true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.02 = { by axiom 3 (cn_2) R->L }
% 2.29/1.02 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y)), implies(implies(x, implies(implies(not(y), y), y)), implies(y, y)))), true, ifeq(is_a_theorem(implies(implies(not(implies(y, y)), implies(y, y)), implies(y, y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(y, y))), true), true), true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.02 = { by axiom 4 (condensed_detachment) }
% 2.29/1.02 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.02 = { by axiom 1 (ifeq_axiom) }
% 2.29/1.02 ifeq(is_a_theorem(implies(implies(implies(y, y), implies(implies(not(y), y), y)), implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y)))), true, ifeq(is_a_theorem(implies(implies(y, y), implies(implies(not(y), y), y))), true, is_a_theorem(implies(implies(x, implies(implies(not(y), y), y)), implies(implies(not(y), y), y))), true), true)
% 2.29/1.02 = { by axiom 4 (condensed_detachment) }
% 2.29/1.02 true
% 2.29/1.02 % SZS output end Proof
% 2.29/1.02
% 2.29/1.02 RESULT: Unsatisfiable (the axioms are contradictory).
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