%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL112-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 11:49:04 AM UTC 2026
% Result : Unsatisfiable 2.78s 0.88s
% Output : Proof 3.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL112-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:24:38 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.78/0.88 Command-line arguments: --no-flatten-goal
% 2.78/0.88
% 2.78/0.88 % SZS status Unsatisfiable
% 2.78/0.88
% 3.50/0.96 % SZS output start Proof
% 3.50/0.96 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.50/0.96 Axiom 2 (mv_1): is_a_theorem(implies(X, implies(Y, X))) = true.
% 3.50/0.96 Axiom 3 (mv_5): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 3.50/0.96 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.
% 3.50/0.96 Axiom 5 (mv_2): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 3.50/0.97 Axiom 6 (mv_3): is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) = true.
% 3.50/0.97
% 3.50/0.97 Goal 1 (prove_mv_29): is_a_theorem(implies(a, not(not(a)))) = true.
% 3.50/0.97 Proof:
% 3.50/0.97 is_a_theorem(implies(a, not(not(a))))
% 3.50/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/0.97 ifeq(true, true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 4 (condensed_detachment) R->L }
% 3.50/0.97 ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true, ifeq(is_a_theorem(implies(X, implies(Y, X))), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 2 (mv_1) }
% 3.50/0.97 ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true, ifeq(true, true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.50/0.97 ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/0.97 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 4 (condensed_detachment) R->L }
% 3.50/0.97 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))), implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 5 (mv_2) }
% 3.50/0.97 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.50/0.97 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/0.97 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.98 = { by axiom 3 (mv_5) R->L }
% 3.50/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.98 = { by axiom 4 (condensed_detachment) R->L }
% 3.50/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.98 = { by axiom 5 (mv_2) }
% 3.50/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.98 = { by axiom 1 (ifeq_axiom) }
% 3.50/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/0.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.99 = { by axiom 3 (mv_5) R->L }
% 3.50/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.99 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.99 = { by axiom 4 (condensed_detachment) R->L }
% 3.50/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(a))))), implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/0.99 = { by axiom 2 (mv_1) }
% 3.50/0.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(a))))), implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, implies(Y, X)))), not(not(not(a))))), implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 5 (mv_2) }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, implies(Y, X)))), not(not(not(a)))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, implies(Y, X)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 4 (condensed_detachment) }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a))), implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a))))), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, implies(Y, X)))), implies(implies(X, implies(Y, X)), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, implies(Y, X)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 4 (condensed_detachment) }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.00 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/1.00 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 4 (condensed_detachment) R->L }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))))), true, ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.00 = { by axiom 5 (mv_2) }
% 3.50/1.00 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.01 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.01 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.01 = { by axiom 6 (mv_3) R->L }
% 3.50/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.01 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.01 = { by axiom 4 (condensed_detachment) R->L }
% 3.50/1.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X)))), implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))))), true, ifeq(is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))))), true, is_a_theorem(implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.01 = { by axiom 2 (mv_1) }
% 3.50/1.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X)))), implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, X)), implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X)))), implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))))), true, is_a_theorem(implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 5 (mv_2) }
% 3.50/1.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.02 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))), implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(a), implies(X, implies(Y, X))), implies(X, implies(Y, X))), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(implies(implies(X, implies(Y, X)), not(a)), not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 4 (condensed_detachment) }
% 3.50/1.02 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.02 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a))), implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, X)), not(a)), not(a)), implies(not(not(not(a))), not(a)))), true, is_a_theorem(implies(implies(X, implies(Y, X)), implies(not(not(not(a))), not(a)))), true), true), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 4 (condensed_detachment) }
% 3.50/1.02 ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 1 (ifeq_axiom) }
% 3.50/1.02 ifeq(is_a_theorem(implies(not(not(not(a))), not(a))), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.50/1.02 = { by axiom 1 (ifeq_axiom) R->L }
% 3.50/1.02 ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(a))), not(a))), true, is_a_theorem(implies(a, not(not(a)))), true), true)
% 3.50/1.02 = { by axiom 3 (mv_5) R->L }
% 3.50/1.02 ifeq(is_a_theorem(implies(implies(not(not(not(a))), not(a)), implies(a, not(not(a))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), not(a))), true, is_a_theorem(implies(a, not(not(a)))), true), true)
% 3.50/1.02 = { by axiom 4 (condensed_detachment) }
% 3.50/1.02 true
% 3.50/1.02 % SZS output end Proof
% 3.50/1.02
% 3.50/1.02 RESULT: Unsatisfiable (the axioms are contradictory).
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