%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL077-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:58 AM UTC 2026
% Result : Unsatisfiable 1.24s 0.65s
% Output : Proof 1.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL077-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:16:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.24/0.65 Command-line arguments: --no-flatten-goal
% 1.24/0.65
% 1.24/0.65 % SZS status Unsatisfiable
% 1.24/0.65
% 1.79/0.72 % SZS output start Proof
% 1.79/0.72 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.79/0.73 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 1.79/0.73 Axiom 3 (cn_49): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 1.79/0.73 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.
% 1.79/0.73 Axiom 5 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 1.79/0.73
% 1.79/0.73 Goal 1 (prove_cn_39): is_a_theorem(implies(not(not(a)), a)) = true.
% 1.79/0.73 Proof:
% 1.79/0.73 is_a_theorem(implies(not(not(a)), a))
% 1.79/0.73 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.73 ifeq(true, true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.73 = { by axiom 4 (condensed_detachment) R->L }
% 1.79/0.73 ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(X, not(not(a))), a)), implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a)))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.73 = { by axiom 5 (cn_35) }
% 1.79/0.73 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.73 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.73 ifeq(ifeq(is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.73 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.73 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.73 = { by axiom 4 (condensed_detachment) R->L }
% 1.79/0.73 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a))), implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.73 = { by axiom 5 (cn_35) }
% 1.79/0.74 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.74 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.74 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.74 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.74 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.74 = { by axiom 3 (cn_49) R->L }
% 1.79/0.74 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a))), true, is_a_theorem(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.74 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.75 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a))), true, is_a_theorem(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.75 = { by axiom 2 (cn_18) R->L }
% 1.79/0.75 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)), implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a))))), true, ifeq(is_a_theorem(implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a))), true, is_a_theorem(implies(not(not(a)), implies(implies(not(a), not(implies(X, not(not(a))))), implies(implies(X, not(not(a))), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.75 = { by axiom 4 (condensed_detachment) }
% 1.79/0.75 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.75 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.75 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.75 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.75 = { by axiom 4 (condensed_detachment) R->L }
% 1.79/0.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a))))), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.76 = { by axiom 2 (cn_18) }
% 1.79/0.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.76 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.76 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.77 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.77 = { by axiom 4 (condensed_detachment) R->L }
% 1.79/0.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a))))))), true, is_a_theorem(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.77 = { by axiom 2 (cn_18) }
% 1.79/0.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a))))))), true, is_a_theorem(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.77 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a))))))), true, is_a_theorem(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.77 = { by axiom 3 (cn_49) }
% 1.79/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.78 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.78 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.78 = { by axiom 5 (cn_35) R->L }
% 1.79/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a))))))), implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(not(not(implies(X, not(not(a))))), not(not(a))), implies(not(a), not(implies(X, not(not(a)))))))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(implies(X, not(not(a))))), not(not(a)))), implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.78 = { by axiom 4 (condensed_detachment) }
% 1.79/0.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.79 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a)))))), implies(not(not(a)), implies(implies(X, not(not(a))), a)))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(a), not(implies(X, not(not(a))))))), true, is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), a))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.79 = { by axiom 4 (condensed_detachment) }
% 1.79/0.79 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.79 = { by axiom 1 (ifeq_axiom) }
% 1.79/0.79 ifeq(is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.79/0.79 = { by axiom 1 (ifeq_axiom) R->L }
% 1.79/0.79 ifeq(is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true, ifeq(true, true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.79/0.79 = { by axiom 2 (cn_18) R->L }
% 1.79/0.79 ifeq(is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), a))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(X, not(not(a))))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.79/0.79 = { by axiom 4 (condensed_detachment) }
% 1.79/0.79 true
% 1.79/0.79 % SZS output end Proof
% 1.79/0.79
% 1.79/0.79 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------