%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL076-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 11:48:58 AM UTC 2026
% Result : Unsatisfiable 0.47s 0.53s
% Output : Proof 1.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL076-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 15:23:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.53 Command-line arguments: --no-flatten-goal
% 0.47/0.53
% 0.47/0.53 % SZS status Unsatisfiable
% 0.47/0.53
% 0.47/0.59 % SZS output start Proof
% 0.47/0.59 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.47/0.59 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 0.47/0.59 Axiom 3 (cn_49): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 0.47/0.59 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.
% 0.47/0.59 Axiom 5 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 0.47/0.59
% 0.47/0.59 Goal 1 (prove_cn_40): is_a_theorem(implies(a, not(not(a)))) = true.
% 0.47/0.59 Proof:
% 0.47/0.59 is_a_theorem(implies(a, not(not(a))))
% 0.47/0.59 = { by axiom 1 (ifeq_axiom) R->L }
% 0.47/0.59 ifeq(true, true, is_a_theorem(implies(a, not(not(a)))), true)
% 0.47/0.59 = { by axiom 4 (condensed_detachment) R->L }
% 0.47/0.59 ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), implies(not(not(not(a))), not(a)))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(X, not(not(not(a)))))), true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 0.47/0.60 = { by axiom 2 (cn_18) }
% 0.47/0.60 ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 0.47/0.60 = { by axiom 1 (ifeq_axiom) }
% 0.47/0.60 ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 0.47/0.60 = { by axiom 1 (ifeq_axiom) R->L }
% 0.47/0.60 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 0.47/0.60 = { by axiom 4 (condensed_detachment) R->L }
% 0.47/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 0.47/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 0.47/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 0.47/0.61 = { by axiom 4 (condensed_detachment) R->L }
% 0.47/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 0.47/0.61 = { by axiom 5 (cn_35) }
% 0.47/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 0.47/0.61 = { by axiom 1 (ifeq_axiom) }
% 0.47/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.61 = { by axiom 1 (ifeq_axiom) R->L }
% 1.47/0.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.61 = { by axiom 3 (cn_49) R->L }
% 1.47/0.62 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.62 = { by axiom 1 (ifeq_axiom) R->L }
% 1.47/0.62 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.62 = { by axiom 2 (cn_18) R->L }
% 1.47/0.62 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.62 = { by axiom 4 (condensed_detachment) }
% 1.47/0.62 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.62 = { by axiom 1 (ifeq_axiom) }
% 1.47/0.62 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 2 (cn_18) R->L }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a))))), implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(not(not(implies(X, not(not(not(a)))))), not(not(not(a)))))), true, is_a_theorem(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a)))))))), true), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 4 (condensed_detachment) }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 1 (ifeq_axiom) }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 1 (ifeq_axiom) R->L }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 4 (condensed_detachment) R->L }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))), implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a)))))), true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 2 (cn_18) }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))))), true), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 1 (ifeq_axiom) }
% 1.47/0.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a)))), true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.63 = { by axiom 3 (cn_49) }
% 1.47/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 1 (ifeq_axiom) }
% 1.47/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 1 (ifeq_axiom) R->L }
% 1.47/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 5 (cn_35) R->L }
% 1.47/0.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a)))), implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(not(not(a)), not(implies(X, not(not(not(a)))))), implies(implies(X, not(not(not(a)))), not(a))))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(not(not(a)), not(implies(X, not(not(not(a))))))), implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))))), true), true), true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 4 (condensed_detachment) }
% 1.47/0.64 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 1 (ifeq_axiom) }
% 1.47/0.64 ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 1 (ifeq_axiom) R->L }
% 1.47/0.64 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 5 (cn_35) R->L }
% 1.47/0.64 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a))), implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), implies(not(not(not(a))), not(a))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), implies(implies(X, not(not(not(a)))), not(a)))), true, is_a_theorem(implies(implies(not(not(not(a))), implies(X, not(not(not(a))))), 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)
% 1.47/0.64 = { by axiom 4 (condensed_detachment) }
% 1.47/0.64 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)
% 1.47/0.64 = { by axiom 1 (ifeq_axiom) }
% 1.47/0.64 ifeq(is_a_theorem(implies(not(not(not(a))), not(a))), true, is_a_theorem(implies(a, not(not(a)))), true)
% 1.47/0.64 = { by axiom 1 (ifeq_axiom) R->L }
% 1.47/0.64 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)
% 1.47/0.64 = { by axiom 3 (cn_49) R->L }
% 1.47/0.64 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)
% 1.47/0.64 = { by axiom 4 (condensed_detachment) }
% 1.47/0.64 true
% 1.47/0.64 % SZS output end Proof
% 1.47/0.64
% 1.47/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------