%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL065-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 11:48:57 AM UTC 2026
% Result : Unsatisfiable 3.44s 1.00s
% Output : Proof 4.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL065-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:20:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/1.00 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 3.44/1.00
% 3.44/1.00 % SZS status Unsatisfiable
% 3.44/1.00
% 3.44/1.07 % SZS output start Proof
% 3.44/1.07 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.44/1.07 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 3.44/1.07 Axiom 3 (cn_49): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 3.44/1.07 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.
% 3.44/1.08 Axiom 5 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 3.44/1.08
% 3.44/1.08 Goal 1 (prove_cn_2): is_a_theorem(implies(implies(not(a), a), a)) = true.
% 3.44/1.08 Proof:
% 3.44/1.08 is_a_theorem(implies(implies(not(a), a), a))
% 3.44/1.08 = { by axiom 1 (ifeq_axiom) R->L }
% 3.44/1.08 ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 3.44/1.08 = { by axiom 1 (ifeq_axiom) R->L }
% 3.44/1.08 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 3.44/1.08 = { by axiom 4 (condensed_detachment) R->L }
% 3.44/1.08 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 3.44/1.08 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.08 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.08 = { by axiom 5 (cn_35) R->L }
% 4.12/1.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(implies(not(a), a), implies(not(a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.08 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.08 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(implies(not(a), a), implies(not(a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.08 = { by axiom 5 (cn_35) R->L }
% 4.12/1.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(implies(not(a), a), implies(not(a), a)), implies(implies(not(a), a), a))), implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(implies(not(a), a), implies(not(a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.08 = { by axiom 4 (condensed_detachment) }
% 4.12/1.08 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.08 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.08 ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.08 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.09 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 5 (cn_35) R->L }
% 4.12/1.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(implies(not(a), a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(implies(not(a), a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 2 (cn_18) R->L }
% 4.12/1.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(implies(not(a), a), a), implies(not(a), a))), implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a))))), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(implies(implies(not(a), a), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 4 (condensed_detachment) }
% 4.12/1.09 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.09 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 4 (condensed_detachment) R->L }
% 4.12/1.09 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.09 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 4 (condensed_detachment) R->L }
% 4.12/1.09 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)), implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a))))), true, ifeq(is_a_theorem(implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 2 (cn_18) }
% 4.12/1.09 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.09 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.09 = { by axiom 3 (cn_49) }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 5 (cn_35) R->L }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a))))), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), not(implies(not(a), a))), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))), implies(implies(not(a), a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 4 (condensed_detachment) }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 4 (condensed_detachment) R->L }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(implies(not(a), a))), not(a)))), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 2 (cn_18) }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, ifeq(true, true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.10 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.10 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.11 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 4 (condensed_detachment) R->L }
% 4.12/1.11 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))), implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a))))), true, is_a_theorem(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 2 (cn_18) }
% 4.12/1.11 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a))))), true, is_a_theorem(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.11 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a))))), true, is_a_theorem(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 3 (cn_49) }
% 4.12/1.11 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.11 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.11 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.11 = { by axiom 5 (cn_35) R->L }
% 4.12/1.12 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a))))), implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a))))))), true, ifeq(is_a_theorem(implies(not(a), implies(implies(not(not(implies(not(a), a))), not(a)), implies(a, not(implies(not(a), a)))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(implies(not(a), a))), not(a))), implies(not(a), implies(a, not(implies(not(a), a)))))), true), true), true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.12 = { by axiom 4 (condensed_detachment) }
% 4.12/1.12 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.12 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.12 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.12 = { by axiom 1 (ifeq_axiom) R->L }
% 4.12/1.12 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.12 = { by axiom 5 (cn_35) R->L }
% 4.12/1.12 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(a, not(implies(not(a), a)))), implies(implies(not(a), a), implies(not(a), not(implies(not(a), a)))))), true, ifeq(is_a_theorem(implies(not(a), implies(a, not(implies(not(a), a))))), true, is_a_theorem(implies(implies(not(a), a), implies(not(a), not(implies(not(a), a))))), true), true), true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.12 = { by axiom 4 (condensed_detachment) }
% 4.12/1.12 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.12 = { by axiom 1 (ifeq_axiom) }
% 4.12/1.12 ifeq(is_a_theorem(implies(implies(implies(not(a), a), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, ifeq(is_a_theorem(implies(implies(not(a), a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 4.12/1.12 = { by axiom 4 (condensed_detachment) }
% 4.12/1.12 true
% 4.12/1.12 % SZS output end Proof
% 4.12/1.12
% 4.12/1.12 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------