%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL045-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 11:48:54 AM UTC 2026
% Result : Unsatisfiable 0.30s 0.91s
% Output : Proof 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL045-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n011.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 15:18:44 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.91 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.30/0.91
% 0.30/0.91 % SZS status Unsatisfiable
% 0.30/0.92
% 0.30/0.93 % SZS output start Proof
% 0.30/0.93 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.30/0.93 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 0.30/0.93 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 0.30/0.93 Axiom 4 (cn_54): is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))) = true.
% 0.30/0.93 Axiom 5 (cn_22): is_a_theorem(implies(implies(X, Y), implies(implies(Z, X), implies(Z, Y)))) = true.
% 0.30/0.93 Axiom 6 (cn_21): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(Y, implies(X, Z)))) = true.
% 0.30/0.93 Axiom 7 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 0.30/0.93
% 0.30/0.93 Goal 1 (prove_cn_46): is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))) = true.
% 0.30/0.93 Proof:
% 0.30/0.93 is_a_theorem(implies(implies(a, b), implies(not(b), not(a))))
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 0.30/0.93 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 7 (condensed_detachment) R->L }
% 0.30/0.93 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(not(a), implies(not(b), not(a)))), implies(not(a), implies(implies(a, b), implies(not(b), not(a)))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(not(a), implies(not(b), not(a))))), true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 6 (cn_21) }
% 0.30/0.93 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(not(a), implies(not(b), not(a))))), true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) }
% 0.30/0.93 ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(not(a), implies(not(b), not(a))))), true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 0.30/0.93 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(not(a), implies(not(b), not(a))))), true), true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 2 (cn_18) R->L }
% 0.30/0.93 ifeq(ifeq(ifeq(is_a_theorem(implies(not(a), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(a, b), implies(not(a), implies(not(b), not(a))))), true), true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 0.30/0.93 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(a, b), implies(not(a), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 2 (cn_18) R->L }
% 0.30/0.93 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(b), not(a))), implies(implies(a, b), implies(not(a), implies(not(b), not(a)))))), true, ifeq(is_a_theorem(implies(not(a), implies(not(b), not(a)))), true, is_a_theorem(implies(implies(a, b), implies(not(a), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 7 (condensed_detachment) }
% 0.30/0.93 ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) }
% 0.30/0.93 ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true)
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 0.30/0.93 ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.93 = { by axiom 7 (condensed_detachment) R->L }
% 0.30/0.93 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(a, b), implies(not(b), not(a)))), implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a)))))), true, ifeq(is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.93 = { by axiom 4 (cn_54) }
% 0.30/0.93 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) }
% 0.30/0.93 ifeq(ifeq(is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 0.30/0.94 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 7 (condensed_detachment) R->L }
% 0.30/0.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(a))), implies(implies(a, b), implies(a, implies(not(b), not(a)))))), true, ifeq(is_a_theorem(implies(b, implies(not(b), not(a)))), true, is_a_theorem(implies(implies(a, b), implies(a, implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 3 (cn_3) }
% 0.30/0.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(a))), implies(implies(a, b), implies(a, implies(not(b), not(a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(a, implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 1 (ifeq_axiom) }
% 0.30/0.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(a))), implies(implies(a, b), implies(a, implies(not(b), not(a)))))), true, is_a_theorem(implies(implies(a, b), implies(a, implies(not(b), not(a))))), true), true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 5 (cn_22) }
% 0.30/0.94 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(a, implies(not(b), not(a))))), true), true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 1 (ifeq_axiom) }
% 0.30/0.94 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(a, implies(not(b), not(a))))), true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 0.30/0.94 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(a, implies(not(b), not(a))))), true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 6 (cn_21) R->L }
% 0.30/0.94 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(not(b), not(a)))), implies(a, implies(implies(a, b), implies(not(b), not(a)))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(a, implies(not(b), not(a))))), true, is_a_theorem(implies(a, implies(implies(a, b), implies(not(b), not(a))))), true), true), true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 7 (condensed_detachment) }
% 0.30/0.94 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 1 (ifeq_axiom) }
% 0.30/0.94 ifeq(is_a_theorem(implies(implies(not(a), implies(implies(a, b), implies(not(b), not(a)))), implies(implies(a, b), implies(not(b), not(a))))), true, ifeq(is_a_theorem(implies(not(a), implies(implies(a, b), implies(not(b), not(a))))), true, is_a_theorem(implies(implies(a, b), implies(not(b), not(a)))), true), true)
% 0.30/0.94 = { by axiom 7 (condensed_detachment) }
% 0.30/0.94 true
% 0.30/0.94 % SZS output end Proof
% 0.30/0.94
% 0.30/0.94 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------