%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL076-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 3.30s 0.94s
% Output : Proof 3.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL076-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n015.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 15:24:30 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.30/0.94 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
% 3.30/0.94
% 3.30/0.94 % SZS status Unsatisfiable
% 3.30/0.94
% 3.30/0.96 % SZS output start Proof
% 3.30/0.96 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.30/0.96 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 3.30/0.96 Axiom 3 (cn_49): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 3.30/0.96 Axiom 4 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 3.30/0.96 Axiom 5 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 3.30/0.97 Axiom 6 (transitivity): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(implies(Z, X)), true, is_a_theorem(implies(Z, Y)), true), true) = true.
% 3.30/0.97
% 3.30/0.97 Goal 1 (prove_cn_40): is_a_theorem(implies(a, not(not(a)))) = true.
% 3.30/0.97 Proof:
% 3.30/0.97 is_a_theorem(implies(a, not(not(a))))
% 3.30/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.30/0.97 ifeq(true, true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.30/0.97 = { by axiom 5 (condensed_detachment) R->L }
% 3.30/0.97 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)
% 3.30/0.97 = { by axiom 2 (cn_18) }
% 3.30/0.97 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)
% 3.30/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.30/0.97 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)
% 3.30/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.30/0.97 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)
% 3.30/0.97 = { by axiom 6 (transitivity) R->L }
% 3.30/0.97 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, 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)
% 3.30/0.97 = { by axiom 3 (cn_49) }
% 3.30/0.97 ifeq(ifeq(ifeq(ifeq(true, 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)
% 3.30/0.97 = { by axiom 1 (ifeq_axiom) }
% 3.30/0.97 ifeq(ifeq(ifeq(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, 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)
% 3.30/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 3.30/0.98 ifeq(ifeq(ifeq(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, 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)
% 3.30/0.98 = { by axiom 3 (cn_49) R->L }
% 3.30/0.98 ifeq(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(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, 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)
% 3.30/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 3.30/0.98 ifeq(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, 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, 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)
% 3.30/0.98 = { by axiom 2 (cn_18) R->L }
% 3.30/0.98 ifeq(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, 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, 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)
% 3.30/0.98 = { by axiom 6 (transitivity) }
% 3.30/0.98 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)
% 3.30/0.98 = { by axiom 1 (ifeq_axiom) }
% 3.30/0.98 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)
% 3.30/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 3.30/0.98 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)
% 3.30/0.98 = { by axiom 4 (cn_35) R->L }
% 3.30/0.98 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)
% 3.30/0.98 = { by axiom 5 (condensed_detachment) }
% 3.30/0.98 ifeq(ifeq(true, true, is_a_theorem(implies(not(not(not(a))), not(a))), true), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.30/0.98 = { by axiom 1 (ifeq_axiom) }
% 3.30/0.98 ifeq(is_a_theorem(implies(not(not(not(a))), not(a))), true, is_a_theorem(implies(a, not(not(a)))), true)
% 3.30/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 3.30/0.98 ifeq(true, true, ifeq(is_a_theorem(implies(not(not(not(a))), not(a))), true, is_a_theorem(implies(a, not(not(a)))), true), true)
% 3.30/0.98 = { by axiom 3 (cn_49) R->L }
% 3.30/0.99 ifeq(is_a_theorem(implies(implies(not(not(not(a))), not(a)), implies(a, not(not(a))))), true, ifeq(is_a_theorem(implies(not(not(not(a))), not(a))), true, is_a_theorem(implies(a, not(not(a)))), true), true)
% 3.30/0.99 = { by axiom 5 (condensed_detachment) }
% 3.30/0.99 true
% 3.30/0.99 % SZS output end Proof
% 3.30/0.99
% 3.30/0.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------