%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.84s 0.77s
% Output : Proof 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n002.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 15:23:36 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.84/0.77 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
% 0.84/0.77
% 0.84/0.77 % SZS status Unsatisfiable
% 0.84/0.77
% 1.23/0.81 % SZS output start Proof
% 1.23/0.81 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.23/0.81 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 1.23/0.81 Axiom 3 (cn_49): is_a_theorem(implies(implies(not(X), not(Y)), implies(Y, X))) = true.
% 1.23/0.81 Axiom 4 (cn_35): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 1.23/0.81 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.
% 1.23/0.82 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.
% 1.23/0.82
% 1.23/0.82 Goal 1 (prove_cn_39): is_a_theorem(implies(not(not(a)), a)) = true.
% 1.23/0.82 Proof:
% 1.23/0.82 is_a_theorem(implies(not(not(a)), a))
% 1.23/0.82 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.82 ifeq(true, true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 5 (condensed_detachment) R->L }
% 1.23/0.82 ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(X, not(not(a))))), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 2 (cn_18) }
% 1.23/0.82 ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a))))), true, ifeq(true, true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.82 ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a))))), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.82 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 4 (cn_35) R->L }
% 1.23/0.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(X, not(not(a))), not(not(a)))), implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(X, not(not(a))), not(not(a)))), implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a))))), true), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 2 (cn_18) R->L }
% 1.23/0.82 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(X, not(not(a))), not(not(a)))), implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a)))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(X, not(not(a))), not(not(a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(X, not(not(a)))), implies(not(not(a)), not(not(a))))), true), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 5 (condensed_detachment) }
% 1.23/0.82 ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.82 ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true)
% 1.23/0.82 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.82 ifeq(true, true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.82 = { by axiom 5 (condensed_detachment) R->L }
% 1.23/0.82 ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true, ifeq(is_a_theorem(implies(Y, implies(Z, Y))), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.82 = { by axiom 2 (cn_18) }
% 1.23/0.82 ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.82 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.83 ifeq(ifeq(is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.83 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 6 (transitivity) R->L }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), not(not(not(a)))), implies(not(not(a)), a))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(a), not(not(not(a)))))), true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 3 (cn_49) }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(a), not(not(not(a)))))), true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(a)), implies(not(a), not(not(not(a)))))), true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(not(a), not(not(not(a)))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 3 (cn_49) R->L }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(a)))), not(not(a))), implies(not(a), not(not(not(a)))))), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(not(not(a)))))), true), true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(a)))), not(not(a))), implies(not(a), not(not(not(a)))))), true, ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(not(a), not(not(not(a)))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 2 (cn_18) R->L }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(not(a)))), not(not(a))), implies(not(a), not(not(not(a)))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(not(not(a)))), not(not(a))))), true, is_a_theorem(implies(not(not(a)), implies(not(a), not(not(not(a)))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 6 (transitivity) }
% 1.23/0.83 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.83 ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.83 = { by axiom 1 (ifeq_axiom) R->L }
% 1.23/0.84 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 6 (transitivity) R->L }
% 1.23/0.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)), implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))))), true, ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))))), true), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 2 (cn_18) }
% 1.23/0.84 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))))), true), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))))), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 4 (cn_35) }
% 1.23/0.84 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))))), true), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.84 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(not(not(a)), a)), implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(Y, implies(Z, Y)), implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 5 (condensed_detachment) }
% 1.23/0.84 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 1 (ifeq_axiom) }
% 1.23/0.84 ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(not(not(a)), a))), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 1.23/0.84 = { by axiom 5 (condensed_detachment) }
% 1.23/0.84 true
% 1.23/0.84 % SZS output end Proof
% 1.23/0.84
% 1.23/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------