%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL043-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 11:48:53 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.59s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL043-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n002.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 15:21:06 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.59 Command-line arguments: --no-flatten-goal
% 0.21/0.59
% 0.21/0.59 % SZS status Unsatisfiable
% 0.21/0.59
% 0.21/0.59 % SZS output start Proof
% 0.21/0.59 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.21/0.59 Axiom 2 (cn_18): is_a_theorem(implies(X, implies(Y, X))) = true.
% 0.21/0.59 Axiom 3 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 0.21/0.59 Axiom 4 (cn_54): is_a_theorem(implies(implies(X, Y), implies(implies(not(X), Y), Y))) = true.
% 0.21/0.59 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.
% 0.21/0.59
% 0.21/0.59 Goal 1 (prove_cn_39): is_a_theorem(implies(not(not(a)), a)) = true.
% 0.21/0.59 Proof:
% 0.21/0.59 is_a_theorem(implies(not(not(a)), a))
% 0.21/0.59 = { by axiom 1 (ifeq_axiom) R->L }
% 0.21/0.59 ifeq(true, true, is_a_theorem(implies(not(not(a)), a)), true)
% 0.21/0.59 = { by axiom 3 (cn_3) R->L }
% 0.21/0.59 ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true)
% 0.21/0.59 = { by axiom 1 (ifeq_axiom) R->L }
% 0.21/0.59 ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 0.21/0.59 = { by axiom 5 (condensed_detachment) R->L }
% 0.21/0.59 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(not(a)), a)), implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a)))), true, ifeq(is_a_theorem(implies(a, implies(not(not(a)), a))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 0.21/0.59 = { by axiom 2 (cn_18) }
% 0.21/0.59 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(not(a)), a)), implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 0.21/0.59 = { by axiom 1 (ifeq_axiom) }
% 0.21/0.59 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(not(a)), a)), implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a)))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 0.21/0.59 = { by axiom 4 (cn_54) }
% 0.21/0.59 ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a))), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 0.21/0.59 = { by axiom 1 (ifeq_axiom) }
% 0.21/0.59 ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(not(a)), a))), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(not(not(a)), a)), true), true)
% 0.21/0.59 = { by axiom 5 (condensed_detachment) }
% 0.21/0.59 true
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60
% 0.21/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------