%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 11:48:50 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.39 % Computer : n006.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 15:16:56 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 Command-line arguments: --no-flatten-goal
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.48 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 0.20/0.48 Axiom 3 (xgf): is_a_theorem(equivalent(X, equivalent(equivalent(Y, equivalent(X, Z)), equivalent(Z, Y)))) = true.
% 0.20/0.48
% 0.20/0.48 Goal 1 (prove_um): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))) = true.
% 0.20/0.48 Proof:
% 0.20/0.48 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))
% 0.20/0.48 = { by axiom 1 (ifeq_axiom) R->L }
% 0.20/0.48 ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true)
% 0.20/0.48 = { by axiom 2 (condensed_detachment) R->L }
% 0.20/0.48 ifeq(ifeq(is_a_theorem(equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))))), true, ifeq(is_a_theorem(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true)
% 0.20/0.48 = { by axiom 3 (xgf) }
% 0.20/0.48 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true)
% 0.20/0.48 = { by axiom 1 (ifeq_axiom) }
% 0.20/0.48 ifeq(ifeq(is_a_theorem(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true)
% 0.20/0.48 = { by axiom 3 (xgf) }
% 0.20/0.48 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true)
% 0.20/0.48 = { by axiom 1 (ifeq_axiom) }
% 0.20/0.48 ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true)
% 0.20/0.48 = { by axiom 1 (ifeq_axiom) R->L }
% 0.20/0.48 ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true), true)
% 0.20/0.48 = { by axiom 3 (xgf) R->L }
% 0.20/0.48 ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(c, a)), equivalent(equivalent(c, equivalent(equivalent(b, equivalent(c, a)), equivalent(a, b))), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(b, equivalent(c, a)))), true), true)
% 0.20/0.48 = { by axiom 2 (condensed_detachment) }
% 0.20/0.48 true
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48
% 0.20/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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