%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL106-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 11:49:02 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.51s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL106-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:22:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.51 Command-line arguments: --no-flatten-goal
% 0.15/0.51
% 0.15/0.51 % SZS status Unsatisfiable
% 0.15/0.51
% 0.75/0.54 % SZS output start Proof
% 0.75/0.54 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.75/0.54 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.
% 0.75/0.54 Axiom 3 (q_1): is_a_theorem(equivalent(X, equivalent(equivalent(Y, Z), equivalent(equivalent(Z, Y), X)))) = true.
% 0.75/0.54 Axiom 4 (q_4): is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z))) = true.
% 0.75/0.54
% 0.75/0.54 Goal 1 (prove_q_2): is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))) = true.
% 0.75/0.54 Proof:
% 0.75/0.54 is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))
% 0.75/0.54 = { by axiom 1 (ifeq_axiom) R->L }
% 0.75/0.54 ifeq(true, true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.54 = { by axiom 2 (condensed_detachment) R->L }
% 0.75/0.54 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.54 = { by axiom 4 (q_4) }
% 0.75/0.54 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.54 = { by axiom 1 (ifeq_axiom) }
% 0.75/0.54 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.54 = { by axiom 1 (ifeq_axiom) R->L }
% 0.75/0.54 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.54 = { by axiom 2 (condensed_detachment) R->L }
% 0.75/0.54 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 3 (q_1) }
% 0.75/0.55 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 1 (ifeq_axiom) }
% 0.75/0.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 3 (q_1) }
% 0.75/0.55 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 1 (ifeq_axiom) }
% 0.75/0.55 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 1 (ifeq_axiom) R->L }
% 0.75/0.55 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 4 (q_4) R->L }
% 0.75/0.55 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b)), equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(c, b))), true, is_a_theorem(equivalent(equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(a, b))), equivalent(equivalent(c, b), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 2 (condensed_detachment) }
% 0.75/0.55 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 1 (ifeq_axiom) }
% 0.75/0.55 ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true)
% 0.75/0.55 = { by axiom 1 (ifeq_axiom) R->L }
% 0.75/0.55 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true), true)
% 0.75/0.55 = { by axiom 4 (q_4) R->L }
% 0.75/0.55 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b)))), equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, b)), equivalent(equivalent(a, c), equivalent(equivalent(c, a), equivalent(c, b))))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, a), equivalent(c, b)))), true), true)
% 0.75/0.55 = { by axiom 2 (condensed_detachment) }
% 0.75/0.55 true
% 0.75/0.55 % SZS output end Proof
% 0.75/0.55
% 0.75/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------