%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HWC002-1 : TPTP v9.3.1. Released v1.1.0.
% 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 10:19:21 AM UTC 2026
% Result : Unsatisfiable 2.66s 0.83s
% Output : Proof 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HWC002-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n015.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 10:55:15 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.66/0.83 Command-line arguments: --no-flatten-goal
% 2.66/0.83
% 2.66/0.83 % SZS status Unsatisfiable
% 2.66/0.83
% 2.66/0.84 % SZS output start Proof
% 2.66/0.84 Axiom 1 (and_definition5): and(nil, X) = X.
% 2.66/0.84 Axiom 2 (and_definition1): and(n0, n0) = n0.
% 2.66/0.84 Axiom 3 (and_definition2): and(n0, n1) = n0.
% 2.66/0.84 Axiom 4 (connect_definition1): connect(nil, X) = X.
% 2.66/0.84 Axiom 5 (empty_table): table(n0, n0, n0, n0) = nil.
% 2.66/0.84 Axiom 6 (subsume_symmetric): circuit(top(X), Y, bottom(X)) = true.
% 2.66/0.84 Axiom 7 (and_table_definition): and(table(X, Y, Z, W), table(V, U, T, S)) = table(and(X, V), and(Y, U), and(Z, T), and(W, S)).
% 2.66/0.84
% 2.66/0.84 Lemma 8: table(n0, and(n0, X), and(n0, Y), and(n0, Z)) = table(n0, X, Y, Z).
% 2.66/0.84 Proof:
% 2.66/0.84 table(n0, and(n0, X), and(n0, Y), and(n0, Z))
% 2.66/0.84 = { by axiom 2 (and_definition1) R->L }
% 2.66/0.84 table(and(n0, n0), and(n0, X), and(n0, Y), and(n0, Z))
% 2.66/0.84 = { by axiom 7 (and_table_definition) R->L }
% 2.66/0.84 and(table(n0, n0, n0, n0), table(n0, X, Y, Z))
% 2.66/0.84 = { by axiom 5 (empty_table) }
% 2.66/0.84 and(nil, table(n0, X, Y, Z))
% 2.66/0.84 = { by axiom 1 (and_definition5) }
% 2.66/0.84 table(n0, X, Y, Z)
% 2.66/0.84
% 2.66/0.84 Lemma 9: table(n0, n0, and(n0, X), and(n0, Y)) = table(n0, n0, X, Y).
% 2.66/0.84 Proof:
% 2.66/0.84 table(n0, n0, and(n0, X), and(n0, Y))
% 2.66/0.84 = { by axiom 2 (and_definition1) R->L }
% 2.66/0.84 table(n0, and(n0, n0), and(n0, X), and(n0, Y))
% 2.66/0.84 = { by lemma 8 }
% 2.66/0.84 table(n0, n0, X, Y)
% 2.66/0.84
% 2.66/0.84 Lemma 10: table(n0, n0, n0, and(n0, X)) = table(n0, n0, n0, X).
% 2.66/0.84 Proof:
% 2.66/0.84 table(n0, n0, n0, and(n0, X))
% 2.66/0.84 = { by axiom 2 (and_definition1) R->L }
% 2.66/0.84 table(n0, n0, and(n0, n0), and(n0, X))
% 2.66/0.84 = { by lemma 9 }
% 2.66/0.84 table(n0, n0, n0, X)
% 2.66/0.84
% 2.66/0.84 Lemma 11: table(n0, n0, n0, n1) = nil.
% 2.66/0.84 Proof:
% 2.66/0.84 table(n0, n0, n0, n1)
% 2.66/0.84 = { by lemma 10 R->L }
% 2.66/0.84 table(n0, n0, n0, and(n0, n1))
% 2.66/0.84 = { by axiom 3 (and_definition2) }
% 2.66/0.84 table(n0, n0, n0, n0)
% 2.66/0.84 = { by axiom 5 (empty_table) }
% 2.66/0.84 nil
% 2.66/0.84
% 2.66/0.84 Goal 1 (prove_output_configuration): circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, n1, n1), nil))) = true.
% 2.66/0.84 Proof:
% 2.66/0.84 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, n1, n1), nil)))
% 2.66/0.84 = { by lemma 9 R->L }
% 2.66/0.84 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, and(n0, n1), and(n0, n1)), nil)))
% 2.66/0.84 = { by axiom 3 (and_definition2) }
% 2.66/0.84 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, n0, and(n0, n1)), nil)))
% 2.66/0.84 = { by lemma 10 }
% 2.66/0.84 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(table(n0, n0, n0, n1), nil)))
% 2.66/0.84 = { by lemma 11 }
% 2.66/0.84 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(connect(nil, nil)))
% 2.66/0.84 = { by axiom 4 (connect_definition1) }
% 2.66/0.84 circuit(top(connect(table(n0, n1, n0, n1), nil)), nil, bottom(nil))
% 2.66/0.84 = { by lemma 8 R->L }
% 2.66/0.84 circuit(top(connect(table(n0, and(n0, n1), and(n0, n0), and(n0, n1)), nil)), nil, bottom(nil))
% 2.66/0.84 = { by axiom 2 (and_definition1) }
% 2.66/0.84 circuit(top(connect(table(n0, and(n0, n1), n0, and(n0, n1)), nil)), nil, bottom(nil))
% 2.66/0.84 = { by axiom 3 (and_definition2) }
% 2.66/0.84 circuit(top(connect(table(n0, n0, n0, and(n0, n1)), nil)), nil, bottom(nil))
% 2.66/0.84 = { by lemma 10 }
% 2.66/0.84 circuit(top(connect(table(n0, n0, n0, n1), nil)), nil, bottom(nil))
% 2.66/0.84 = { by lemma 11 }
% 2.66/0.84 circuit(top(connect(nil, nil)), nil, bottom(nil))
% 2.66/0.84 = { by axiom 4 (connect_definition1) }
% 2.66/0.84 circuit(top(nil), nil, bottom(nil))
% 2.66/0.84 = { by axiom 6 (subsume_symmetric) }
% 2.66/0.84 true
% 2.66/0.84 % SZS output end Proof
% 2.66/0.84
% 2.66/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------