%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LDA004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:01:21 PM UTC 2026
% Result : Unsatisfiable 237.31s 30.44s
% Output : Proof 237.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n001.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sun Sep 27 17:15:45 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 237.31/30.44 Command-line arguments: --no-flatten-goal
% 237.31/30.44
% 237.31/30.44 % SZS status Unsatisfiable
% 237.31/30.44
% 237.31/30.45 % SZS output start Proof
% 237.31/30.46 Axiom 1 (clause_11): b = f(u1, u3).
% 237.31/30.46 Axiom 2 (clause_4): n2 = f(n1, n1).
% 237.31/30.46 Axiom 3 (clause_9): u3 = f(u, n3).
% 237.31/30.46 Axiom 4 (clause_7): u1 = f(u, n1).
% 237.31/30.46 Axiom 5 (clause_8): u2 = f(u, n2).
% 237.31/30.46 Axiom 6 (clause_5): n3 = f(n2, n1).
% 237.31/30.46 Axiom 7 (clause_6): u = f(n2, n2).
% 237.31/30.46 Axiom 8 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 237.31/30.46 Axiom 9 (a2): left(X, f(X, Y)) = true.
% 237.31/30.46 Axiom 10 (clause_10): a = f(f(n3, n2), u2).
% 237.31/30.46 Axiom 11 (a1): f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)).
% 237.31/30.46 Axiom 12 (a3): ifeq(left(X, Y), true, ifeq(left(Z, X), true, left(Z, Y), true), true) = true.
% 237.31/30.46
% 237.31/30.46 Lemma 13: f(n1, n2) = u.
% 237.31/30.46 Proof:
% 237.31/30.46 f(n1, n2)
% 237.31/30.46 = { by axiom 2 (clause_4) }
% 237.31/30.46 f(n1, f(n1, n1))
% 237.31/30.46 = { by axiom 11 (a1) }
% 237.31/30.46 f(f(n1, n1), f(n1, n1))
% 237.31/30.46 = { by axiom 2 (clause_4) R->L }
% 237.31/30.46 f(n2, f(n1, n1))
% 237.31/30.46 = { by axiom 2 (clause_4) R->L }
% 237.31/30.46 f(n2, n2)
% 237.31/30.46 = { by axiom 7 (clause_6) R->L }
% 237.31/30.46 u
% 237.31/30.46
% 237.31/30.46 Lemma 14: f(n2, f(n1, X)) = f(n3, f(n2, X)).
% 237.31/30.46 Proof:
% 237.31/30.46 f(n2, f(n1, X))
% 237.31/30.46 = { by axiom 11 (a1) }
% 237.31/30.46 f(f(n2, n1), f(n2, X))
% 237.31/30.46 = { by axiom 6 (clause_5) R->L }
% 237.31/30.46 f(n3, f(n2, X))
% 237.31/30.46
% 237.31/30.46 Lemma 15: f(n3, n3) = u.
% 237.31/30.46 Proof:
% 237.31/30.46 f(n3, n3)
% 237.31/30.46 = { by axiom 6 (clause_5) }
% 237.31/30.46 f(n3, f(n2, n1))
% 237.31/30.46 = { by lemma 14 R->L }
% 237.31/30.46 f(n2, f(n1, n1))
% 237.31/30.46 = { by axiom 2 (clause_4) R->L }
% 237.31/30.46 f(n2, n2)
% 237.31/30.46 = { by axiom 7 (clause_6) R->L }
% 237.31/30.46 u
% 237.31/30.46
% 237.31/30.46 Lemma 16: f(u, u) = f(u1, u2).
% 237.31/30.46 Proof:
% 237.31/30.46 f(u, u)
% 237.31/30.46 = { by lemma 13 R->L }
% 237.31/30.46 f(u, f(n1, n2))
% 237.31/30.46 = { by axiom 11 (a1) }
% 237.31/30.46 f(f(u, n1), f(u, n2))
% 237.31/30.46 = { by axiom 4 (clause_7) R->L }
% 237.31/30.46 f(u1, f(u, n2))
% 237.31/30.46 = { by axiom 5 (clause_8) R->L }
% 237.31/30.46 f(u1, u2)
% 237.31/30.46
% 237.31/30.46 Lemma 17: f(n3, u) = f(u1, u2).
% 237.31/30.46 Proof:
% 237.31/30.46 f(n3, u)
% 237.31/30.46 = { by axiom 7 (clause_6) }
% 237.31/30.46 f(n3, f(n2, n2))
% 237.31/30.46 = { by lemma 14 R->L }
% 237.31/30.46 f(n2, f(n1, n2))
% 237.31/30.46 = { by lemma 13 }
% 237.31/30.46 f(n2, u)
% 237.31/30.46 = { by axiom 7 (clause_6) }
% 237.31/30.46 f(n2, f(n2, n2))
% 237.31/30.46 = { by axiom 11 (a1) }
% 237.31/30.46 f(f(n2, n2), f(n2, n2))
% 237.31/30.46 = { by axiom 7 (clause_6) R->L }
% 237.31/30.46 f(u, f(n2, n2))
% 237.31/30.46 = { by axiom 7 (clause_6) R->L }
% 237.31/30.46 f(u, u)
% 237.31/30.46 = { by lemma 16 }
% 237.31/30.46 f(u1, u2)
% 237.31/30.46
% 237.31/30.46 Goal 1 (prove_equation): left(a, b) = true.
% 237.31/30.46 Proof:
% 237.31/30.46 left(a, b)
% 237.31/30.46 = { by axiom 1 (clause_11) }
% 237.31/30.46 left(a, f(u1, u3))
% 237.31/30.46 = { by axiom 4 (clause_7) }
% 237.31/30.46 left(a, f(f(u, n1), u3))
% 237.31/30.46 = { by axiom 3 (clause_9) }
% 237.31/30.46 left(a, f(f(u, n1), f(u, n3)))
% 237.31/30.46 = { by axiom 11 (a1) R->L }
% 237.31/30.46 left(a, f(u, f(n1, n3)))
% 237.31/30.46 = { by axiom 6 (clause_5) }
% 237.31/30.46 left(a, f(u, f(n1, f(n2, n1))))
% 237.31/30.46 = { by axiom 11 (a1) }
% 237.31/30.46 left(a, f(u, f(f(n1, n2), f(n1, n1))))
% 237.31/30.46 = { by axiom 2 (clause_4) R->L }
% 237.31/30.46 left(a, f(u, f(f(n1, n2), n2)))
% 237.31/30.46 = { by lemma 13 }
% 237.31/30.46 left(a, f(u, f(u, n2)))
% 237.31/30.46 = { by axiom 11 (a1) }
% 237.31/30.46 left(a, f(f(u, u), f(u, n2)))
% 237.31/30.46 = { by lemma 16 }
% 237.31/30.46 left(a, f(f(u1, u2), f(u, n2)))
% 237.31/30.46 = { by axiom 11 (a1) }
% 237.31/30.46 left(a, f(f(f(u1, u2), u), f(f(u1, u2), n2)))
% 237.31/30.46 = { by lemma 17 R->L }
% 237.31/30.46 left(a, f(f(f(n3, u), u), f(f(u1, u2), n2)))
% 237.31/30.46 = { by lemma 15 R->L }
% 237.31/30.47 left(a, f(f(f(n3, u), f(n3, n3)), f(f(u1, u2), n2)))
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 left(a, f(f(n3, f(u, n3)), f(f(u1, u2), n2)))
% 237.31/30.47 = { by axiom 3 (clause_9) R->L }
% 237.31/30.47 left(a, f(f(n3, u3), f(f(u1, u2), n2)))
% 237.31/30.47 = { by lemma 17 R->L }
% 237.31/30.47 left(a, f(f(n3, u3), f(f(n3, u), n2)))
% 237.31/30.47 = { by axiom 11 (a1) }
% 237.31/30.47 left(a, f(f(f(n3, u3), f(n3, u)), f(f(n3, u3), n2)))
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2)))
% 237.31/30.47 = { by axiom 8 (ifeq_axiom) R->L }
% 237.31/30.47 ifeq(true, true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 12 (a3) R->L }
% 237.31/30.47 ifeq(ifeq(left(f(a, f(f(n3, n2), u1)), f(f(a, f(f(n3, n2), u1)), f(f(n3, n2), u2))), true, ifeq(left(a, f(a, f(f(n3, n2), u1))), true, left(a, f(f(a, f(f(n3, n2), u1)), f(f(n3, n2), u2))), true), true), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 9 (a2) }
% 237.31/30.47 ifeq(ifeq(true, true, ifeq(left(a, f(a, f(f(n3, n2), u1))), true, left(a, f(f(a, f(f(n3, n2), u1)), f(f(n3, n2), u2))), true), true), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 8 (ifeq_axiom) }
% 237.31/30.47 ifeq(ifeq(left(a, f(a, f(f(n3, n2), u1))), true, left(a, f(f(a, f(f(n3, n2), u1)), f(f(n3, n2), u2))), true), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 9 (a2) }
% 237.31/30.47 ifeq(ifeq(true, true, left(a, f(f(a, f(f(n3, n2), u1)), f(f(n3, n2), u2))), true), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 8 (ifeq_axiom) }
% 237.31/30.47 ifeq(left(a, f(f(a, f(f(n3, n2), u1)), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 10 (clause_10) }
% 237.31/30.47 ifeq(left(a, f(f(f(f(n3, n2), u2), f(f(n3, n2), u1)), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 ifeq(left(a, f(f(f(n3, n2), f(u2, u1)), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 5 (clause_8) }
% 237.31/30.47 ifeq(left(a, f(f(f(n3, n2), f(f(u, n2), u1)), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 4 (clause_7) }
% 237.31/30.47 ifeq(left(a, f(f(f(n3, n2), f(f(u, n2), f(u, n1))), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 ifeq(left(a, f(f(f(n3, n2), f(u, f(n2, n1))), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 6 (clause_5) R->L }
% 237.31/30.47 ifeq(left(a, f(f(f(n3, n2), f(u, n3)), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 3 (clause_9) R->L }
% 237.31/30.47 ifeq(left(a, f(f(f(n3, n2), u3), f(f(n3, n2), u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 ifeq(left(a, f(f(n3, n2), f(u3, u2))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 5 (clause_8) }
% 237.31/30.47 ifeq(left(a, f(f(n3, n2), f(u3, f(u, n2)))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 3 (clause_9) }
% 237.31/30.47 ifeq(left(a, f(f(n3, n2), f(f(u, n3), f(u, n2)))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 ifeq(left(a, f(f(n3, n2), f(u, f(n3, n2)))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by lemma 15 R->L }
% 237.31/30.47 ifeq(left(a, f(f(n3, n2), f(f(n3, n3), f(n3, n2)))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 ifeq(left(a, f(f(n3, n2), f(n3, f(n3, n2)))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) R->L }
% 237.31/30.47 ifeq(left(a, f(n3, f(n2, f(n3, n2)))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) }
% 237.31/30.47 ifeq(left(a, f(n3, f(f(n2, n3), f(n2, n2)))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 7 (clause_6) R->L }
% 237.31/30.47 ifeq(left(a, f(n3, f(f(n2, n3), u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 6 (clause_5) }
% 237.31/30.47 ifeq(left(a, f(n3, f(f(n2, f(n2, n1)), u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 11 (a1) }
% 237.31/30.47 ifeq(left(a, f(n3, f(f(f(n2, n2), f(n2, n1)), u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 6 (clause_5) R->L }
% 237.31/30.47 ifeq(left(a, f(n3, f(f(f(n2, n2), n3), u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 7 (clause_6) R->L }
% 237.31/30.47 ifeq(left(a, f(n3, f(f(u, n3), u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 3 (clause_9) R->L }
% 237.31/30.47 ifeq(left(a, f(n3, f(u3, u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true)
% 237.31/30.47 = { by axiom 8 (ifeq_axiom) R->L }
% 237.31/30.47 ifeq(true, true, ifeq(left(a, f(n3, f(u3, u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true), true)
% 237.31/30.47 = { by axiom 9 (a2) R->L }
% 237.31/30.47 ifeq(left(f(n3, f(u3, u)), f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true, ifeq(left(a, f(n3, f(u3, u))), true, left(a, f(f(n3, f(u3, u)), f(f(n3, u3), n2))), true), true)
% 237.31/30.47 = { by axiom 12 (a3) }
% 237.31/30.47 true
% 237.31/30.47 % SZS output end Proof
% 237.31/30.47
% 237.31/30.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------