TSTP Solution File: LDA002-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:04:46 EDT 2023
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:11:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.46 Command-line arguments: --no-flatten-goal
% 0.20/0.46
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 Axiom 1 (clause_10): b = f(u1, u3).
% 0.20/0.48 Axiom 2 (clause_11): v = f(uu, uu).
% 0.20/0.48 Axiom 3 (clause_2): n2 = f(n1, n1).
% 0.20/0.48 Axiom 4 (clause_3): n3 = f(n2, n1).
% 0.20/0.48 Axiom 5 (clause_4): u = f(n2, n2).
% 0.20/0.48 Axiom 6 (clause_7): u3 = f(u, n3).
% 0.20/0.48 Axiom 7 (clause_5): u1 = f(u, n1).
% 0.20/0.48 Axiom 8 (clause_6): u2 = f(u, n2).
% 0.20/0.48 Axiom 9 (clause_8): uu = f(u, u).
% 0.20/0.48 Axiom 10 (clause_9): a = f(f(n3, n2), u2).
% 0.20/0.48 Axiom 11 (a1): f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)).
% 0.20/0.48
% 0.20/0.48 Lemma 12: f(n2, f(n1, X)) = f(n1, f(n1, X)).
% 0.20/0.48 Proof:
% 0.20/0.48 f(n2, f(n1, X))
% 0.20/0.48 = { by axiom 3 (clause_2) }
% 0.20/0.48 f(f(n1, n1), f(n1, X))
% 0.20/0.48 = { by axiom 11 (a1) R->L }
% 0.20/0.48 f(n1, f(n1, X))
% 0.20/0.48
% 0.20/0.48 Lemma 13: f(n1, n2) = u.
% 0.20/0.48 Proof:
% 0.20/0.48 f(n1, n2)
% 0.20/0.48 = { by axiom 3 (clause_2) }
% 0.20/0.48 f(n1, f(n1, n1))
% 0.20/0.48 = { by lemma 12 R->L }
% 0.20/0.48 f(n2, f(n1, n1))
% 0.20/0.48 = { by axiom 3 (clause_2) R->L }
% 0.20/0.48 f(n2, n2)
% 0.20/0.48 = { by axiom 5 (clause_4) R->L }
% 0.20/0.48 u
% 0.20/0.48
% 0.20/0.48 Lemma 14: f(n2, u) = f(n1, u).
% 0.20/0.48 Proof:
% 0.20/0.48 f(n2, u)
% 0.20/0.48 = { by lemma 13 R->L }
% 0.20/0.48 f(n2, f(n1, n2))
% 0.20/0.48 = { by lemma 12 }
% 0.20/0.48 f(n1, f(n1, n2))
% 0.20/0.48 = { by lemma 13 }
% 0.20/0.48 f(n1, u)
% 0.20/0.48
% 0.20/0.48 Lemma 15: f(n2, f(n1, X)) = f(n3, f(n2, X)).
% 0.20/0.48 Proof:
% 0.20/0.48 f(n2, f(n1, X))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(f(n2, n1), f(n2, X))
% 0.20/0.48 = { by axiom 4 (clause_3) R->L }
% 0.20/0.48 f(n3, f(n2, X))
% 0.20/0.48
% 0.20/0.48 Lemma 16: f(n1, u) = f(n3, u).
% 0.20/0.48 Proof:
% 0.20/0.48 f(n1, u)
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 f(n2, u)
% 0.20/0.48 = { by lemma 13 R->L }
% 0.20/0.48 f(n2, f(n1, n2))
% 0.20/0.48 = { by lemma 15 }
% 0.20/0.48 f(n3, f(n2, n2))
% 0.20/0.48 = { by axiom 5 (clause_4) R->L }
% 0.20/0.48 f(n3, u)
% 0.20/0.48
% 0.20/0.48 Lemma 17: f(u, f(n2, X)) = f(n2, f(n2, X)).
% 0.20/0.48 Proof:
% 0.20/0.48 f(u, f(n2, X))
% 0.20/0.48 = { by axiom 5 (clause_4) }
% 0.20/0.48 f(f(n2, n2), f(n2, X))
% 0.20/0.48 = { by axiom 11 (a1) R->L }
% 0.20/0.48 f(n2, f(n2, X))
% 0.20/0.48
% 0.20/0.48 Lemma 18: f(n3, u) = uu.
% 0.20/0.48 Proof:
% 0.20/0.48 f(n3, u)
% 0.20/0.48 = { by lemma 16 R->L }
% 0.20/0.48 f(n1, u)
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 f(n2, u)
% 0.20/0.48 = { by axiom 5 (clause_4) }
% 0.20/0.48 f(n2, f(n2, n2))
% 0.20/0.48 = { by lemma 17 R->L }
% 0.20/0.48 f(u, f(n2, n2))
% 0.20/0.48 = { by axiom 5 (clause_4) R->L }
% 0.20/0.48 f(u, u)
% 0.20/0.48 = { by axiom 9 (clause_8) R->L }
% 0.20/0.48 uu
% 0.20/0.48
% 0.20/0.48 Lemma 19: f(u, f(n2, X)) = f(u2, f(u, X)).
% 0.20/0.48 Proof:
% 0.20/0.48 f(u, f(n2, X))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(f(u, n2), f(u, X))
% 0.20/0.48 = { by axiom 8 (clause_6) R->L }
% 0.20/0.48 f(u2, f(u, X))
% 0.20/0.48
% 0.20/0.48 Lemma 20: f(u, f(n1, X)) = f(u1, f(u, X)).
% 0.20/0.48 Proof:
% 0.20/0.48 f(u, f(n1, X))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(f(u, n1), f(u, X))
% 0.20/0.48 = { by axiom 7 (clause_5) R->L }
% 0.20/0.48 f(u1, f(u, X))
% 0.20/0.48
% 0.20/0.48 Lemma 21: f(u2, uu) = f(u1, uu).
% 0.20/0.48 Proof:
% 0.20/0.48 f(u2, uu)
% 0.20/0.48 = { by axiom 9 (clause_8) }
% 0.20/0.48 f(u2, f(u, u))
% 0.20/0.48 = { by lemma 19 R->L }
% 0.20/0.48 f(u, f(n2, u))
% 0.20/0.48 = { by lemma 14 }
% 0.20/0.48 f(u, f(n1, u))
% 0.20/0.48 = { by lemma 20 }
% 0.20/0.48 f(u1, f(u, u))
% 0.20/0.48 = { by axiom 9 (clause_8) R->L }
% 0.20/0.48 f(u1, uu)
% 0.20/0.48
% 0.20/0.48 Lemma 22: f(u, f(n3, X)) = f(u3, f(u, X)).
% 0.20/0.48 Proof:
% 0.20/0.48 f(u, f(n3, X))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(f(u, n3), f(u, X))
% 0.20/0.48 = { by axiom 6 (clause_7) R->L }
% 0.20/0.48 f(u3, f(u, X))
% 0.20/0.48
% 0.20/0.48 Lemma 23: f(u3, uu) = f(u1, uu).
% 0.20/0.48 Proof:
% 0.20/0.48 f(u3, uu)
% 0.20/0.48 = { by axiom 9 (clause_8) }
% 0.20/0.48 f(u3, f(u, u))
% 0.20/0.48 = { by lemma 22 R->L }
% 0.20/0.48 f(u, f(n3, u))
% 0.20/0.48 = { by lemma 16 R->L }
% 0.20/0.48 f(u, f(n1, u))
% 0.20/0.48 = { by lemma 20 }
% 0.20/0.48 f(u1, f(u, u))
% 0.20/0.48 = { by axiom 9 (clause_8) R->L }
% 0.20/0.48 f(u1, uu)
% 0.20/0.48
% 0.20/0.48 Lemma 24: f(u, uu) = f(u3, uu).
% 0.20/0.48 Proof:
% 0.20/0.48 f(u, uu)
% 0.20/0.48 = { by lemma 18 R->L }
% 0.20/0.48 f(u, f(n3, u))
% 0.20/0.48 = { by lemma 22 }
% 0.20/0.48 f(u3, f(u, u))
% 0.20/0.48 = { by axiom 9 (clause_8) R->L }
% 0.20/0.48 f(u3, uu)
% 0.20/0.48
% 0.20/0.48 Lemma 25: f(u1, uu) = v.
% 0.20/0.48 Proof:
% 0.20/0.48 f(u1, uu)
% 0.20/0.48 = { by lemma 23 R->L }
% 0.20/0.48 f(u3, uu)
% 0.20/0.48 = { by lemma 24 R->L }
% 0.20/0.48 f(u, uu)
% 0.20/0.48 = { by axiom 9 (clause_8) }
% 0.20/0.48 f(u, f(u, u))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(f(u, u), f(u, u))
% 0.20/0.48 = { by axiom 9 (clause_8) R->L }
% 0.20/0.48 f(uu, f(u, u))
% 0.20/0.48 = { by axiom 9 (clause_8) R->L }
% 0.20/0.48 f(uu, uu)
% 0.20/0.48 = { by axiom 2 (clause_11) R->L }
% 0.20/0.48 v
% 0.20/0.48
% 0.20/0.48 Lemma 26: f(n3, uu) = v.
% 0.20/0.48 Proof:
% 0.20/0.48 f(n3, uu)
% 0.20/0.48 = { by lemma 18 R->L }
% 0.20/0.48 f(n3, f(n3, u))
% 0.20/0.48 = { by lemma 16 R->L }
% 0.20/0.48 f(n3, f(n1, u))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 f(n3, f(n2, u))
% 0.20/0.48 = { by lemma 15 R->L }
% 0.20/0.48 f(n2, f(n1, u))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 f(n2, f(n2, u))
% 0.20/0.48 = { by lemma 17 R->L }
% 0.20/0.48 f(u, f(n2, u))
% 0.20/0.48 = { by lemma 19 }
% 0.20/0.48 f(u2, f(u, u))
% 0.20/0.48 = { by axiom 9 (clause_8) R->L }
% 0.20/0.48 f(u2, uu)
% 0.20/0.48 = { by lemma 21 }
% 0.20/0.48 f(u1, uu)
% 0.20/0.48 = { by lemma 25 }
% 0.20/0.48 v
% 0.20/0.48
% 0.20/0.48 Lemma 27: f(n3, f(n3, X)) = f(u3, f(u, X)).
% 0.20/0.48 Proof:
% 0.20/0.48 f(n3, f(n3, X))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(f(n3, n3), f(n3, X))
% 0.20/0.48 = { by axiom 4 (clause_3) }
% 0.20/0.48 f(f(n3, f(n2, n1)), f(n3, X))
% 0.20/0.48 = { by lemma 15 R->L }
% 0.20/0.48 f(f(n2, f(n1, n1)), f(n3, X))
% 0.20/0.48 = { by axiom 3 (clause_2) R->L }
% 0.20/0.48 f(f(n2, n2), f(n3, X))
% 0.20/0.48 = { by axiom 5 (clause_4) R->L }
% 0.20/0.48 f(u, f(n3, X))
% 0.20/0.48 = { by lemma 22 }
% 0.20/0.48 f(u3, f(u, X))
% 0.20/0.48
% 0.20/0.48 Goal 1 (prove_equation): f(a, v) = f(b, v).
% 0.20/0.48 Proof:
% 0.20/0.48 f(a, v)
% 0.20/0.48 = { by lemma 25 R->L }
% 0.20/0.48 f(a, f(u1, uu))
% 0.20/0.48 = { by lemma 23 R->L }
% 0.20/0.48 f(a, f(u3, uu))
% 0.20/0.48 = { by axiom 9 (clause_8) }
% 0.20/0.48 f(a, f(u3, f(u, u)))
% 0.20/0.48 = { by lemma 27 R->L }
% 0.20/0.48 f(a, f(n3, f(n3, u)))
% 0.20/0.48 = { by lemma 16 R->L }
% 0.20/0.48 f(a, f(n3, f(n1, u)))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 f(a, f(n3, f(n2, u)))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(a, f(f(n3, n2), f(n3, u)))
% 0.20/0.48 = { by lemma 18 }
% 0.20/0.48 f(a, f(f(n3, n2), uu))
% 0.20/0.48 = { by axiom 10 (clause_9) }
% 0.20/0.48 f(f(f(n3, n2), u2), f(f(n3, n2), uu))
% 0.20/0.48 = { by axiom 11 (a1) R->L }
% 0.20/0.48 f(f(n3, n2), f(u2, uu))
% 0.20/0.48 = { by lemma 21 }
% 0.20/0.48 f(f(n3, n2), f(u1, uu))
% 0.20/0.48 = { by lemma 25 }
% 0.20/0.48 f(f(n3, n2), v)
% 0.20/0.48 = { by lemma 26 R->L }
% 0.20/0.48 f(f(n3, n2), f(n3, uu))
% 0.20/0.48 = { by axiom 11 (a1) R->L }
% 0.20/0.48 f(n3, f(n2, uu))
% 0.20/0.48 = { by lemma 18 R->L }
% 0.20/0.48 f(n3, f(n2, f(n3, u)))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(n3, f(f(n2, n3), f(n2, u)))
% 0.20/0.48 = { by axiom 4 (clause_3) }
% 0.20/0.48 f(n3, f(f(n2, f(n2, n1)), f(n2, u)))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(n3, f(f(f(n2, n2), f(n2, n1)), f(n2, u)))
% 0.20/0.48 = { by axiom 4 (clause_3) R->L }
% 0.20/0.48 f(n3, f(f(f(n2, n2), n3), f(n2, u)))
% 0.20/0.48 = { by axiom 5 (clause_4) R->L }
% 0.20/0.48 f(n3, f(f(u, n3), f(n2, u)))
% 0.20/0.48 = { by axiom 6 (clause_7) R->L }
% 0.20/0.48 f(n3, f(u3, f(n2, u)))
% 0.20/0.48 = { by lemma 14 }
% 0.20/0.48 f(n3, f(u3, f(n1, u)))
% 0.20/0.48 = { by lemma 16 }
% 0.20/0.48 f(n3, f(u3, f(n3, u)))
% 0.20/0.48 = { by lemma 18 }
% 0.20/0.48 f(n3, f(u3, uu))
% 0.20/0.48 = { by lemma 23 }
% 0.20/0.48 f(n3, f(u1, uu))
% 0.20/0.48 = { by lemma 25 }
% 0.20/0.48 f(n3, v)
% 0.20/0.48 = { by lemma 26 R->L }
% 0.20/0.48 f(n3, f(n3, uu))
% 0.20/0.48 = { by lemma 27 }
% 0.20/0.48 f(u3, f(u, uu))
% 0.20/0.48 = { by lemma 22 R->L }
% 0.20/0.48 f(u, f(n3, uu))
% 0.20/0.48 = { by lemma 18 R->L }
% 0.20/0.48 f(u, f(n3, f(n3, u)))
% 0.20/0.48 = { by lemma 16 R->L }
% 0.20/0.48 f(u, f(n3, f(n1, u)))
% 0.20/0.48 = { by lemma 14 R->L }
% 0.20/0.48 f(u, f(n3, f(n2, u)))
% 0.20/0.48 = { by lemma 15 R->L }
% 0.20/0.48 f(u, f(n2, f(n1, u)))
% 0.20/0.48 = { by lemma 12 }
% 0.20/0.48 f(u, f(n1, f(n1, u)))
% 0.20/0.48 = { by lemma 16 }
% 0.20/0.48 f(u, f(n1, f(n3, u)))
% 0.20/0.48 = { by lemma 18 }
% 0.20/0.48 f(u, f(n1, uu))
% 0.20/0.48 = { by lemma 20 }
% 0.20/0.48 f(u1, f(u, uu))
% 0.20/0.48 = { by lemma 24 }
% 0.20/0.48 f(u1, f(u3, uu))
% 0.20/0.48 = { by axiom 11 (a1) }
% 0.20/0.48 f(f(u1, u3), f(u1, uu))
% 0.20/0.48 = { by axiom 1 (clause_10) R->L }
% 0.20/0.48 f(b, f(u1, uu))
% 0.20/0.48 = { by lemma 25 }
% 0.20/0.48 f(b, v)
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48
% 0.20/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------