TSTP Solution File: BOO020-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO020-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n010.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 : Wed Aug 30 18:11:28 EDT 2023
% Result : Unsatisfiable 13.24s 2.25s
% Output : Proof 13.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO020-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 07:42:04 EDT 2023
% 0.15/0.34 % CPUTime :
% 13.24/2.25 Command-line arguments: --ground-connectedness --complete-subsets
% 13.24/2.25
% 13.24/2.25 % SZS status Unsatisfiable
% 13.24/2.25
% 13.24/2.29 % SZS output start Proof
% 13.24/2.29 Take the following subset of the input axioms:
% 13.24/2.29 fof(frink1, axiom, ![X]: add(X, X)=X).
% 13.24/2.29 fof(frink2, axiom, ![Y, Z, U, X2]: (add(add(add(X2, Y), Z), U)!=add(add(Y, Z), X2) | add(add(add(X2, Y), Z), inverse(U))=n0)).
% 13.24/2.29 fof(frink3, axiom, ![X2, Y2, Z2, U2]: (add(add(add(X2, Y2), Z2), inverse(U2))!=n0 | add(add(add(X2, Y2), Z2), U2)=add(add(Y2, Z2), X2))).
% 13.24/2.29 fof(prove_huntington, negated_conjecture, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))!=b | (add(add(a, b), c)!=add(a, add(b, c)) | add(b, a)!=add(a, b))).
% 13.24/2.29
% 13.24/2.29 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.24/2.29 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.24/2.29 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.24/2.29 fresh(y, y, x1...xn) = u
% 13.24/2.29 C => fresh(s, t, x1...xn) = v
% 13.24/2.29 where fresh is a fresh function symbol and x1..xn are the free
% 13.24/2.29 variables of u and v.
% 13.24/2.29 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.24/2.29 input problem has no model of domain size 1).
% 13.24/2.29
% 13.24/2.29 The encoding turns the above axioms into the following unit equations and goals:
% 13.24/2.29
% 13.24/2.29 Axiom 1 (frink1): add(X, X) = X.
% 13.24/2.29 Axiom 2 (frink2): fresh(X, X, Y, Z, W, V) = n0.
% 13.24/2.29 Axiom 3 (frink3): fresh2(X, X, Y, Z, W, V) = add(add(Z, W), Y).
% 13.24/2.29 Axiom 4 (frink3): fresh2(add(add(add(X, Y), Z), inverse(W)), n0, X, Y, Z, W) = add(add(add(X, Y), Z), W).
% 13.24/2.29 Axiom 5 (frink2): fresh(add(add(add(X, Y), Z), W), add(add(Y, Z), X), X, Y, Z, W) = add(add(add(X, Y), Z), inverse(W)).
% 13.24/2.29
% 13.24/2.29 Lemma 6: fresh2(add(add(X, Y), inverse(Z)), n0, X, X, Y, Z) = add(add(X, Y), Z).
% 13.24/2.29 Proof:
% 13.24/2.29 fresh2(add(add(X, Y), inverse(Z)), n0, X, X, Y, Z)
% 13.24/2.29 = { by axiom 1 (frink1) R->L }
% 13.24/2.29 fresh2(add(add(add(X, X), Y), inverse(Z)), n0, X, X, Y, Z)
% 13.24/2.29 = { by axiom 4 (frink3) }
% 13.24/2.29 add(add(add(X, X), Y), Z)
% 13.24/2.29 = { by axiom 1 (frink1) }
% 13.24/2.29 add(add(X, Y), Z)
% 13.24/2.29
% 13.24/2.29 Lemma 7: fresh2(add(X, inverse(Y)), n0, X, X, X, Y) = add(X, Y).
% 13.24/2.29 Proof:
% 13.24/2.29 fresh2(add(X, inverse(Y)), n0, X, X, X, Y)
% 13.24/2.29 = { by axiom 1 (frink1) R->L }
% 13.24/2.29 fresh2(add(add(X, X), inverse(Y)), n0, X, X, X, Y)
% 13.24/2.29 = { by lemma 6 }
% 13.24/2.29 add(add(X, X), Y)
% 13.24/2.29 = { by axiom 1 (frink1) }
% 13.24/2.29 add(X, Y)
% 13.24/2.29
% 13.24/2.29 Lemma 8: add(add(X, Y), inverse(X)) = n0.
% 13.24/2.29 Proof:
% 13.24/2.29 add(add(X, Y), inverse(X))
% 13.24/2.29 = { by axiom 1 (frink1) R->L }
% 13.24/2.29 add(add(add(X, X), Y), inverse(X))
% 13.24/2.29 = { by axiom 5 (frink2) R->L }
% 13.24/2.29 fresh(add(add(add(X, X), Y), X), add(add(X, Y), X), X, X, Y, X)
% 13.24/2.29 = { by axiom 1 (frink1) }
% 13.24/2.29 fresh(add(add(X, Y), X), add(add(X, Y), X), X, X, Y, X)
% 13.24/2.29 = { by axiom 2 (frink2) }
% 13.24/2.29 n0
% 13.24/2.29
% 13.24/2.29 Lemma 9: add(add(X, Y), X) = add(X, Y).
% 13.24/2.29 Proof:
% 13.24/2.29 add(add(X, Y), X)
% 13.24/2.29 = { by lemma 7 R->L }
% 13.24/2.29 fresh2(add(add(X, Y), inverse(X)), n0, add(X, Y), add(X, Y), add(X, Y), X)
% 13.24/2.29 = { by lemma 8 }
% 13.24/2.29 fresh2(n0, n0, add(X, Y), add(X, Y), add(X, Y), X)
% 13.24/2.29 = { by axiom 3 (frink3) }
% 13.24/2.29 add(add(add(X, Y), add(X, Y)), add(X, Y))
% 13.24/2.29 = { by axiom 1 (frink1) }
% 13.24/2.29 add(add(X, Y), add(X, Y))
% 13.24/2.29 = { by axiom 1 (frink1) }
% 13.24/2.29 add(X, Y)
% 13.24/2.29
% 13.24/2.29 Lemma 10: add(add(X, Y), Z) = add(add(Z, X), Y).
% 13.24/2.29 Proof:
% 13.24/2.29 add(add(X, Y), Z)
% 13.24/2.29 = { by axiom 3 (frink3) R->L }
% 13.24/2.29 fresh2(n0, n0, Z, X, Y, add(Z, X))
% 13.24/2.29 = { by lemma 8 R->L }
% 13.24/2.29 fresh2(add(add(add(Z, X), Y), inverse(add(Z, X))), n0, Z, X, Y, add(Z, X))
% 13.24/2.29 = { by axiom 4 (frink3) }
% 13.24/2.29 add(add(add(Z, X), Y), add(Z, X))
% 13.24/2.29 = { by lemma 9 }
% 13.24/2.29 add(add(Z, X), Y)
% 13.24/2.29
% 13.24/2.29 Lemma 11: add(Y, X) = add(X, Y).
% 13.24/2.29 Proof:
% 13.24/2.29 add(Y, X)
% 13.24/2.29 = { by lemma 9 R->L }
% 13.24/2.29 add(add(Y, X), Y)
% 13.24/2.29 = { by lemma 10 R->L }
% 13.24/2.29 add(add(X, Y), Y)
% 13.24/2.29 = { by lemma 9 R->L }
% 13.24/2.29 add(add(add(X, Y), X), Y)
% 13.24/2.29 = { by lemma 10 R->L }
% 13.24/2.29 add(add(X, Y), add(X, Y))
% 13.24/2.29 = { by axiom 1 (frink1) }
% 13.24/2.29 add(X, Y)
% 13.24/2.29
% 13.24/2.29 Lemma 12: add(X, inverse(X)) = n0.
% 13.24/2.29 Proof:
% 13.24/2.29 add(X, inverse(X))
% 13.24/2.29 = { by axiom 1 (frink1) R->L }
% 13.24/2.29 add(add(X, X), inverse(X))
% 13.24/2.29 = { by lemma 8 }
% 13.24/2.29 n0
% 13.24/2.29
% 13.24/2.29 Lemma 13: add(n0, inverse(add(X, Y))) = n0.
% 13.24/2.29 Proof:
% 13.24/2.29 add(n0, inverse(add(X, Y)))
% 13.24/2.29 = { by lemma 8 R->L }
% 13.24/2.29 add(add(add(X, Y), inverse(X)), inverse(add(X, Y)))
% 13.24/2.29 = { by lemma 8 }
% 13.24/2.29 n0
% 13.24/2.29
% 13.24/2.29 Lemma 14: add(n0, Y) = add(n0, X).
% 13.24/2.29 Proof:
% 13.24/2.29 add(n0, Y)
% 13.24/2.29 = { by lemma 12 R->L }
% 13.24/2.29 add(add(Y, inverse(Y)), Y)
% 13.24/2.29 = { by axiom 3 (frink3) R->L }
% 13.24/2.29 fresh2(n0, n0, Y, Y, inverse(Y), add(Z, W))
% 13.24/2.29 = { by lemma 13 R->L }
% 13.24/2.29 fresh2(add(n0, inverse(add(Z, W))), n0, Y, Y, inverse(Y), add(Z, W))
% 13.24/2.29 = { by lemma 12 R->L }
% 13.24/2.29 fresh2(add(add(Y, inverse(Y)), inverse(add(Z, W))), n0, Y, Y, inverse(Y), add(Z, W))
% 13.24/2.29 = { by lemma 6 }
% 13.24/2.29 add(add(Y, inverse(Y)), add(Z, W))
% 13.24/2.29 = { by lemma 12 }
% 13.24/2.29 add(n0, add(Z, W))
% 13.24/2.29 = { by lemma 12 R->L }
% 13.24/2.29 add(add(X, inverse(X)), add(Z, W))
% 13.24/2.29 = { by lemma 6 R->L }
% 13.24/2.29 fresh2(add(add(X, inverse(X)), inverse(add(Z, W))), n0, X, X, inverse(X), add(Z, W))
% 13.24/2.29 = { by lemma 12 }
% 13.24/2.29 fresh2(add(n0, inverse(add(Z, W))), n0, X, X, inverse(X), add(Z, W))
% 13.24/2.29 = { by lemma 13 }
% 13.24/2.29 fresh2(n0, n0, X, X, inverse(X), add(Z, W))
% 13.24/2.29 = { by axiom 3 (frink3) }
% 13.24/2.29 add(add(X, inverse(X)), X)
% 13.24/2.29 = { by lemma 12 }
% 13.24/2.29 add(n0, X)
% 13.24/2.29
% 13.24/2.29 Lemma 15: add(n0, X) = n0.
% 13.24/2.29 Proof:
% 13.24/2.29 add(n0, X)
% 13.24/2.29 = { by lemma 14 }
% 13.24/2.29 add(n0, inverse(Y))
% 13.24/2.29 = { by lemma 12 R->L }
% 13.24/2.29 add(add(Y, inverse(Y)), inverse(Y))
% 13.24/2.29 = { by lemma 8 }
% 13.24/2.29 n0
% 13.24/2.29
% 13.24/2.29 Lemma 16: add(X, add(Y, X)) = add(X, Y).
% 13.24/2.29 Proof:
% 13.24/2.29 add(X, add(Y, X))
% 13.24/2.29 = { by lemma 11 }
% 13.24/2.29 add(add(Y, X), X)
% 13.24/2.29 = { by lemma 9 R->L }
% 13.24/2.29 add(add(add(Y, X), Y), X)
% 13.24/2.29 = { by lemma 10 R->L }
% 13.24/2.29 add(add(Y, X), add(Y, X))
% 13.24/2.29 = { by axiom 1 (frink1) }
% 13.24/2.29 add(Y, X)
% 13.24/2.29 = { by lemma 11 R->L }
% 13.24/2.29 add(X, Y)
% 13.24/2.29
% 13.24/2.29 Lemma 17: add(add(add(X, Y), Z), X) = add(X, add(Y, Z)).
% 13.24/2.29 Proof:
% 13.24/2.29 add(add(add(X, Y), Z), X)
% 13.24/2.29 = { by lemma 10 R->L }
% 13.24/2.29 add(add(add(Y, Z), X), X)
% 13.24/2.29 = { by lemma 10 }
% 13.24/2.29 add(add(X, add(Y, Z)), X)
% 13.24/2.29 = { by lemma 9 }
% 13.24/2.29 add(X, add(Y, Z))
% 13.24/2.29
% 13.24/2.29 Lemma 18: add(add(X, Y), Z) = add(X, add(Y, Z)).
% 13.24/2.29 Proof:
% 13.24/2.29 add(add(X, Y), Z)
% 13.24/2.29 = { by lemma 10 R->L }
% 13.24/2.29 add(add(Y, Z), X)
% 13.24/2.29 = { by lemma 9 R->L }
% 13.24/2.29 add(add(add(Y, Z), Y), X)
% 13.24/2.29 = { by lemma 10 }
% 13.24/2.29 add(add(X, add(Y, Z)), Y)
% 13.24/2.29 = { by lemma 17 R->L }
% 13.24/2.29 add(add(add(add(X, Y), Z), X), Y)
% 13.24/2.29 = { by lemma 6 R->L }
% 13.24/2.29 fresh2(add(add(add(add(X, Y), Z), X), inverse(Y)), n0, add(add(X, Y), Z), add(add(X, Y), Z), X, Y)
% 13.24/2.29 = { by lemma 17 }
% 13.24/2.29 fresh2(add(add(X, add(Y, Z)), inverse(Y)), n0, add(add(X, Y), Z), add(add(X, Y), Z), X, Y)
% 13.24/2.29 = { by lemma 10 R->L }
% 13.24/2.29 fresh2(add(add(add(Y, Z), inverse(Y)), X), n0, add(add(X, Y), Z), add(add(X, Y), Z), X, Y)
% 13.24/2.29 = { by lemma 8 }
% 13.24/2.29 fresh2(add(n0, X), n0, add(add(X, Y), Z), add(add(X, Y), Z), X, Y)
% 13.24/2.29 = { by lemma 15 }
% 13.24/2.29 fresh2(n0, n0, add(add(X, Y), Z), add(add(X, Y), Z), X, Y)
% 13.24/2.29 = { by axiom 3 (frink3) }
% 13.24/2.29 add(add(add(add(X, Y), Z), X), add(add(X, Y), Z))
% 13.24/2.29 = { by lemma 9 }
% 13.24/2.29 add(add(add(X, Y), Z), X)
% 13.24/2.29 = { by lemma 17 }
% 13.24/2.29 add(X, add(Y, Z))
% 13.24/2.29
% 13.24/2.29 Lemma 19: add(add(X, Y), inverse(Y)) = n0.
% 13.24/2.29 Proof:
% 13.24/2.29 add(add(X, Y), inverse(Y))
% 13.24/2.29 = { by lemma 10 R->L }
% 13.24/2.29 add(add(Y, inverse(Y)), X)
% 13.24/2.29 = { by lemma 12 }
% 13.24/2.29 add(n0, X)
% 13.24/2.29 = { by lemma 14 R->L }
% 13.24/2.29 add(n0, Z)
% 13.24/2.29 = { by lemma 15 }
% 13.24/2.29 n0
% 13.24/2.29
% 13.24/2.29 Lemma 20: add(add(X, inverse(Y)), Y) = n0.
% 13.24/2.29 Proof:
% 13.24/2.29 add(add(X, inverse(Y)), Y)
% 13.24/2.29 = { by axiom 3 (frink3) R->L }
% 13.24/2.29 fresh2(n0, n0, Y, X, inverse(Y), Z)
% 13.24/2.29 = { by lemma 15 R->L }
% 13.24/2.29 fresh2(add(n0, inverse(Z)), n0, Y, X, inverse(Y), Z)
% 13.24/2.29 = { by lemma 8 R->L }
% 13.24/2.29 fresh2(add(add(add(Y, X), inverse(Y)), inverse(Z)), n0, Y, X, inverse(Y), Z)
% 13.24/2.29 = { by axiom 4 (frink3) }
% 13.24/2.29 add(add(add(Y, X), inverse(Y)), Z)
% 13.24/2.29 = { by lemma 8 }
% 13.24/2.29 add(n0, Z)
% 13.24/2.29 = { by lemma 15 }
% 13.24/2.29 n0
% 13.24/2.29
% 13.24/2.29 Lemma 21: fresh2(X, X, Y, Z, W, V) = add(Z, add(W, Y)).
% 13.24/2.29 Proof:
% 13.24/2.29 fresh2(X, X, Y, Z, W, V)
% 13.24/2.29 = { by axiom 3 (frink3) }
% 13.24/2.29 add(add(Z, W), Y)
% 13.24/2.29 = { by lemma 18 }
% 13.24/2.29 add(Z, add(W, Y))
% 13.24/2.29
% 13.24/2.29 Lemma 22: add(X, inverse(inverse(add(Y, inverse(X))))) = n0.
% 13.24/2.29 Proof:
% 13.24/2.29 add(X, inverse(inverse(add(Y, inverse(X)))))
% 13.24/2.30 = { by lemma 11 }
% 13.24/2.30 add(inverse(inverse(add(Y, inverse(X)))), X)
% 13.24/2.30 = { by axiom 1 (frink1) R->L }
% 13.24/2.30 add(add(inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X))))), X)
% 13.24/2.30 = { by lemma 16 R->L }
% 13.24/2.30 add(add(inverse(inverse(add(Y, inverse(X)))), add(inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X)))))), X)
% 13.24/2.30 = { by lemma 21 R->L }
% 13.24/2.30 add(fresh2(n0, n0, inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X)))), add(Y, inverse(X))), X)
% 13.24/2.30 = { by lemma 12 R->L }
% 13.24/2.30 add(fresh2(add(inverse(add(Y, inverse(X))), inverse(inverse(add(Y, inverse(X))))), n0, inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X)))), add(Y, inverse(X))), X)
% 13.24/2.30 = { by lemma 11 }
% 13.24/2.30 add(fresh2(add(inverse(inverse(add(Y, inverse(X)))), inverse(add(Y, inverse(X)))), n0, inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X)))), inverse(inverse(add(Y, inverse(X)))), add(Y, inverse(X))), X)
% 13.24/2.30 = { by lemma 7 }
% 13.24/2.30 add(add(inverse(inverse(add(Y, inverse(X)))), add(Y, inverse(X))), X)
% 13.24/2.30 = { by lemma 11 R->L }
% 13.24/2.30 add(add(add(Y, inverse(X)), inverse(inverse(add(Y, inverse(X))))), X)
% 13.24/2.30 = { by lemma 18 }
% 13.24/2.30 add(add(Y, inverse(X)), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by axiom 1 (frink1) R->L }
% 13.24/2.30 add(add(add(Y, inverse(X)), add(Y, inverse(X))), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by lemma 9 R->L }
% 13.24/2.30 add(add(add(add(Y, inverse(X)), add(Y, inverse(X))), add(Y, inverse(X))), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by axiom 3 (frink3) R->L }
% 13.24/2.30 add(fresh2(n0, n0, add(Y, inverse(X)), add(Y, inverse(X)), add(Y, inverse(X)), inverse(X)), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by lemma 19 R->L }
% 13.24/2.30 add(fresh2(add(add(Y, inverse(X)), inverse(inverse(X))), n0, add(Y, inverse(X)), add(Y, inverse(X)), add(Y, inverse(X)), inverse(X)), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by lemma 7 }
% 13.24/2.30 add(add(add(Y, inverse(X)), inverse(X)), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by lemma 10 R->L }
% 13.24/2.30 add(add(add(inverse(X), inverse(X)), Y), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by axiom 1 (frink1) }
% 13.24/2.30 add(add(inverse(X), Y), add(inverse(inverse(add(Y, inverse(X)))), X))
% 13.24/2.30 = { by lemma 10 }
% 13.24/2.30 add(add(add(inverse(inverse(add(Y, inverse(X)))), X), inverse(X)), Y)
% 13.24/2.30 = { by lemma 11 R->L }
% 13.24/2.30 add(Y, add(add(inverse(inverse(add(Y, inverse(X)))), X), inverse(X)))
% 13.24/2.30 = { by lemma 19 }
% 13.24/2.30 add(Y, n0)
% 13.24/2.30 = { by axiom 1 (frink1) R->L }
% 13.24/2.30 add(add(Y, Y), n0)
% 13.24/2.30 = { by lemma 10 }
% 13.24/2.30 add(add(n0, Y), Y)
% 13.24/2.30 = { by lemma 14 R->L }
% 13.24/2.30 add(add(n0, Z), Y)
% 13.24/2.30 = { by lemma 15 }
% 13.24/2.30 add(n0, Y)
% 13.24/2.30 = { by lemma 14 R->L }
% 13.24/2.30 add(n0, W)
% 13.24/2.30 = { by lemma 15 }
% 13.24/2.30 n0
% 13.24/2.30
% 13.24/2.30 Goal 1 (prove_huntington): tuple(add(add(a, b), c), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(b, a)) = tuple(add(a, add(b, c)), b, add(a, b)).
% 13.24/2.30 Proof:
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(b, a))
% 13.24/2.30 = { by lemma 11 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(a, b))
% 13.24/2.30 = { by axiom 1 (frink1) R->L }
% 13.24/2.30 tuple(add(add(a, b), c), add(add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), add(a, b))
% 13.24/2.30 = { by lemma 9 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), add(add(add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), add(a, b))
% 13.24/2.30 = { by axiom 3 (frink3) R->L }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(n0, n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 20 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(add(add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), inverse(add(a, inverse(b)))), add(a, inverse(b))), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 9 }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(a, inverse(b))), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 11 }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(add(a, inverse(b)), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 10 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(add(inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), a), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 6 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(fresh2(add(add(inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), inverse(a)), n0, inverse(b), inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), a), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 10 }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(fresh2(add(add(inverse(a), inverse(b)), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), n0, inverse(b), inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), a), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 11 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(fresh2(add(add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(a), inverse(b))), n0, inverse(b), inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), a), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 20 }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(fresh2(n0, n0, inverse(b), inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), a), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by axiom 3 (frink3) }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(add(inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), inverse(b)), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 9 }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(inverse(b), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b))))), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 11 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), inverse(b)), n0, add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 7 }
% 13.24/2.30 tuple(add(add(a, b), c), add(add(inverse(add(a, inverse(b))), inverse(add(inverse(a), inverse(b)))), b), add(a, b))
% 13.24/2.30 = { by lemma 10 }
% 13.24/2.30 tuple(add(add(a, b), c), add(add(b, inverse(add(a, inverse(b)))), inverse(add(inverse(a), inverse(b)))), add(a, b))
% 13.24/2.30 = { by lemma 11 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(inverse(a), inverse(b))), add(b, inverse(add(a, inverse(b))))), add(a, b))
% 13.24/2.30 = { by lemma 7 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(inverse(a), inverse(b))), fresh2(add(b, inverse(inverse(add(a, inverse(b))))), n0, b, b, b, inverse(add(a, inverse(b))))), add(a, b))
% 13.24/2.30 = { by lemma 22 }
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(inverse(a), inverse(b))), fresh2(n0, n0, b, b, b, inverse(add(a, inverse(b))))), add(a, b))
% 13.24/2.30 = { by lemma 21 }
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(inverse(a), inverse(b))), add(b, add(b, b))), add(a, b))
% 13.24/2.30 = { by lemma 16 }
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(inverse(a), inverse(b))), add(b, b)), add(a, b))
% 13.24/2.30 = { by axiom 1 (frink1) }
% 13.24/2.30 tuple(add(add(a, b), c), add(inverse(add(inverse(a), inverse(b))), b), add(a, b))
% 13.24/2.30 = { by lemma 11 }
% 13.24/2.30 tuple(add(add(a, b), c), add(b, inverse(add(inverse(a), inverse(b)))), add(a, b))
% 13.24/2.30 = { by lemma 7 R->L }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(add(b, inverse(inverse(add(inverse(a), inverse(b))))), n0, b, b, b, inverse(add(inverse(a), inverse(b)))), add(a, b))
% 13.24/2.30 = { by lemma 22 }
% 13.24/2.30 tuple(add(add(a, b), c), fresh2(n0, n0, b, b, b, inverse(add(inverse(a), inverse(b)))), add(a, b))
% 13.24/2.30 = { by lemma 21 }
% 13.24/2.30 tuple(add(add(a, b), c), add(b, add(b, b)), add(a, b))
% 13.24/2.30 = { by lemma 16 }
% 13.24/2.30 tuple(add(add(a, b), c), add(b, b), add(a, b))
% 13.24/2.30 = { by axiom 1 (frink1) }
% 13.24/2.30 tuple(add(add(a, b), c), b, add(a, b))
% 13.24/2.30 = { by lemma 18 }
% 13.24/2.30 tuple(add(a, add(b, c)), b, add(a, b))
% 13.24/2.30 % SZS output end Proof
% 13.24/2.30
% 13.24/2.30 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------