TSTP Solution File: GRP101-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP101-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n008.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 01:16:59 EDT 2023
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP101-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 23:38:32 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.44 Command-line arguments: --no-flatten-goal
% 0.19/0.44
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 Take the following subset of the input axioms:
% 0.19/0.47 fof(identity, axiom, ![X]: identity=double_divide(X, inverse(X))).
% 0.19/0.47 fof(inverse, axiom, ![X2]: inverse(X2)=double_divide(X2, identity)).
% 0.19/0.47 fof(multiply, axiom, ![Y, X2]: multiply(X2, Y)=double_divide(double_divide(Y, X2), identity)).
% 0.19/0.47 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=identity | (multiply(identity, a2)!=a2 | (multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)) | multiply(a4, b4)!=multiply(b4, a4)))).
% 0.19/0.47 fof(single_axiom, axiom, ![Z, X2, Y2]: double_divide(double_divide(X2, double_divide(double_divide(Y2, double_divide(Z, X2)), double_divide(Z, identity))), double_divide(identity, identity))=Y2).
% 0.19/0.47
% 0.19/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.47 fresh(y, y, x1...xn) = u
% 0.19/0.47 C => fresh(s, t, x1...xn) = v
% 0.19/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.47 variables of u and v.
% 0.19/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.47 input problem has no model of domain size 1).
% 0.19/0.47
% 0.19/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.47
% 0.19/0.47 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.47 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.47 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.47 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), double_divide(Z, identity))), double_divide(identity, identity)) = Y.
% 0.19/0.47
% 0.19/0.47 Lemma 5: double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), inverse(identity)) = Y.
% 0.19/0.47 Proof:
% 0.19/0.47 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), inverse(identity))
% 0.19/0.47 = { by axiom 1 (inverse) }
% 0.19/0.47 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), inverse(Z))), double_divide(identity, identity))
% 0.19/0.47 = { by axiom 1 (inverse) }
% 0.19/0.47 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), double_divide(Z, identity))), double_divide(identity, identity))
% 0.19/0.47 = { by axiom 4 (single_axiom) }
% 0.19/0.47 Y
% 0.19/0.47
% 0.19/0.47 Lemma 6: double_divide(double_divide(inverse(X), double_divide(inverse(Y), inverse(X))), inverse(identity)) = Y.
% 0.19/0.47 Proof:
% 0.19/0.47 double_divide(double_divide(inverse(X), double_divide(inverse(Y), inverse(X))), inverse(identity))
% 0.19/0.47 = { by axiom 1 (inverse) }
% 0.19/0.47 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, identity), inverse(X))), inverse(identity))
% 0.19/0.47 = { by axiom 2 (identity) }
% 0.19/0.47 double_divide(double_divide(inverse(X), double_divide(double_divide(Y, double_divide(X, inverse(X))), inverse(X))), inverse(identity))
% 0.19/0.47 = { by lemma 5 }
% 0.19/0.47 Y
% 0.19/0.47
% 0.19/0.47 Lemma 7: double_divide(inverse(inverse(inverse(X))), inverse(identity)) = X.
% 0.19/0.47 Proof:
% 0.19/0.47 double_divide(inverse(inverse(inverse(X))), inverse(identity))
% 0.19/0.47 = { by axiom 1 (inverse) }
% 0.19/0.47 double_divide(double_divide(inverse(inverse(X)), identity), inverse(identity))
% 0.19/0.47 = { by axiom 2 (identity) }
% 0.19/0.47 double_divide(double_divide(inverse(inverse(X)), double_divide(inverse(X), inverse(inverse(X)))), inverse(identity))
% 0.19/0.47 = { by lemma 6 }
% 0.19/0.47 X
% 0.19/0.47
% 0.19/0.47 Lemma 8: double_divide(double_divide(inverse(identity), X), inverse(identity)) = inverse(inverse(X)).
% 0.19/0.47 Proof:
% 0.19/0.47 double_divide(double_divide(inverse(identity), X), inverse(identity))
% 0.19/0.47 = { by lemma 7 R->L }
% 0.19/0.47 double_divide(double_divide(inverse(identity), double_divide(inverse(inverse(inverse(X))), inverse(identity))), inverse(identity))
% 0.19/0.47 = { by lemma 6 }
% 0.19/0.47 inverse(inverse(X))
% 0.19/0.47
% 0.19/0.47 Lemma 9: inverse(identity) = identity.
% 0.19/0.47 Proof:
% 0.19/0.47 inverse(identity)
% 0.19/0.47 = { by lemma 7 R->L }
% 0.19/0.47 double_divide(inverse(inverse(inverse(inverse(identity)))), inverse(identity))
% 0.19/0.47 = { by lemma 8 R->L }
% 0.19/0.47 double_divide(double_divide(double_divide(inverse(identity), inverse(inverse(identity))), inverse(identity)), inverse(identity))
% 0.19/0.47 = { by axiom 2 (identity) R->L }
% 0.19/0.47 double_divide(double_divide(identity, inverse(identity)), inverse(identity))
% 0.19/0.47 = { by axiom 2 (identity) R->L }
% 0.19/0.47 double_divide(identity, inverse(identity))
% 0.19/0.47 = { by axiom 2 (identity) R->L }
% 0.19/0.47 identity
% 0.19/0.47
% 0.19/0.47 Lemma 10: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.19/0.47 Proof:
% 0.19/0.47 inverse(double_divide(X, Y))
% 0.19/0.47 = { by axiom 1 (inverse) }
% 0.19/0.47 double_divide(double_divide(X, Y), identity)
% 0.19/0.47 = { by axiom 3 (multiply) R->L }
% 0.19/0.47 multiply(Y, X)
% 0.19/0.47
% 0.19/0.47 Lemma 11: multiply(identity, X) = inverse(inverse(X)).
% 0.19/0.47 Proof:
% 0.19/0.47 multiply(identity, X)
% 0.19/0.47 = { by lemma 10 R->L }
% 0.19/0.47 inverse(double_divide(X, identity))
% 0.19/0.47 = { by axiom 1 (inverse) R->L }
% 0.19/0.47 inverse(inverse(X))
% 0.19/0.48
% 0.19/0.48 Lemma 12: inverse(inverse(inverse(inverse(X)))) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(inverse(inverse(inverse(X))))
% 0.19/0.48 = { by lemma 11 R->L }
% 0.19/0.48 inverse(multiply(identity, inverse(X)))
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 inverse(multiply(inverse(identity), inverse(X)))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(inverse(double_divide(inverse(X), inverse(identity))))
% 0.19/0.48 = { by lemma 8 R->L }
% 0.19/0.48 double_divide(double_divide(inverse(identity), double_divide(inverse(X), inverse(identity))), inverse(identity))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 13: inverse(inverse(inverse(multiply(X, Y)))) = double_divide(Y, X).
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(inverse(inverse(multiply(X, Y))))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(inverse(inverse(inverse(double_divide(Y, X)))))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 double_divide(Y, X)
% 0.19/0.48
% 0.19/0.48 Lemma 14: double_divide(identity, X) = inverse(X).
% 0.19/0.48 Proof:
% 0.19/0.48 double_divide(identity, X)
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 inverse(inverse(inverse(multiply(X, identity))))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(inverse(inverse(inverse(double_divide(identity, X)))))
% 0.19/0.48 = { by axiom 1 (inverse) }
% 0.19/0.48 inverse(inverse(inverse(double_divide(double_divide(identity, X), identity))))
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 inverse(inverse(inverse(double_divide(double_divide(identity, X), inverse(identity)))))
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 inverse(inverse(inverse(double_divide(double_divide(inverse(identity), X), inverse(identity)))))
% 0.19/0.48 = { by lemma 8 }
% 0.19/0.48 inverse(inverse(inverse(inverse(inverse(X)))))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 inverse(X)
% 0.19/0.48
% 0.19/0.48 Lemma 15: multiply(inverse(X), X) = inverse(identity).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(inverse(X), X)
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(double_divide(X, inverse(X)))
% 0.19/0.48 = { by axiom 2 (identity) R->L }
% 0.19/0.48 inverse(identity)
% 0.19/0.48
% 0.19/0.48 Lemma 16: multiply(multiply(inverse(X), Y), X) = Y.
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(multiply(inverse(X), Y), X)
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(double_divide(X, multiply(inverse(X), Y)))
% 0.19/0.48 = { by axiom 1 (inverse) }
% 0.19/0.48 double_divide(double_divide(X, multiply(inverse(X), Y)), identity)
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 double_divide(double_divide(X, multiply(inverse(X), Y)), inverse(identity))
% 0.19/0.48 = { by lemma 14 R->L }
% 0.19/0.48 double_divide(double_divide(X, multiply(double_divide(identity, X), Y)), inverse(identity))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 double_divide(double_divide(X, inverse(double_divide(Y, double_divide(identity, X)))), inverse(identity))
% 0.19/0.48 = { by axiom 1 (inverse) }
% 0.19/0.48 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(identity, X)), identity)), inverse(identity))
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(identity, X)), inverse(identity))), inverse(identity))
% 0.19/0.48 = { by lemma 5 }
% 0.19/0.48 Y
% 0.19/0.48
% 0.19/0.48 Lemma 17: inverse(inverse(X)) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(inverse(X))
% 0.19/0.48 = { by lemma 11 R->L }
% 0.19/0.48 multiply(identity, X)
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 multiply(inverse(identity), X)
% 0.19/0.48 = { by lemma 15 R->L }
% 0.19/0.48 multiply(multiply(inverse(X), X), X)
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 18: multiply(X, Y) = multiply(Y, X).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(X, Y)
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(double_divide(Y, X))
% 0.19/0.48 = { by lemma 5 R->L }
% 0.19/0.48 double_divide(double_divide(X, double_divide(double_divide(inverse(double_divide(Y, X)), double_divide(Y, X)), inverse(Y))), inverse(identity))
% 0.19/0.48 = { by lemma 17 R->L }
% 0.19/0.48 double_divide(double_divide(X, double_divide(double_divide(inverse(double_divide(Y, X)), inverse(inverse(double_divide(Y, X)))), inverse(Y))), inverse(identity))
% 0.19/0.48 = { by axiom 2 (identity) R->L }
% 0.19/0.48 double_divide(double_divide(X, double_divide(identity, inverse(Y))), inverse(identity))
% 0.19/0.48 = { by lemma 14 }
% 0.19/0.48 double_divide(double_divide(X, inverse(inverse(Y))), inverse(identity))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 double_divide(double_divide(X, Y), inverse(identity))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 double_divide(double_divide(X, Y), identity)
% 0.19/0.48 = { by axiom 1 (inverse) R->L }
% 0.19/0.48 inverse(double_divide(X, Y))
% 0.19/0.48 = { by lemma 10 }
% 0.19/0.48 multiply(Y, X)
% 0.19/0.48
% 0.19/0.48 Lemma 19: multiply(double_divide(inverse(X), Y), Y) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(double_divide(inverse(X), Y), Y)
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(double_divide(Y, double_divide(inverse(X), Y)))
% 0.19/0.48 = { by axiom 1 (inverse) }
% 0.19/0.48 double_divide(double_divide(Y, double_divide(inverse(X), Y)), identity)
% 0.19/0.48 = { by lemma 9 R->L }
% 0.19/0.48 double_divide(double_divide(Y, double_divide(inverse(X), Y)), inverse(identity))
% 0.19/0.48 = { by lemma 12 R->L }
% 0.19/0.48 double_divide(double_divide(Y, double_divide(inverse(X), inverse(inverse(inverse(inverse(Y)))))), inverse(identity))
% 0.19/0.48 = { by lemma 12 R->L }
% 0.19/0.48 double_divide(double_divide(inverse(inverse(inverse(inverse(Y)))), double_divide(inverse(X), inverse(inverse(inverse(inverse(Y)))))), inverse(identity))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 20: double_divide(X, inverse(Y)) = multiply(Y, inverse(X)).
% 0.19/0.48 Proof:
% 0.19/0.48 double_divide(X, inverse(Y))
% 0.19/0.48 = { by lemma 17 R->L }
% 0.19/0.48 double_divide(X, inverse(inverse(inverse(Y))))
% 0.19/0.48 = { by lemma 19 R->L }
% 0.19/0.48 double_divide(X, multiply(double_divide(inverse(inverse(inverse(inverse(Y)))), inverse(X)), inverse(X)))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 double_divide(X, multiply(double_divide(Y, inverse(X)), inverse(X)))
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 double_divide(X, multiply(inverse(X), double_divide(Y, inverse(X))))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 inverse(inverse(inverse(multiply(multiply(inverse(X), double_divide(Y, inverse(X))), X))))
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 inverse(inverse(inverse(double_divide(Y, inverse(X)))))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 inverse(double_divide(Y, inverse(X)))
% 0.19/0.48 = { by lemma 10 }
% 0.19/0.48 multiply(inverse(X), Y)
% 0.19/0.48 = { by lemma 18 }
% 0.19/0.48 multiply(Y, inverse(X))
% 0.19/0.48
% 0.19/0.48 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.19/0.48 Proof:
% 0.19/0.48 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 11 }
% 0.19/0.48 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 15 }
% 0.19/0.48 tuple(inverse(identity), inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 tuple(identity, a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 18 }
% 0.19/0.48 tuple(identity, a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 tuple(identity, a2, multiply(c3, inverse(double_divide(b3, a3))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 20 R->L }
% 0.19/0.48 tuple(identity, a2, double_divide(double_divide(b3, a3), inverse(c3)), multiply(a4, b4))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 tuple(identity, a2, inverse(inverse(inverse(multiply(inverse(c3), double_divide(b3, a3))))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 tuple(identity, a2, inverse(inverse(inverse(multiply(double_divide(b3, a3), inverse(c3))))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 tuple(identity, a2, inverse(inverse(inverse(inverse(double_divide(inverse(c3), double_divide(b3, a3)))))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 tuple(identity, a2, inverse(inverse(double_divide(inverse(c3), double_divide(b3, a3)))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 tuple(identity, a2, double_divide(inverse(c3), double_divide(b3, a3)), multiply(a4, b4))
% 0.19/0.48 = { by lemma 5 R->L }
% 0.19/0.48 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3))), inverse(identity)), multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(identity, a2, double_divide(double_divide(a3, double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3))), identity), multiply(a4, b4))
% 0.19/0.48 = { by axiom 1 (inverse) R->L }
% 0.19/0.48 tuple(identity, a2, inverse(double_divide(a3, double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3)))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 10 }
% 0.19/0.48 tuple(identity, a2, multiply(double_divide(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)), inverse(b3)), a3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 20 }
% 0.19/0.48 tuple(identity, a2, multiply(multiply(b3, inverse(double_divide(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)))), a3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 10 }
% 0.19/0.48 tuple(identity, a2, multiply(multiply(b3, multiply(double_divide(b3, a3), double_divide(inverse(c3), double_divide(b3, a3)))), a3), multiply(a4, b4))
% 0.19/0.48 = { by lemma 18 }
% 0.19/0.48 tuple(identity, a2, multiply(a3, multiply(b3, multiply(double_divide(b3, a3), double_divide(inverse(c3), double_divide(b3, a3))))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 18 }
% 0.19/0.48 tuple(identity, a2, multiply(a3, multiply(b3, multiply(double_divide(inverse(c3), double_divide(b3, a3)), double_divide(b3, a3)))), multiply(a4, b4))
% 0.19/0.48 = { by lemma 19 }
% 0.19/0.48 tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 tuple(identity, a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48
% 0.19/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------