TSTP Solution File: GRP070-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP070-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 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 : n022.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 01:16:52 EDT 2023
% Result : Unsatisfiable 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP070-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 22:41:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.42 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.42
% 0.22/0.42 % SZS status Unsatisfiable
% 0.22/0.42
% 0.22/0.45 % SZS output start Proof
% 0.22/0.45 Take the following subset of the input axioms:
% 0.22/0.45 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=divide(X, inverse(Y))).
% 0.22/0.45 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)))).
% 0.22/0.45 fof(single_axiom, axiom, ![Z, U, X2, Y2]: divide(divide(X2, X2), divide(Y2, divide(divide(Z, divide(U, Y2)), inverse(U))))=Z).
% 0.22/0.45
% 0.22/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.45 fresh(y, y, x1...xn) = u
% 0.22/0.45 C => fresh(s, t, x1...xn) = v
% 0.22/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.45 variables of u and v.
% 0.22/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.45 input problem has no model of domain size 1).
% 0.22/0.45
% 0.22/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.45
% 0.22/0.45 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.22/0.45 Axiom 2 (single_axiom): divide(divide(X, X), divide(Y, divide(divide(Z, divide(W, Y)), inverse(W)))) = Z.
% 0.22/0.45
% 0.22/0.45 Lemma 3: divide(divide(X, X), divide(Y, multiply(divide(Z, divide(W, Y)), W))) = Z.
% 0.22/0.45 Proof:
% 0.22/0.45 divide(divide(X, X), divide(Y, multiply(divide(Z, divide(W, Y)), W)))
% 0.22/0.45 = { by axiom 1 (multiply) }
% 0.22/0.45 divide(divide(X, X), divide(Y, divide(divide(Z, divide(W, Y)), inverse(W))))
% 0.22/0.45 = { by axiom 2 (single_axiom) }
% 0.22/0.45 Z
% 0.22/0.45
% 0.22/0.45 Lemma 4: divide(multiply(inverse(X), X), divide(Y, multiply(divide(Z, divide(W, Y)), W))) = Z.
% 0.22/0.45 Proof:
% 0.22/0.45 divide(multiply(inverse(X), X), divide(Y, multiply(divide(Z, divide(W, Y)), W)))
% 0.22/0.45 = { by axiom 1 (multiply) }
% 0.22/0.45 divide(divide(inverse(X), inverse(X)), divide(Y, multiply(divide(Z, divide(W, Y)), W)))
% 0.22/0.45 = { by lemma 3 }
% 0.22/0.45 Z
% 0.22/0.45
% 0.22/0.45 Lemma 5: divide(divide(X, X), divide(inverse(Y), multiply(divide(Z, multiply(W, Y)), W))) = Z.
% 0.22/0.45 Proof:
% 0.22/0.45 divide(divide(X, X), divide(inverse(Y), multiply(divide(Z, multiply(W, Y)), W)))
% 0.22/0.45 = { by axiom 1 (multiply) }
% 0.22/0.45 divide(divide(X, X), divide(inverse(Y), multiply(divide(Z, divide(W, inverse(Y))), W)))
% 0.22/0.45 = { by lemma 3 }
% 0.22/0.45 Z
% 0.22/0.45
% 0.22/0.45 Lemma 6: divide(Y, Y) = divide(X, X).
% 0.22/0.45 Proof:
% 0.22/0.45 divide(Y, Y)
% 0.22/0.45 = { by lemma 4 R->L }
% 0.22/0.45 divide(multiply(inverse(Z), Z), divide(multiply(divide(W, multiply(V, U)), V), multiply(divide(divide(Y, Y), divide(inverse(U), multiply(divide(W, multiply(V, U)), V))), inverse(U))))
% 0.22/0.45 = { by lemma 5 }
% 0.22/0.45 divide(multiply(inverse(Z), Z), divide(multiply(divide(W, multiply(V, U)), V), multiply(W, inverse(U))))
% 0.22/0.45 = { by lemma 5 R->L }
% 0.22/0.45 divide(multiply(inverse(Z), Z), divide(multiply(divide(W, multiply(V, U)), V), multiply(divide(divide(X, X), divide(inverse(U), multiply(divide(W, multiply(V, U)), V))), inverse(U))))
% 0.22/0.45 = { by lemma 4 }
% 0.22/0.45 divide(X, X)
% 0.22/0.45
% 0.22/0.45 Lemma 7: divide(multiply(inverse(X), X), divide(inverse(Y), multiply(divide(Z, multiply(W, Y)), W))) = Z.
% 0.22/0.45 Proof:
% 0.22/0.45 divide(multiply(inverse(X), X), divide(inverse(Y), multiply(divide(Z, multiply(W, Y)), W)))
% 0.22/0.45 = { by axiom 1 (multiply) }
% 0.22/0.45 divide(multiply(inverse(X), X), divide(inverse(Y), multiply(divide(Z, divide(W, inverse(Y))), W)))
% 0.22/0.45 = { by lemma 4 }
% 0.22/0.45 Z
% 0.22/0.45
% 0.22/0.45 Lemma 8: multiply(inverse(X), X) = divide(Y, Y).
% 0.22/0.45 Proof:
% 0.22/0.45 multiply(inverse(X), X)
% 0.22/0.45 = { by lemma 4 R->L }
% 0.22/0.45 divide(multiply(inverse(Z), Z), divide(multiply(divide(W, multiply(V, U)), V), multiply(divide(multiply(inverse(X), X), divide(inverse(U), multiply(divide(W, multiply(V, U)), V))), inverse(U))))
% 0.22/0.45 = { by lemma 7 }
% 0.22/0.45 divide(multiply(inverse(Z), Z), divide(multiply(divide(W, multiply(V, U)), V), multiply(W, inverse(U))))
% 0.22/0.45 = { by lemma 5 R->L }
% 0.22/0.45 divide(multiply(inverse(Z), Z), divide(multiply(divide(W, multiply(V, U)), V), multiply(divide(divide(Y, Y), divide(inverse(U), multiply(divide(W, multiply(V, U)), V))), inverse(U))))
% 0.22/0.45 = { by lemma 4 }
% 0.22/0.45 divide(Y, Y)
% 0.22/0.45
% 0.22/0.45 Lemma 9: divide(divide(X, X), divide(inverse(Y), multiply(divide(Z, Z), W))) = multiply(W, Y).
% 0.22/0.45 Proof:
% 0.22/0.45 divide(divide(X, X), divide(inverse(Y), multiply(divide(Z, Z), W)))
% 0.22/0.45 = { by lemma 8 R->L }
% 0.22/0.45 divide(multiply(inverse(V), V), divide(inverse(Y), multiply(divide(Z, Z), W)))
% 0.22/0.45 = { by lemma 6 }
% 0.22/0.45 divide(multiply(inverse(V), V), divide(inverse(Y), multiply(divide(multiply(W, Y), multiply(W, Y)), W)))
% 0.22/0.45 = { by lemma 7 }
% 0.22/0.45 multiply(W, Y)
% 0.22/0.45
% 0.22/0.45 Lemma 10: divide(divide(X, X), divide(Y, multiply(divide(Z, Z), W))) = divide(W, Y).
% 0.22/0.45 Proof:
% 0.22/0.45 divide(divide(X, X), divide(Y, multiply(divide(Z, Z), W)))
% 0.22/0.45 = { by lemma 6 }
% 0.22/0.45 divide(divide(X, X), divide(Y, multiply(divide(divide(W, Y), divide(W, Y)), W)))
% 0.22/0.45 = { by lemma 3 }
% 0.22/0.45 divide(W, Y)
% 0.22/0.45
% 0.22/0.45 Lemma 11: multiply(divide(X, X), Y) = Y.
% 0.22/0.45 Proof:
% 0.22/0.45 multiply(divide(X, X), Y)
% 0.22/0.45 = { by lemma 9 R->L }
% 0.22/0.45 divide(divide(Z, Z), divide(inverse(Y), multiply(divide(divide(multiply(divide(X, X), Y), multiply(divide(X, X), Y)), divide(multiply(divide(X, X), Y), multiply(divide(X, X), Y))), divide(X, X))))
% 0.22/0.45 = { by lemma 8 R->L }
% 0.22/0.45 divide(multiply(inverse(W), W), divide(inverse(Y), multiply(divide(divide(multiply(divide(X, X), Y), multiply(divide(X, X), Y)), divide(multiply(divide(X, X), Y), multiply(divide(X, X), Y))), divide(X, X))))
% 0.22/0.45 = { by lemma 10 }
% 0.22/0.45 divide(multiply(inverse(W), W), divide(inverse(Y), multiply(divide(Y, multiply(divide(X, X), Y)), divide(X, X))))
% 0.22/0.45 = { by lemma 7 }
% 0.22/0.45 Y
% 0.22/0.45
% 0.22/0.45 Lemma 12: divide(X, multiply(divide(X, Y), Y)) = divide(Z, Z).
% 0.22/0.45 Proof:
% 0.22/0.45 divide(X, multiply(divide(X, Y), Y))
% 0.22/0.45 = { by lemma 11 R->L }
% 0.22/0.45 divide(multiply(divide(W, W), X), multiply(divide(X, Y), Y))
% 0.22/0.45 = { by lemma 10 R->L }
% 0.22/0.45 divide(divide(V, V), divide(multiply(divide(X, Y), Y), multiply(divide(U, U), multiply(divide(W, W), X))))
% 0.22/0.45 = { by lemma 8 R->L }
% 0.22/0.45 divide(multiply(inverse(T), T), divide(multiply(divide(X, Y), Y), multiply(divide(U, U), multiply(divide(W, W), X))))
% 0.22/0.45 = { by lemma 10 R->L }
% 0.22/0.46 divide(multiply(inverse(T), T), divide(multiply(divide(divide(U, U), divide(Y, multiply(divide(W, W), X))), Y), multiply(divide(U, U), multiply(divide(W, W), X))))
% 0.22/0.46 = { by lemma 4 R->L }
% 0.22/0.46 divide(multiply(inverse(T), T), divide(multiply(divide(divide(U, U), divide(Y, multiply(divide(W, W), X))), Y), multiply(divide(multiply(inverse(S), S), divide(multiply(divide(W, W), X), multiply(divide(divide(U, U), divide(Y, multiply(divide(W, W), X))), Y))), multiply(divide(W, W), X))))
% 0.22/0.46 = { by lemma 4 }
% 0.22/0.46 multiply(inverse(S), S)
% 0.22/0.46 = { by lemma 8 }
% 0.22/0.46 divide(Z, Z)
% 0.22/0.46
% 0.22/0.46 Lemma 13: divide(divide(X, X), divide(inverse(Y), Z)) = multiply(Z, Y).
% 0.22/0.46 Proof:
% 0.22/0.46 divide(divide(X, X), divide(inverse(Y), Z))
% 0.22/0.46 = { by lemma 11 R->L }
% 0.22/0.46 divide(divide(X, X), divide(inverse(Y), multiply(divide(W, W), Z)))
% 0.22/0.46 = { by lemma 9 }
% 0.22/0.46 multiply(Z, Y)
% 0.22/0.46
% 0.22/0.46 Lemma 14: multiply(multiply(divide(X, multiply(Y, Z)), Y), Z) = X.
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(divide(X, multiply(Y, Z)), Y), Z)
% 0.22/0.46 = { by axiom 1 (multiply) }
% 0.22/0.46 multiply(multiply(divide(X, divide(Y, inverse(Z))), Y), Z)
% 0.22/0.46 = { by lemma 13 R->L }
% 0.22/0.46 divide(divide(W, W), divide(inverse(Z), multiply(divide(X, divide(Y, inverse(Z))), Y)))
% 0.22/0.46 = { by lemma 3 }
% 0.22/0.46 X
% 0.22/0.46
% 0.22/0.46 Lemma 15: multiply(multiply(X, Y), inverse(Y)) = X.
% 0.22/0.46 Proof:
% 0.22/0.46 multiply(multiply(X, Y), inverse(Y))
% 0.22/0.46 = { by lemma 11 R->L }
% 0.22/0.46 multiply(multiply(divide(Z, Z), multiply(X, Y)), inverse(Y))
% 0.22/0.46 = { by lemma 12 R->L }
% 0.22/0.46 multiply(multiply(divide(X, multiply(divide(X, inverse(Y)), inverse(Y))), multiply(X, Y)), inverse(Y))
% 0.22/0.46 = { by axiom 1 (multiply) R->L }
% 0.22/0.46 multiply(multiply(divide(X, multiply(multiply(X, Y), inverse(Y))), multiply(X, Y)), inverse(Y))
% 0.22/0.46 = { by lemma 14 }
% 0.22/0.46 X
% 0.22/0.46
% 0.22/0.46 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.22/0.46 Proof:
% 0.22/0.46 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.22/0.46 = { by lemma 8 }
% 0.22/0.46 tuple(divide(X, X), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.22/0.46 = { by lemma 8 }
% 0.22/0.46 tuple(divide(X, X), multiply(divide(Y, Y), a2), multiply(multiply(a3, b3), c3))
% 0.22/0.46 = { by lemma 11 }
% 0.22/0.46 tuple(divide(X, X), a2, multiply(multiply(a3, b3), c3))
% 0.22/0.46 = { by lemma 13 R->L }
% 0.22/0.46 tuple(divide(X, X), a2, divide(divide(Z, Z), divide(inverse(c3), multiply(a3, b3))))
% 0.22/0.46 = { by lemma 8 R->L }
% 0.22/0.46 tuple(divide(X, X), a2, divide(multiply(inverse(W), W), divide(inverse(c3), multiply(a3, b3))))
% 0.22/0.46 = { by lemma 15 R->L }
% 0.22/0.46 tuple(divide(X, X), a2, divide(multiply(inverse(W), W), divide(inverse(c3), multiply(multiply(multiply(a3, multiply(b3, c3)), inverse(multiply(b3, c3))), b3))))
% 0.22/0.46 = { by lemma 14 R->L }
% 0.22/0.46 tuple(divide(X, X), a2, divide(multiply(inverse(W), W), divide(inverse(c3), multiply(multiply(multiply(multiply(divide(multiply(a3, multiply(b3, c3)), multiply(divide(multiply(a3, multiply(b3, c3)), multiply(b3, c3)), multiply(b3, c3))), divide(multiply(a3, multiply(b3, c3)), multiply(b3, c3))), multiply(b3, c3)), inverse(multiply(b3, c3))), b3))))
% 0.22/0.46 = { by lemma 12 }
% 0.22/0.46 tuple(divide(X, X), a2, divide(multiply(inverse(W), W), divide(inverse(c3), multiply(multiply(multiply(multiply(divide(V, V), divide(multiply(a3, multiply(b3, c3)), multiply(b3, c3))), multiply(b3, c3)), inverse(multiply(b3, c3))), b3))))
% 0.22/0.46 = { by lemma 11 }
% 0.22/0.46 tuple(divide(X, X), a2, divide(multiply(inverse(W), W), divide(inverse(c3), multiply(multiply(multiply(divide(multiply(a3, multiply(b3, c3)), multiply(b3, c3)), multiply(b3, c3)), inverse(multiply(b3, c3))), b3))))
% 0.22/0.46 = { by lemma 15 }
% 0.22/0.46 tuple(divide(X, X), a2, divide(multiply(inverse(W), W), divide(inverse(c3), multiply(divide(multiply(a3, multiply(b3, c3)), multiply(b3, c3)), b3))))
% 0.22/0.46 = { by lemma 7 }
% 0.22/0.46 tuple(divide(X, X), a2, multiply(a3, multiply(b3, c3)))
% 0.22/0.46 = { by lemma 8 R->L }
% 0.22/0.46 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.22/0.46 % SZS output end Proof
% 0.22/0.46
% 0.22/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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