TSTP Solution File: GRP098-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP098-1 : 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 : n009.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 01:16:58 EDT 2023
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP098-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 00:36:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.39 Command-line arguments: --no-flatten-goal
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 Take the following subset of the input axioms:
% 0.18/0.40 fof(multiply, axiom, ![X, Y]: multiply(X, Y)=divide(X, inverse(Y))).
% 0.18/0.40 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)) | multiply(a4, b4)!=multiply(b4, a4)))).
% 0.18/0.40 fof(single_axiom, axiom, ![Z, X2, Y2]: divide(divide(divide(X2, inverse(Y2)), Z), divide(X2, Z))=Y2).
% 0.18/0.40
% 0.18/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.40 fresh(y, y, x1...xn) = u
% 0.18/0.40 C => fresh(s, t, x1...xn) = v
% 0.18/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.40 variables of u and v.
% 0.18/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.40 input problem has no model of domain size 1).
% 0.18/0.40
% 0.18/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.40
% 0.18/0.40 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.18/0.40 Axiom 2 (single_axiom): divide(divide(divide(X, inverse(Y)), Z), divide(X, Z)) = Y.
% 0.18/0.40
% 0.18/0.40 Lemma 3: divide(divide(multiply(X, Y), Z), divide(X, Z)) = Y.
% 0.18/0.40 Proof:
% 0.18/0.40 divide(divide(multiply(X, Y), Z), divide(X, Z))
% 0.18/0.40 = { by axiom 1 (multiply) }
% 0.18/0.40 divide(divide(divide(X, inverse(Y)), Z), divide(X, Z))
% 0.18/0.40 = { by axiom 2 (single_axiom) }
% 0.18/0.40 Y
% 0.18/0.40
% 0.18/0.40 Lemma 4: divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y) = W.
% 0.18/0.40 Proof:
% 0.18/0.40 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y)
% 0.18/0.40 = { by lemma 3 R->L }
% 0.18/0.40 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), divide(divide(multiply(X, Y), Z), divide(X, Z)))
% 0.18/0.40 = { by lemma 3 }
% 0.18/0.40 W
% 0.18/0.40
% 0.18/0.40 Lemma 5: multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y) = W.
% 0.18/0.40 Proof:
% 0.18/0.40 multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y)
% 0.18/0.40 = { by axiom 1 (multiply) }
% 0.18/0.40 divide(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), inverse(Y))
% 0.18/0.40 = { by lemma 4 }
% 0.18/0.41 W
% 0.18/0.41
% 0.18/0.41 Lemma 6: divide(multiply(X, Y), X) = Y.
% 0.18/0.41 Proof:
% 0.18/0.41 divide(multiply(X, Y), X)
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 divide(divide(X, inverse(Y)), X)
% 0.18/0.41 = { by lemma 3 R->L }
% 0.18/0.41 divide(divide(X, divide(divide(multiply(Z, inverse(Y)), W), divide(Z, W))), X)
% 0.18/0.41 = { by lemma 5 R->L }
% 0.18/0.41 divide(divide(multiply(divide(multiply(divide(multiply(Z, inverse(Y)), W), X), divide(Z, W)), Y), divide(divide(multiply(Z, inverse(Y)), W), divide(Z, W))), X)
% 0.18/0.41 = { by lemma 4 }
% 0.18/0.41 Y
% 0.18/0.41
% 0.18/0.41 Lemma 7: divide(multiply(multiply(X, Y), Z), multiply(X, Z)) = Y.
% 0.18/0.41 Proof:
% 0.18/0.41 divide(multiply(multiply(X, Y), Z), multiply(X, Z))
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 divide(multiply(multiply(X, Y), Z), divide(X, inverse(Z)))
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 divide(divide(multiply(X, Y), inverse(Z)), divide(X, inverse(Z)))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 Y
% 0.18/0.41
% 0.18/0.41 Lemma 8: multiply(inverse(X), Y) = divide(Y, X).
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(inverse(X), Y)
% 0.18/0.41 = { by lemma 3 R->L }
% 0.18/0.41 divide(divide(multiply(multiply(inverse(X), Y), multiply(inverse(X), Y)), multiply(inverse(X), multiply(inverse(X), Y))), divide(multiply(inverse(X), Y), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.41 = { by lemma 7 }
% 0.18/0.41 divide(Y, divide(multiply(inverse(X), Y), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.41 = { by lemma 5 R->L }
% 0.18/0.41 divide(Y, divide(multiply(divide(multiply(divide(multiply(divide(multiply(Z, inverse(multiply(inverse(X), Y))), W), inverse(X)), divide(Z, W)), multiply(inverse(X), Y)), divide(divide(multiply(Z, inverse(multiply(inverse(X), Y))), W), divide(Z, W))), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.41 = { by lemma 5 }
% 0.18/0.41 divide(Y, divide(multiply(divide(inverse(X), divide(divide(multiply(Z, inverse(multiply(inverse(X), Y))), W), divide(Z, W))), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.41 = { by lemma 3 }
% 0.18/0.41 divide(Y, divide(multiply(divide(inverse(X), inverse(multiply(inverse(X), Y))), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.41 = { by axiom 1 (multiply) R->L }
% 0.18/0.41 divide(Y, divide(multiply(multiply(inverse(X), multiply(inverse(X), Y)), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.41 = { by lemma 6 }
% 0.18/0.41 divide(Y, X)
% 0.18/0.41
% 0.18/0.41 Lemma 9: multiply(divide(X, Y), Y) = X.
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(divide(X, Y), Y)
% 0.18/0.41 = { by axiom 1 (multiply) }
% 0.18/0.41 divide(divide(X, Y), inverse(Y))
% 0.18/0.41 = { by lemma 8 R->L }
% 0.18/0.41 divide(multiply(inverse(Y), X), inverse(Y))
% 0.18/0.41 = { by lemma 6 }
% 0.18/0.41 X
% 0.18/0.41
% 0.18/0.41 Lemma 10: multiply(Y, X) = multiply(X, Y).
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(Y, X)
% 0.18/0.41 = { by lemma 6 R->L }
% 0.18/0.41 multiply(divide(multiply(X, Y), X), X)
% 0.18/0.41 = { by lemma 9 }
% 0.18/0.41 multiply(X, Y)
% 0.18/0.41
% 0.18/0.41 Lemma 11: multiply(divide(X, X), Y) = Y.
% 0.18/0.41 Proof:
% 0.18/0.41 multiply(divide(X, X), Y)
% 0.18/0.41 = { by lemma 3 R->L }
% 0.18/0.41 divide(divide(multiply(X, multiply(divide(X, X), Y)), X), divide(X, X))
% 0.18/0.41 = { by lemma 6 }
% 0.18/0.41 divide(multiply(divide(X, X), Y), divide(X, X))
% 0.18/0.41 = { by lemma 6 }
% 0.18/0.41 Y
% 0.18/0.41
% 0.18/0.41 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.18/0.41 Proof:
% 0.18/0.41 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.18/0.41 = { by lemma 8 }
% 0.18/0.41 tuple(divide(a1, a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.18/0.41 = { by lemma 8 }
% 0.18/0.41 tuple(divide(a1, a1), multiply(divide(b2, b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.18/0.41 = { by lemma 11 }
% 0.18/0.41 tuple(divide(a1, a1), a2, multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.18/0.41 = { by lemma 10 R->L }
% 0.18/0.41 tuple(divide(a1, a1), a2, multiply(c3, multiply(a3, b3)), multiply(a4, b4))
% 0.18/0.41 = { by lemma 10 }
% 0.18/0.41 tuple(divide(a1, a1), a2, multiply(c3, multiply(b3, a3)), multiply(a4, b4))
% 0.18/0.41 = { by lemma 10 }
% 0.18/0.41 tuple(divide(a1, a1), a2, multiply(multiply(b3, a3), c3), multiply(a4, b4))
% 0.18/0.41 = { by lemma 9 R->L }
% 0.18/0.41 tuple(divide(a1, a1), a2, multiply(divide(multiply(multiply(b3, a3), c3), multiply(b3, c3)), multiply(b3, c3)), multiply(a4, b4))
% 0.18/0.41 = { by lemma 7 }
% 0.18/0.41 tuple(divide(a1, a1), a2, multiply(a3, multiply(b3, c3)), multiply(a4, b4))
% 0.18/0.41 = { by lemma 10 }
% 0.18/0.41 tuple(divide(a1, a1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.18/0.41 = { by lemma 11 R->L }
% 0.18/0.41 tuple(divide(multiply(divide(b1, b1), a1), a1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.18/0.41 = { by lemma 11 R->L }
% 0.18/0.41 tuple(divide(multiply(divide(b1, b1), a1), multiply(divide(X, X), a1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.18/0.41 = { by lemma 11 R->L }
% 0.18/0.41 tuple(divide(multiply(multiply(divide(X, X), divide(b1, b1)), a1), multiply(divide(X, X), a1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.18/0.41 = { by lemma 7 }
% 0.18/0.41 tuple(divide(b1, b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.18/0.41 = { by lemma 8 R->L }
% 0.18/0.41 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41
% 0.18/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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