TSTP Solution File: ROB015-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ROB015-2 : 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 : n029.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 14:09:09 EDT 2023
% Result : Unsatisfiable 7.09s 1.34s
% Output : Proof 7.09s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB015-2 : 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
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 07:16:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.09/1.34 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 7.09/1.34
% 7.09/1.34 % SZS status Unsatisfiable
% 7.09/1.34
% 7.09/1.35 % SZS output start Proof
% 7.09/1.35 Take the following subset of the input axioms:
% 7.09/1.35 fof(base_step, axiom, negate(add(e, multiply(k, add(d, negate(add(d, negate(e)))))))!=negate(e)).
% 7.09/1.35 fof(commutativity_of_add, axiom, ![X, Y]: add(X, Y)=add(Y, X)).
% 7.09/1.35 fof(condition, hypothesis, negate(add(negate(e), negate(add(d, negate(e)))))=d).
% 7.09/1.35 fof(k_positive, axiom, positive_integer(k)).
% 7.09/1.35 fof(lemma_3_2, axiom, ![Z, X2, Y2]: (negate(add(X2, negate(add(Y2, Z))))!=negate(add(Y2, negate(add(X2, Z)))) | X2=Y2)).
% 7.09/1.35 fof(lemma_3_4, axiom, ![Vk, X2, Y2, Z2]: (negate(add(X2, negate(Y2)))!=Z2 | (~positive_integer(Vk) | negate(add(X2, negate(add(Y2, multiply(Vk, add(X2, Z2))))))=Z2))).
% 7.09/1.35
% 7.09/1.35 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.09/1.35 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.09/1.35 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.09/1.35 fresh(y, y, x1...xn) = u
% 7.09/1.35 C => fresh(s, t, x1...xn) = v
% 7.09/1.35 where fresh is a fresh function symbol and x1..xn are the free
% 7.09/1.35 variables of u and v.
% 7.09/1.35 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.09/1.35 input problem has no model of domain size 1).
% 7.09/1.35
% 7.09/1.35 The encoding turns the above axioms into the following unit equations and goals:
% 7.09/1.35
% 7.09/1.35 Axiom 1 (k_positive): positive_integer(k) = true.
% 7.09/1.35 Axiom 2 (commutativity_of_add): add(X, Y) = add(Y, X).
% 7.09/1.35 Axiom 3 (lemma_3_2): fresh(X, X, Y, Z) = Z.
% 7.09/1.35 Axiom 4 (lemma_3_4): fresh2(X, X, Y, Z, W, V) = W.
% 7.09/1.35 Axiom 5 (condition): negate(add(negate(e), negate(add(d, negate(e))))) = d.
% 7.09/1.35 Axiom 6 (lemma_3_4): fresh4(X, X, Y, Z, W, V) = negate(add(Y, negate(add(Z, multiply(V, add(Y, W)))))).
% 7.09/1.35 Axiom 7 (lemma_3_4): fresh4(positive_integer(X), true, Y, Z, W, X) = fresh2(negate(add(Y, negate(Z))), W, Y, Z, W, X).
% 7.09/1.35 Axiom 8 (lemma_3_2): fresh(negate(add(X, negate(add(Y, Z)))), negate(add(Y, negate(add(X, Z)))), X, Y) = X.
% 7.09/1.35
% 7.09/1.35 Lemma 9: negate(add(negate(add(d, negate(e))), negate(e))) = d.
% 7.09/1.35 Proof:
% 7.09/1.35 negate(add(negate(add(d, negate(e))), negate(e)))
% 7.09/1.35 = { by axiom 2 (commutativity_of_add) R->L }
% 7.09/1.35 negate(add(negate(e), negate(add(d, negate(e)))))
% 7.09/1.35 = { by axiom 5 (condition) }
% 7.09/1.35 d
% 7.09/1.35
% 7.09/1.35 Lemma 10: fresh4(positive_integer(X), true, Y, Z, negate(add(Y, negate(Z))), X) = negate(add(Y, negate(Z))).
% 7.09/1.35 Proof:
% 7.09/1.35 fresh4(positive_integer(X), true, Y, Z, negate(add(Y, negate(Z))), X)
% 7.09/1.35 = { by axiom 7 (lemma_3_4) }
% 7.09/1.35 fresh2(negate(add(Y, negate(Z))), negate(add(Y, negate(Z))), Y, Z, negate(add(Y, negate(Z))), X)
% 7.09/1.35 = { by axiom 4 (lemma_3_4) }
% 7.09/1.35 negate(add(Y, negate(Z)))
% 7.09/1.35
% 7.09/1.35 Goal 1 (base_step): negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))) = negate(e).
% 7.09/1.35 Proof:
% 7.09/1.35 negate(add(e, multiply(k, add(d, negate(add(d, negate(e)))))))
% 7.09/1.35 = { by axiom 8 (lemma_3_2) R->L }
% 7.09/1.35 fresh(negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(add(negate(e), d)))), negate(add(negate(e), negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), d)))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 2 (commutativity_of_add) }
% 7.09/1.35 fresh(negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(add(d, negate(e))))), negate(add(negate(e), negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), d)))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 2 (commutativity_of_add) }
% 7.09/1.35 fresh(negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(add(d, negate(e))))), negate(add(negate(e), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 6 (lemma_3_4) R->L }
% 7.09/1.35 fresh(negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(add(d, negate(e))))), negate(add(negate(e), fresh4(true, true, d, e, negate(add(d, negate(e))), k))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 1 (k_positive) R->L }
% 7.09/1.35 fresh(negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(add(d, negate(e))))), negate(add(negate(e), fresh4(positive_integer(k), true, d, e, negate(add(d, negate(e))), k))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by lemma 10 }
% 7.09/1.35 fresh(negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(add(d, negate(e))))), negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 2 (commutativity_of_add) R->L }
% 7.09/1.35 fresh(negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))), negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 2 (commutativity_of_add) R->L }
% 7.09/1.35 fresh(negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(negate(add(d, negate(e))), d)))))), negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 6 (lemma_3_4) R->L }
% 7.09/1.35 fresh(fresh4(true, true, negate(add(d, negate(e))), e, d, k), negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 1 (k_positive) R->L }
% 7.09/1.35 fresh(fresh4(positive_integer(k), true, negate(add(d, negate(e))), e, d, k), negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by lemma 9 R->L }
% 7.09/1.35 fresh(fresh4(positive_integer(k), true, negate(add(d, negate(e))), e, negate(add(negate(add(d, negate(e))), negate(e))), k), negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by lemma 10 }
% 7.09/1.35 fresh(negate(add(negate(add(d, negate(e))), negate(e))), negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by lemma 9 }
% 7.09/1.35 fresh(d, negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 2 (commutativity_of_add) }
% 7.09/1.35 fresh(d, negate(add(negate(add(d, negate(e))), negate(e))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by lemma 9 }
% 7.09/1.35 fresh(d, d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e))
% 7.09/1.35 = { by axiom 3 (lemma_3_2) }
% 7.09/1.35 negate(e)
% 7.09/1.35 % SZS output end Proof
% 7.09/1.35
% 7.09/1.35 RESULT: Unsatisfiable (the axioms are contradictory).
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