TSTP Solution File: ROB014-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ROB014-2 : 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 0.19s 0.59s
% Output : Proof 0.19s
% 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 : ROB014-2 : 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
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 07:13:26 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.59 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.59
% 0.19/0.59 % SZS status Unsatisfiable
% 0.19/0.59
% 0.19/0.60 % SZS output start Proof
% 0.19/0.60 Take the following subset of the input axioms:
% 0.19/0.60 fof(associativity_of_add, axiom, ![X, Y, Z]: add(add(X, Y), Z)=add(X, add(Y, Z))).
% 0.19/0.60 fof(commutativity_of_add, axiom, ![X2, Y2]: add(X2, Y2)=add(Y2, X2)).
% 0.19/0.60 fof(condition, hypothesis, negate(add(negate(e), negate(add(d, negate(e)))))=d).
% 0.19/0.60 fof(one_times_x, axiom, ![X2]: multiply(one, X2)=X2).
% 0.19/0.60 fof(prove_base_step, negated_conjecture, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))!=negate(e)).
% 0.19/0.60 fof(robbins_axiom, axiom, ![X2, Y2]: negate(add(negate(add(X2, Y2)), negate(add(X2, negate(Y2)))))=X2).
% 0.19/0.60
% 0.19/0.60 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.60 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.60 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.60 fresh(y, y, x1...xn) = u
% 0.19/0.60 C => fresh(s, t, x1...xn) = v
% 0.19/0.60 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.60 variables of u and v.
% 0.19/0.60 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.60 input problem has no model of domain size 1).
% 0.19/0.60
% 0.19/0.60 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.60
% 0.19/0.60 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.19/0.60 Axiom 2 (one_times_x): multiply(one, X) = X.
% 0.19/0.60 Axiom 3 (associativity_of_add): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 0.19/0.60 Axiom 4 (condition): negate(add(negate(e), negate(add(d, negate(e))))) = d.
% 0.19/0.60 Axiom 5 (robbins_axiom): negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X.
% 0.19/0.60
% 0.19/0.60 Lemma 6: add(X, add(Y, Z)) = add(Y, add(X, Z)).
% 0.19/0.60 Proof:
% 0.19/0.60 add(X, add(Y, Z))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) R->L }
% 0.19/0.60 add(add(Y, Z), X)
% 0.19/0.60 = { by axiom 3 (associativity_of_add) }
% 0.19/0.60 add(Y, add(Z, X))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) }
% 0.19/0.60 add(Y, add(X, Z))
% 0.19/0.60
% 0.19/0.60 Lemma 7: negate(add(negate(add(d, negate(e))), negate(e))) = d.
% 0.19/0.60 Proof:
% 0.19/0.60 negate(add(negate(add(d, negate(e))), negate(e)))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) R->L }
% 0.19/0.60 negate(add(negate(e), negate(add(d, negate(e)))))
% 0.19/0.60 = { by axiom 4 (condition) }
% 0.19/0.60 d
% 0.19/0.60
% 0.19/0.60 Goal 1 (prove_base_step): negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))) = negate(e).
% 0.19/0.60 Proof:
% 0.19/0.60 negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))
% 0.19/0.60 = { by axiom 5 (robbins_axiom) R->L }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), negate(add(d, negate(e)))))))
% 0.19/0.60 = { by axiom 2 (one_times_x) }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), negate(add(negate(add(e, add(d, negate(add(d, negate(e)))))), negate(add(d, negate(e)))))))
% 0.19/0.60 = { by lemma 6 R->L }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), negate(add(negate(add(d, add(e, negate(add(d, negate(e)))))), negate(add(d, negate(e)))))))
% 0.19/0.60 = { by axiom 5 (robbins_axiom) R->L }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), negate(add(negate(add(d, add(e, negate(add(d, negate(e)))))), negate(add(negate(add(negate(add(d, negate(e))), e)), negate(add(negate(add(d, negate(e))), negate(e)))))))))
% 0.19/0.60 = { by lemma 7 }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), negate(add(negate(add(d, add(e, negate(add(d, negate(e)))))), negate(add(negate(add(negate(add(d, negate(e))), e)), d))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), negate(add(negate(add(d, add(e, negate(add(d, negate(e)))))), negate(add(d, negate(add(negate(add(d, negate(e))), e))))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), negate(add(negate(add(d, add(e, negate(add(d, negate(e)))))), negate(add(d, negate(add(e, negate(add(d, negate(e)))))))))))
% 0.19/0.60 = { by axiom 5 (robbins_axiom) }
% 0.19/0.60 negate(add(negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e)))), d))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) }
% 0.19/0.60 negate(add(d, negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), add(d, negate(e))))))
% 0.19/0.60 = { by lemma 6 R->L }
% 0.19/0.60 negate(add(d, negate(add(d, add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), negate(e))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) }
% 0.19/0.60 negate(add(d, negate(add(d, add(negate(e), negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))))))))
% 0.19/0.60 = { by lemma 6 R->L }
% 0.19/0.60 negate(add(d, negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))))))))
% 0.19/0.60 = { by lemma 7 R->L }
% 0.19/0.60 negate(add(negate(add(negate(add(d, negate(e))), negate(e))), negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) R->L }
% 0.19/0.60 negate(add(negate(add(negate(e), negate(add(d, negate(e))))), negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) R->L }
% 0.19/0.60 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(d, negate(e)))))))
% 0.19/0.60 = { by axiom 5 (robbins_axiom) R->L }
% 0.19/0.60 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(negate(add(negate(add(d, negate(e))), add(e, d))), negate(add(negate(add(d, negate(e))), negate(add(e, d))))))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) }
% 0.19/0.60 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(negate(add(add(e, d), negate(add(d, negate(e))))), negate(add(negate(add(d, negate(e))), negate(add(e, d))))))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) R->L }
% 0.19/0.60 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(negate(add(add(e, d), negate(add(d, negate(e))))), negate(add(negate(add(d, negate(e))), negate(add(d, e))))))))))
% 0.19/0.60 = { by axiom 1 (commutativity_of_add) R->L }
% 0.19/0.60 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(negate(add(add(e, d), negate(add(d, negate(e))))), negate(add(negate(add(d, e)), negate(add(d, negate(e)))))))))))
% 0.19/0.61 = { by axiom 5 (robbins_axiom) }
% 0.19/0.61 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(negate(add(add(e, d), negate(add(d, negate(e))))), d))))))
% 0.19/0.61 = { by axiom 3 (associativity_of_add) }
% 0.19/0.61 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(negate(add(e, add(d, negate(add(d, negate(e)))))), d))))))
% 0.19/0.61 = { by axiom 2 (one_times_x) R->L }
% 0.19/0.61 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(negate(add(e, multiply(one, add(d, negate(add(d, negate(e))))))), d))))))
% 0.19/0.61 = { by axiom 1 (commutativity_of_add) }
% 0.19/0.61 negate(add(negate(add(negate(e), add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))), negate(add(negate(e), negate(add(d, negate(add(e, multiply(one, add(d, negate(add(d, negate(e)))))))))))))
% 0.19/0.61 = { by axiom 5 (robbins_axiom) }
% 0.19/0.61 negate(e)
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61
% 0.19/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
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