TSTP Solution File: SWV547-1.004 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV547-1.004 : TPTP v8.1.2. Released v4.0.0.
% 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 : 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 23:05:10 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV547-1.004 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % 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 : Tue Aug 29 03:14:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.40 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Take the following subset of the input axioms:
% 0.21/0.41 fof(a1, axiom, ![A, I, E]: select(store(A, I, E), I)=E).
% 0.21/0.41 fof(a3, axiom, ![J, A2, I2]: store(store(A2, I2, select(A2, J)), J, select(A2, I2))=store(store(A2, J, select(A2, I2)), I2, select(A2, J))).
% 0.21/0.41 fof(goal, negated_conjecture, e_491!=e_492).
% 0.21/0.41 fof(hyp10, hypothesis, a_483=store(a_481, i3, e_482)).
% 0.21/0.41 fof(hyp11, hypothesis, a_485=store(a_483, i2, e_484)).
% 0.21/0.41 fof(hyp12, hypothesis, a_487=store(a_485, i0, e_486)).
% 0.21/0.41 fof(hyp13, hypothesis, a_489=store(a_487, i2, e_488)).
% 0.21/0.41 fof(hyp15, hypothesis, e_468=select(a_467, i3)).
% 0.21/0.41 fof(hyp16, hypothesis, e_470=select(a_467, i0)).
% 0.21/0.41 fof(hyp17, hypothesis, e_472=select(a_471, i2)).
% 0.21/0.41 fof(hyp18, hypothesis, e_474=select(a_471, i3)).
% 0.21/0.41 fof(hyp19, hypothesis, e_476=select(a_475, i0)).
% 0.21/0.41 fof(hyp2, hypothesis, a_469=store(a_467, i0, e_468)).
% 0.21/0.41 fof(hyp20, hypothesis, e_478=select(a_475, i2)).
% 0.21/0.41 fof(hyp21, hypothesis, e_482=select(a_481, i2)).
% 0.21/0.41 fof(hyp22, hypothesis, e_484=select(a_481, i3)).
% 0.21/0.41 fof(hyp23, hypothesis, e_486=select(a_485, i2)).
% 0.21/0.41 fof(hyp24, hypothesis, e_488=select(a_485, i0)).
% 0.21/0.41 fof(hyp25, hypothesis, e_491=select(a_479, i_490)).
% 0.21/0.41 fof(hyp26, hypothesis, e_492=select(a_489, i_490)).
% 0.21/0.41 fof(hyp3, hypothesis, a_471=store(a_469, i3, e_470)).
% 0.21/0.41 fof(hyp4, hypothesis, a_473=store(a_471, i3, e_472)).
% 0.21/0.41 fof(hyp5, hypothesis, a_475=store(a_473, i2, e_474)).
% 0.21/0.41 fof(hyp6, hypothesis, a_477=store(a_475, i2, e_476)).
% 0.21/0.41 fof(hyp7, hypothesis, a_479=store(a_477, i0, e_478)).
% 0.21/0.41 fof(hyp8, hypothesis, a_480=store(a_467, i3, e_470)).
% 0.21/0.41 fof(hyp9, hypothesis, a_481=store(a_480, i0, e_468)).
% 0.21/0.41
% 0.21/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.41 fresh(y, y, x1...xn) = u
% 0.21/0.41 C => fresh(s, t, x1...xn) = v
% 0.21/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.41 variables of u and v.
% 0.21/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.41 input problem has no model of domain size 1).
% 0.21/0.41
% 0.21/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.41
% 0.21/0.41 Axiom 1 (hyp16): e_470 = select(a_467, i0).
% 0.21/0.41 Axiom 2 (hyp15): e_468 = select(a_467, i3).
% 0.21/0.41 Axiom 3 (hyp17): e_472 = select(a_471, i2).
% 0.21/0.41 Axiom 4 (hyp18): e_474 = select(a_471, i3).
% 0.21/0.41 Axiom 5 (hyp20): e_478 = select(a_475, i2).
% 0.21/0.41 Axiom 6 (hyp19): e_476 = select(a_475, i0).
% 0.21/0.41 Axiom 7 (hyp21): e_482 = select(a_481, i2).
% 0.21/0.41 Axiom 8 (hyp22): e_484 = select(a_481, i3).
% 0.21/0.41 Axiom 9 (hyp23): e_486 = select(a_485, i2).
% 0.21/0.41 Axiom 10 (hyp24): e_488 = select(a_485, i0).
% 0.21/0.41 Axiom 11 (hyp25): e_491 = select(a_479, i_490).
% 0.21/0.41 Axiom 12 (hyp26): e_492 = select(a_489, i_490).
% 0.21/0.41 Axiom 13 (hyp2): a_469 = store(a_467, i0, e_468).
% 0.21/0.41 Axiom 14 (hyp8): a_480 = store(a_467, i3, e_470).
% 0.21/0.41 Axiom 15 (hyp4): a_473 = store(a_471, i3, e_472).
% 0.21/0.41 Axiom 16 (hyp6): a_477 = store(a_475, i2, e_476).
% 0.21/0.41 Axiom 17 (hyp10): a_483 = store(a_481, i3, e_482).
% 0.21/0.41 Axiom 18 (hyp12): a_487 = store(a_485, i0, e_486).
% 0.21/0.41 Axiom 19 (hyp3): a_471 = store(a_469, i3, e_470).
% 0.21/0.41 Axiom 20 (hyp5): a_475 = store(a_473, i2, e_474).
% 0.21/0.41 Axiom 21 (hyp7): a_479 = store(a_477, i0, e_478).
% 0.21/0.41 Axiom 22 (hyp9): a_481 = store(a_480, i0, e_468).
% 0.21/0.41 Axiom 23 (hyp11): a_485 = store(a_483, i2, e_484).
% 0.21/0.41 Axiom 24 (hyp13): a_489 = store(a_487, i2, e_488).
% 0.21/0.41 Axiom 25 (a1): select(store(X, Y, Z), Y) = Z.
% 0.21/0.41 Axiom 26 (a3): store(store(X, Y, select(X, Z)), Z, select(X, Y)) = store(store(X, Z, select(X, Y)), Y, select(X, Z)).
% 0.21/0.41
% 0.21/0.41 Lemma 27: select(a_471, i3) = e_470.
% 0.21/0.41 Proof:
% 0.21/0.41 select(a_471, i3)
% 0.21/0.41 = { by axiom 19 (hyp3) }
% 0.21/0.41 select(store(a_469, i3, e_470), i3)
% 0.21/0.41 = { by axiom 25 (a1) }
% 0.21/0.41 e_470
% 0.21/0.41
% 0.21/0.41 Lemma 28: e_474 = e_470.
% 0.21/0.41 Proof:
% 0.21/0.41 e_474
% 0.21/0.41 = { by axiom 4 (hyp18) }
% 0.21/0.41 select(a_471, i3)
% 0.21/0.41 = { by lemma 27 }
% 0.21/0.41 e_470
% 0.21/0.41
% 0.21/0.41 Lemma 29: select(a_475, i2) = e_474.
% 0.21/0.41 Proof:
% 0.21/0.41 select(a_475, i2)
% 0.21/0.41 = { by axiom 20 (hyp5) }
% 0.21/0.41 select(store(a_473, i2, e_474), i2)
% 0.21/0.41 = { by axiom 25 (a1) }
% 0.21/0.41 e_474
% 0.21/0.41
% 0.21/0.41 Lemma 30: e_478 = e_470.
% 0.21/0.41 Proof:
% 0.21/0.41 e_478
% 0.21/0.41 = { by axiom 5 (hyp20) }
% 0.21/0.41 select(a_475, i2)
% 0.21/0.41 = { by lemma 29 }
% 0.21/0.41 e_474
% 0.21/0.41 = { by lemma 28 }
% 0.21/0.41 e_470
% 0.21/0.41
% 0.21/0.41 Lemma 31: a_481 = a_471.
% 0.21/0.41 Proof:
% 0.21/0.41 a_481
% 0.21/0.41 = { by axiom 22 (hyp9) }
% 0.21/0.41 store(a_480, i0, e_468)
% 0.21/0.41 = { by axiom 2 (hyp15) }
% 0.21/0.41 store(a_480, i0, select(a_467, i3))
% 0.21/0.41 = { by axiom 14 (hyp8) }
% 0.21/0.41 store(store(a_467, i3, e_470), i0, select(a_467, i3))
% 0.21/0.41 = { by axiom 1 (hyp16) }
% 0.21/0.41 store(store(a_467, i3, select(a_467, i0)), i0, select(a_467, i3))
% 0.21/0.41 = { by axiom 26 (a3) }
% 0.21/0.41 store(store(a_467, i0, select(a_467, i3)), i3, select(a_467, i0))
% 0.21/0.41 = { by axiom 1 (hyp16) R->L }
% 0.21/0.41 store(store(a_467, i0, select(a_467, i3)), i3, e_470)
% 0.21/0.41 = { by axiom 2 (hyp15) R->L }
% 0.21/0.41 store(store(a_467, i0, e_468), i3, e_470)
% 0.21/0.41 = { by axiom 13 (hyp2) R->L }
% 0.21/0.41 store(a_469, i3, e_470)
% 0.21/0.41 = { by axiom 19 (hyp3) R->L }
% 0.21/0.41 a_471
% 0.21/0.41
% 0.21/0.41 Lemma 32: e_484 = e_470.
% 0.21/0.41 Proof:
% 0.21/0.41 e_484
% 0.21/0.41 = { by axiom 8 (hyp22) }
% 0.21/0.41 select(a_481, i3)
% 0.21/0.41 = { by lemma 31 }
% 0.21/0.41 select(a_471, i3)
% 0.21/0.41 = { by lemma 27 }
% 0.21/0.41 e_470
% 0.21/0.41
% 0.21/0.41 Lemma 33: a_485 = a_475.
% 0.21/0.41 Proof:
% 0.21/0.41 a_485
% 0.21/0.41 = { by axiom 23 (hyp11) }
% 0.21/0.41 store(a_483, i2, e_484)
% 0.21/0.41 = { by axiom 17 (hyp10) }
% 0.21/0.41 store(store(a_481, i3, e_482), i2, e_484)
% 0.21/0.41 = { by axiom 7 (hyp21) }
% 0.21/0.41 store(store(a_481, i3, select(a_481, i2)), i2, e_484)
% 0.21/0.41 = { by lemma 31 }
% 0.21/0.41 store(store(a_481, i3, select(a_471, i2)), i2, e_484)
% 0.21/0.41 = { by axiom 3 (hyp17) R->L }
% 0.21/0.41 store(store(a_481, i3, e_472), i2, e_484)
% 0.21/0.41 = { by lemma 31 }
% 0.21/0.41 store(store(a_471, i3, e_472), i2, e_484)
% 0.21/0.41 = { by axiom 15 (hyp4) R->L }
% 0.21/0.41 store(a_473, i2, e_484)
% 0.21/0.41 = { by lemma 32 }
% 0.21/0.41 store(a_473, i2, e_470)
% 0.21/0.41 = { by lemma 28 R->L }
% 0.21/0.41 store(a_473, i2, e_474)
% 0.21/0.41 = { by axiom 20 (hyp5) R->L }
% 0.21/0.41 a_475
% 0.21/0.41
% 0.21/0.41 Goal 1 (goal): e_491 = e_492.
% 0.21/0.41 Proof:
% 0.21/0.41 e_491
% 0.21/0.41 = { by axiom 11 (hyp25) }
% 0.21/0.41 select(a_479, i_490)
% 0.21/0.41 = { by axiom 21 (hyp7) }
% 0.21/0.41 select(store(a_477, i0, e_478), i_490)
% 0.21/0.41 = { by lemma 30 }
% 0.21/0.41 select(store(a_477, i0, e_470), i_490)
% 0.21/0.41 = { by axiom 16 (hyp6) }
% 0.21/0.41 select(store(store(a_475, i2, e_476), i0, e_470), i_490)
% 0.21/0.41 = { by axiom 6 (hyp19) }
% 0.21/0.41 select(store(store(a_475, i2, select(a_475, i0)), i0, e_470), i_490)
% 0.21/0.42 = { by lemma 28 R->L }
% 0.21/0.42 select(store(store(a_475, i2, select(a_475, i0)), i0, e_474), i_490)
% 0.21/0.42 = { by lemma 29 R->L }
% 0.21/0.42 select(store(store(a_475, i2, select(a_475, i0)), i0, select(a_475, i2)), i_490)
% 0.21/0.42 = { by axiom 26 (a3) R->L }
% 0.21/0.42 select(store(store(a_475, i0, select(a_475, i2)), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by axiom 5 (hyp20) R->L }
% 0.21/0.42 select(store(store(a_475, i0, e_478), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by lemma 30 }
% 0.21/0.42 select(store(store(a_475, i0, e_470), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by lemma 33 R->L }
% 0.21/0.42 select(store(store(a_485, i0, e_470), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by lemma 32 R->L }
% 0.21/0.42 select(store(store(a_485, i0, e_484), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by axiom 25 (a1) R->L }
% 0.21/0.42 select(store(store(a_485, i0, select(store(a_483, i2, e_484), i2)), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by axiom 23 (hyp11) R->L }
% 0.21/0.42 select(store(store(a_485, i0, select(a_485, i2)), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by axiom 9 (hyp23) R->L }
% 0.21/0.42 select(store(store(a_485, i0, e_486), i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by axiom 18 (hyp12) R->L }
% 0.21/0.42 select(store(a_487, i2, select(a_475, i0)), i_490)
% 0.21/0.42 = { by lemma 33 R->L }
% 0.21/0.42 select(store(a_487, i2, select(a_485, i0)), i_490)
% 0.21/0.42 = { by axiom 10 (hyp24) R->L }
% 0.21/0.42 select(store(a_487, i2, e_488), i_490)
% 0.21/0.42 = { by axiom 24 (hyp13) R->L }
% 0.21/0.42 select(a_489, i_490)
% 0.21/0.42 = { by axiom 12 (hyp26) R->L }
% 0.21/0.42 e_492
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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