TSTP Solution File: SWV543-1.004 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV543-1.004 : 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 : n028.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 23:05:07 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% 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
% 0.06/0.12 % Problem : SWV543-1.004 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n028.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 : Tue Aug 29 04:47:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.41 fof(a1, axiom, ![A, I, E]: select(store(A, I, E), I)=E).
% 0.19/0.41 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))).
% 0.19/0.41 fof(goal, negated_conjecture, a_430!=a_440).
% 0.19/0.41 fof(hyp10, hypothesis, a_434=store(a_432, i3, e_433)).
% 0.19/0.41 fof(hyp11, hypothesis, a_436=store(a_434, i2, e_435)).
% 0.19/0.41 fof(hyp12, hypothesis, a_438=store(a_436, i0, e_437)).
% 0.19/0.41 fof(hyp13, hypothesis, a_440=store(a_438, i2, e_439)).
% 0.19/0.41 fof(hyp15, hypothesis, e_419=select(a_418, i3)).
% 0.19/0.41 fof(hyp16, hypothesis, e_421=select(a_418, i0)).
% 0.19/0.41 fof(hyp17, hypothesis, e_423=select(a_422, i2)).
% 0.19/0.41 fof(hyp18, hypothesis, e_425=select(a_422, i3)).
% 0.19/0.41 fof(hyp19, hypothesis, e_427=select(a_426, i0)).
% 0.19/0.41 fof(hyp2, hypothesis, a_420=store(a_418, i0, e_419)).
% 0.19/0.41 fof(hyp20, hypothesis, e_429=select(a_426, i2)).
% 0.19/0.41 fof(hyp21, hypothesis, e_433=select(a_432, i2)).
% 0.19/0.41 fof(hyp22, hypothesis, e_435=select(a_432, i3)).
% 0.19/0.41 fof(hyp23, hypothesis, e_437=select(a_436, i2)).
% 0.19/0.41 fof(hyp24, hypothesis, e_439=select(a_436, i0)).
% 0.19/0.41 fof(hyp3, hypothesis, a_422=store(a_420, i3, e_421)).
% 0.19/0.41 fof(hyp4, hypothesis, a_424=store(a_422, i3, e_423)).
% 0.19/0.41 fof(hyp5, hypothesis, a_426=store(a_424, i2, e_425)).
% 0.19/0.41 fof(hyp6, hypothesis, a_428=store(a_426, i2, e_427)).
% 0.19/0.41 fof(hyp7, hypothesis, a_430=store(a_428, i0, e_429)).
% 0.19/0.41 fof(hyp8, hypothesis, a_431=store(a_418, i3, e_421)).
% 0.19/0.41 fof(hyp9, hypothesis, a_432=store(a_431, i0, e_419)).
% 0.19/0.41
% 0.19/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.41 fresh(y, y, x1...xn) = u
% 0.19/0.41 C => fresh(s, t, x1...xn) = v
% 0.19/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.41 variables of u and v.
% 0.19/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.41 input problem has no model of domain size 1).
% 0.19/0.41
% 0.19/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.41
% 0.19/0.41 Axiom 1 (hyp16): e_421 = select(a_418, i0).
% 0.19/0.41 Axiom 2 (hyp15): e_419 = select(a_418, i3).
% 0.19/0.41 Axiom 3 (hyp17): e_423 = select(a_422, i2).
% 0.19/0.41 Axiom 4 (hyp18): e_425 = select(a_422, i3).
% 0.19/0.41 Axiom 5 (hyp20): e_429 = select(a_426, i2).
% 0.19/0.41 Axiom 6 (hyp19): e_427 = select(a_426, i0).
% 0.19/0.41 Axiom 7 (hyp21): e_433 = select(a_432, i2).
% 0.19/0.41 Axiom 8 (hyp22): e_435 = select(a_432, i3).
% 0.19/0.42 Axiom 9 (hyp23): e_437 = select(a_436, i2).
% 0.19/0.42 Axiom 10 (hyp24): e_439 = select(a_436, i0).
% 0.19/0.42 Axiom 11 (hyp2): a_420 = store(a_418, i0, e_419).
% 0.19/0.42 Axiom 12 (hyp8): a_431 = store(a_418, i3, e_421).
% 0.19/0.42 Axiom 13 (hyp4): a_424 = store(a_422, i3, e_423).
% 0.19/0.42 Axiom 14 (hyp6): a_428 = store(a_426, i2, e_427).
% 0.19/0.42 Axiom 15 (hyp10): a_434 = store(a_432, i3, e_433).
% 0.19/0.42 Axiom 16 (hyp12): a_438 = store(a_436, i0, e_437).
% 0.19/0.42 Axiom 17 (hyp3): a_422 = store(a_420, i3, e_421).
% 0.19/0.42 Axiom 18 (hyp5): a_426 = store(a_424, i2, e_425).
% 0.19/0.42 Axiom 19 (hyp7): a_430 = store(a_428, i0, e_429).
% 0.19/0.42 Axiom 20 (hyp9): a_432 = store(a_431, i0, e_419).
% 0.19/0.42 Axiom 21 (hyp11): a_436 = store(a_434, i2, e_435).
% 0.19/0.42 Axiom 22 (hyp13): a_440 = store(a_438, i2, e_439).
% 0.19/0.42 Axiom 23 (a1): select(store(X, Y, Z), Y) = Z.
% 0.19/0.42 Axiom 24 (a3): store(store(X, Y, select(X, Z)), Z, select(X, Y)) = store(store(X, Z, select(X, Y)), Y, select(X, Z)).
% 0.19/0.42
% 0.19/0.42 Lemma 25: select(a_422, i3) = e_421.
% 0.19/0.42 Proof:
% 0.19/0.42 select(a_422, i3)
% 0.19/0.42 = { by axiom 17 (hyp3) }
% 0.19/0.42 select(store(a_420, i3, e_421), i3)
% 0.19/0.42 = { by axiom 23 (a1) }
% 0.19/0.42 e_421
% 0.19/0.42
% 0.19/0.42 Lemma 26: e_425 = e_421.
% 0.19/0.42 Proof:
% 0.19/0.42 e_425
% 0.19/0.42 = { by axiom 4 (hyp18) }
% 0.19/0.42 select(a_422, i3)
% 0.19/0.42 = { by lemma 25 }
% 0.19/0.42 e_421
% 0.19/0.42
% 0.19/0.42 Lemma 27: select(a_426, i2) = e_425.
% 0.19/0.42 Proof:
% 0.19/0.42 select(a_426, i2)
% 0.19/0.42 = { by axiom 18 (hyp5) }
% 0.19/0.42 select(store(a_424, i2, e_425), i2)
% 0.19/0.42 = { by axiom 23 (a1) }
% 0.19/0.42 e_425
% 0.19/0.42
% 0.19/0.42 Lemma 28: e_429 = e_421.
% 0.19/0.42 Proof:
% 0.19/0.42 e_429
% 0.19/0.42 = { by axiom 5 (hyp20) }
% 0.19/0.42 select(a_426, i2)
% 0.19/0.42 = { by lemma 27 }
% 0.19/0.42 e_425
% 0.19/0.42 = { by lemma 26 }
% 0.19/0.42 e_421
% 0.19/0.42
% 0.19/0.42 Lemma 29: a_432 = a_422.
% 0.19/0.42 Proof:
% 0.19/0.42 a_432
% 0.19/0.42 = { by axiom 20 (hyp9) }
% 0.19/0.42 store(a_431, i0, e_419)
% 0.19/0.42 = { by axiom 2 (hyp15) }
% 0.19/0.42 store(a_431, i0, select(a_418, i3))
% 0.19/0.42 = { by axiom 12 (hyp8) }
% 0.19/0.42 store(store(a_418, i3, e_421), i0, select(a_418, i3))
% 0.19/0.42 = { by axiom 1 (hyp16) }
% 0.19/0.42 store(store(a_418, i3, select(a_418, i0)), i0, select(a_418, i3))
% 0.19/0.42 = { by axiom 24 (a3) }
% 0.19/0.42 store(store(a_418, i0, select(a_418, i3)), i3, select(a_418, i0))
% 0.19/0.42 = { by axiom 1 (hyp16) R->L }
% 0.19/0.42 store(store(a_418, i0, select(a_418, i3)), i3, e_421)
% 0.19/0.42 = { by axiom 2 (hyp15) R->L }
% 0.19/0.42 store(store(a_418, i0, e_419), i3, e_421)
% 0.19/0.42 = { by axiom 11 (hyp2) R->L }
% 0.19/0.42 store(a_420, i3, e_421)
% 0.19/0.42 = { by axiom 17 (hyp3) R->L }
% 0.19/0.42 a_422
% 0.19/0.42
% 0.19/0.42 Lemma 30: e_435 = e_421.
% 0.19/0.42 Proof:
% 0.19/0.42 e_435
% 0.19/0.42 = { by axiom 8 (hyp22) }
% 0.19/0.42 select(a_432, i3)
% 0.19/0.42 = { by lemma 29 }
% 0.19/0.42 select(a_422, i3)
% 0.19/0.42 = { by lemma 25 }
% 0.19/0.42 e_421
% 0.19/0.42
% 0.19/0.42 Lemma 31: a_436 = a_426.
% 0.19/0.42 Proof:
% 0.19/0.42 a_436
% 0.19/0.42 = { by axiom 21 (hyp11) }
% 0.19/0.42 store(a_434, i2, e_435)
% 0.19/0.42 = { by axiom 15 (hyp10) }
% 0.19/0.42 store(store(a_432, i3, e_433), i2, e_435)
% 0.19/0.42 = { by axiom 7 (hyp21) }
% 0.19/0.42 store(store(a_432, i3, select(a_432, i2)), i2, e_435)
% 0.19/0.42 = { by lemma 29 }
% 0.19/0.42 store(store(a_432, i3, select(a_422, i2)), i2, e_435)
% 0.19/0.42 = { by axiom 3 (hyp17) R->L }
% 0.19/0.42 store(store(a_432, i3, e_423), i2, e_435)
% 0.19/0.42 = { by lemma 29 }
% 0.19/0.42 store(store(a_422, i3, e_423), i2, e_435)
% 0.19/0.42 = { by axiom 13 (hyp4) R->L }
% 0.19/0.42 store(a_424, i2, e_435)
% 0.19/0.42 = { by lemma 30 }
% 0.19/0.42 store(a_424, i2, e_421)
% 0.19/0.42 = { by lemma 26 R->L }
% 0.19/0.42 store(a_424, i2, e_425)
% 0.19/0.42 = { by axiom 18 (hyp5) R->L }
% 0.19/0.42 a_426
% 0.19/0.42
% 0.19/0.42 Goal 1 (goal): a_430 = a_440.
% 0.19/0.42 Proof:
% 0.19/0.42 a_430
% 0.19/0.42 = { by axiom 19 (hyp7) }
% 0.19/0.42 store(a_428, i0, e_429)
% 0.19/0.42 = { by lemma 28 }
% 0.19/0.42 store(a_428, i0, e_421)
% 0.19/0.42 = { by axiom 14 (hyp6) }
% 0.19/0.42 store(store(a_426, i2, e_427), i0, e_421)
% 0.19/0.42 = { by axiom 6 (hyp19) }
% 0.19/0.42 store(store(a_426, i2, select(a_426, i0)), i0, e_421)
% 0.19/0.42 = { by lemma 26 R->L }
% 0.19/0.42 store(store(a_426, i2, select(a_426, i0)), i0, e_425)
% 0.19/0.42 = { by lemma 27 R->L }
% 0.19/0.42 store(store(a_426, i2, select(a_426, i0)), i0, select(a_426, i2))
% 0.19/0.42 = { by axiom 24 (a3) R->L }
% 0.19/0.42 store(store(a_426, i0, select(a_426, i2)), i2, select(a_426, i0))
% 0.19/0.42 = { by axiom 5 (hyp20) R->L }
% 0.19/0.42 store(store(a_426, i0, e_429), i2, select(a_426, i0))
% 0.19/0.42 = { by lemma 28 }
% 0.19/0.42 store(store(a_426, i0, e_421), i2, select(a_426, i0))
% 0.19/0.42 = { by lemma 31 R->L }
% 0.19/0.42 store(store(a_436, i0, e_421), i2, select(a_426, i0))
% 0.19/0.42 = { by lemma 30 R->L }
% 0.19/0.42 store(store(a_436, i0, e_435), i2, select(a_426, i0))
% 0.19/0.42 = { by axiom 23 (a1) R->L }
% 0.19/0.42 store(store(a_436, i0, select(store(a_434, i2, e_435), i2)), i2, select(a_426, i0))
% 0.19/0.42 = { by axiom 21 (hyp11) R->L }
% 0.19/0.42 store(store(a_436, i0, select(a_436, i2)), i2, select(a_426, i0))
% 0.19/0.42 = { by axiom 9 (hyp23) R->L }
% 0.19/0.42 store(store(a_436, i0, e_437), i2, select(a_426, i0))
% 0.19/0.42 = { by axiom 16 (hyp12) R->L }
% 0.19/0.42 store(a_438, i2, select(a_426, i0))
% 0.19/0.42 = { by lemma 31 R->L }
% 0.19/0.42 store(a_438, i2, select(a_436, i0))
% 0.19/0.42 = { by axiom 10 (hyp24) R->L }
% 0.19/0.42 store(a_438, i2, e_439)
% 0.19/0.42 = { by axiom 22 (hyp13) R->L }
% 0.19/0.42 a_440
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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