TSTP Solution File: SWV558-1.007 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV558-1.007 : 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 : n016.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 23:05:17 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV558-1.007 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 04:54:00 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Take the following subset of the input axioms:
% 0.20/0.42 fof(a1, axiom, ![A, I, E]: select(store(A, I, E), I)=E).
% 0.20/0.42 fof(a3, axiom, ![A2, I2]: store(A2, I2, select(A2, I2))=A2).
% 0.20/0.42 fof(goal, negated_conjecture, a1!=a2).
% 0.20/0.42 fof(hyp0, hypothesis, a_29=store(a1, i1, e_28)).
% 0.20/0.42 fof(hyp1, hypothesis, a_31=store(a2, i1, e_30)).
% 0.20/0.42 fof(hyp10, hypothesis, a_49=store(a_45, i6, e_48)).
% 0.20/0.42 fof(hyp11, hypothesis, a_51=store(a_47, i6, e_50)).
% 0.20/0.42 fof(hyp12, hypothesis, a_53=store(a_49, i7, e_52)).
% 0.20/0.42 fof(hyp13, hypothesis, a_55=store(a_51, i7, e_54)).
% 0.20/0.42 fof(hyp14, hypothesis, e_28=select(a2, i1)).
% 0.20/0.42 fof(hyp15, hypothesis, e_30=select(a1, i1)).
% 0.20/0.42 fof(hyp16, hypothesis, e_32=select(a_31, i2)).
% 0.20/0.42 fof(hyp17, hypothesis, e_34=select(a_29, i2)).
% 0.20/0.42 fof(hyp18, hypothesis, e_36=select(a_35, i3)).
% 0.20/0.42 fof(hyp19, hypothesis, e_38=select(a_33, i3)).
% 0.20/0.42 fof(hyp2, hypothesis, a_33=store(a_29, i2, e_32)).
% 0.20/0.42 fof(hyp20, hypothesis, e_40=select(a_39, i4)).
% 0.20/0.42 fof(hyp21, hypothesis, e_42=select(a_37, i4)).
% 0.20/0.42 fof(hyp22, hypothesis, e_44=select(a_43, i5)).
% 0.20/0.42 fof(hyp23, hypothesis, e_46=select(a_41, i5)).
% 0.20/0.42 fof(hyp24, hypothesis, e_48=select(a_47, i6)).
% 0.20/0.42 fof(hyp25, hypothesis, e_50=select(a_45, i6)).
% 0.20/0.42 fof(hyp26, hypothesis, e_52=select(a_51, i7)).
% 0.20/0.42 fof(hyp27, hypothesis, e_54=select(a_49, i7)).
% 0.20/0.42 fof(hyp28, hypothesis, a_53=a_55).
% 0.20/0.42 fof(hyp3, hypothesis, a_35=store(a_31, i2, e_34)).
% 0.20/0.42 fof(hyp4, hypothesis, a_37=store(a_33, i3, e_36)).
% 0.20/0.42 fof(hyp5, hypothesis, a_39=store(a_35, i3, e_38)).
% 0.20/0.42 fof(hyp6, hypothesis, a_41=store(a_37, i4, e_40)).
% 0.20/0.42 fof(hyp7, hypothesis, a_43=store(a_39, i4, e_42)).
% 0.20/0.42 fof(hyp8, hypothesis, a_45=store(a_41, i5, e_44)).
% 0.20/0.42 fof(hyp9, hypothesis, a_47=store(a_43, i5, e_46)).
% 0.20/0.42
% 0.20/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.42 fresh(y, y, x1...xn) = u
% 0.20/0.42 C => fresh(s, t, x1...xn) = v
% 0.20/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.42 variables of u and v.
% 0.20/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.42 input problem has no model of domain size 1).
% 0.20/0.42
% 0.20/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.42
% 0.20/0.42 Axiom 1 (hyp28): a_53 = a_55.
% 0.20/0.42 Axiom 2 (hyp15): e_30 = select(a1, i1).
% 0.20/0.42 Axiom 3 (hyp14): e_28 = select(a2, i1).
% 0.20/0.42 Axiom 4 (hyp17): e_34 = select(a_29, i2).
% 0.20/0.42 Axiom 5 (hyp16): e_32 = select(a_31, i2).
% 0.20/0.42 Axiom 6 (hyp19): e_38 = select(a_33, i3).
% 0.20/0.42 Axiom 7 (hyp18): e_36 = select(a_35, i3).
% 0.20/0.42 Axiom 8 (hyp21): e_42 = select(a_37, i4).
% 0.20/0.42 Axiom 9 (hyp20): e_40 = select(a_39, i4).
% 0.20/0.42 Axiom 10 (hyp23): e_46 = select(a_41, i5).
% 0.20/0.42 Axiom 11 (hyp22): e_44 = select(a_43, i5).
% 0.20/0.42 Axiom 12 (hyp25): e_50 = select(a_45, i6).
% 0.20/0.42 Axiom 13 (hyp24): e_48 = select(a_47, i6).
% 0.20/0.42 Axiom 14 (hyp27): e_54 = select(a_49, i7).
% 0.20/0.42 Axiom 15 (hyp26): e_52 = select(a_51, i7).
% 0.20/0.42 Axiom 16 (hyp0): a_29 = store(a1, i1, e_28).
% 0.20/0.42 Axiom 17 (hyp1): a_31 = store(a2, i1, e_30).
% 0.20/0.42 Axiom 18 (hyp2): a_33 = store(a_29, i2, e_32).
% 0.20/0.42 Axiom 19 (hyp3): a_35 = store(a_31, i2, e_34).
% 0.20/0.42 Axiom 20 (hyp4): a_37 = store(a_33, i3, e_36).
% 0.20/0.42 Axiom 21 (hyp5): a_39 = store(a_35, i3, e_38).
% 0.20/0.42 Axiom 22 (hyp6): a_41 = store(a_37, i4, e_40).
% 0.20/0.42 Axiom 23 (hyp7): a_43 = store(a_39, i4, e_42).
% 0.20/0.42 Axiom 24 (hyp8): a_45 = store(a_41, i5, e_44).
% 0.20/0.42 Axiom 25 (hyp9): a_47 = store(a_43, i5, e_46).
% 0.20/0.42 Axiom 26 (hyp10): a_49 = store(a_45, i6, e_48).
% 0.20/0.42 Axiom 27 (hyp11): a_51 = store(a_47, i6, e_50).
% 0.20/0.42 Axiom 28 (hyp12): a_53 = store(a_49, i7, e_52).
% 0.20/0.42 Axiom 29 (hyp13): a_55 = store(a_51, i7, e_54).
% 0.20/0.42 Axiom 30 (a3): store(X, Y, select(X, Y)) = X.
% 0.20/0.42 Axiom 31 (a1): select(store(X, Y, Z), Y) = Z.
% 0.20/0.42
% 0.20/0.42 Lemma 32: store(a_51, i7, e_54) = a_53.
% 0.20/0.42 Proof:
% 0.20/0.42 store(a_51, i7, e_54)
% 0.20/0.42 = { by axiom 29 (hyp13) R->L }
% 0.20/0.42 a_55
% 0.20/0.42 = { by axiom 1 (hyp28) R->L }
% 0.20/0.42 a_53
% 0.20/0.42
% 0.20/0.42 Lemma 33: e_54 = e_52.
% 0.20/0.42 Proof:
% 0.20/0.42 e_54
% 0.20/0.42 = { by axiom 31 (a1) R->L }
% 0.20/0.42 select(store(a_51, i7, e_54), i7)
% 0.20/0.42 = { by lemma 32 }
% 0.20/0.42 select(a_53, i7)
% 0.20/0.42 = { by axiom 28 (hyp12) }
% 0.20/0.42 select(store(a_49, i7, e_52), i7)
% 0.20/0.42 = { by axiom 31 (a1) }
% 0.20/0.42 e_52
% 0.20/0.42
% 0.20/0.42 Lemma 34: a_51 = a_49.
% 0.20/0.42 Proof:
% 0.20/0.42 a_51
% 0.20/0.42 = { by axiom 30 (a3) R->L }
% 0.20/0.42 store(a_51, i7, select(a_51, i7))
% 0.20/0.42 = { by axiom 15 (hyp26) R->L }
% 0.20/0.42 store(a_51, i7, e_52)
% 0.20/0.42 = { by lemma 33 R->L }
% 0.20/0.42 store(a_51, i7, e_54)
% 0.20/0.42 = { by lemma 32 }
% 0.20/0.42 a_53
% 0.20/0.42 = { by axiom 28 (hyp12) }
% 0.20/0.42 store(a_49, i7, e_52)
% 0.20/0.42 = { by lemma 33 R->L }
% 0.20/0.42 store(a_49, i7, e_54)
% 0.20/0.42 = { by axiom 14 (hyp27) }
% 0.20/0.42 store(a_49, i7, select(a_49, i7))
% 0.20/0.42 = { by axiom 30 (a3) }
% 0.20/0.42 a_49
% 0.20/0.42
% 0.20/0.42 Lemma 35: e_50 = e_48.
% 0.20/0.42 Proof:
% 0.20/0.42 e_50
% 0.20/0.42 = { by axiom 31 (a1) R->L }
% 0.20/0.42 select(store(a_47, i6, e_50), i6)
% 0.20/0.42 = { by axiom 27 (hyp11) R->L }
% 0.20/0.42 select(a_51, i6)
% 0.20/0.42 = { by lemma 34 }
% 0.20/0.42 select(a_49, i6)
% 0.20/0.42 = { by axiom 26 (hyp10) }
% 0.20/0.42 select(store(a_45, i6, e_48), i6)
% 0.20/0.42 = { by axiom 31 (a1) }
% 0.20/0.42 e_48
% 0.20/0.42
% 0.20/0.42 Lemma 36: a_47 = a_45.
% 0.20/0.42 Proof:
% 0.20/0.42 a_47
% 0.20/0.42 = { by axiom 30 (a3) R->L }
% 0.20/0.42 store(a_47, i6, select(a_47, i6))
% 0.20/0.42 = { by axiom 13 (hyp24) R->L }
% 0.20/0.42 store(a_47, i6, e_48)
% 0.20/0.42 = { by lemma 35 R->L }
% 0.20/0.42 store(a_47, i6, e_50)
% 0.20/0.42 = { by axiom 27 (hyp11) R->L }
% 0.20/0.42 a_51
% 0.20/0.42 = { by lemma 34 }
% 0.20/0.42 a_49
% 0.20/0.42 = { by axiom 26 (hyp10) }
% 0.20/0.42 store(a_45, i6, e_48)
% 0.20/0.42 = { by lemma 35 R->L }
% 0.20/0.42 store(a_45, i6, e_50)
% 0.20/0.42 = { by axiom 12 (hyp25) }
% 0.20/0.42 store(a_45, i6, select(a_45, i6))
% 0.20/0.42 = { by axiom 30 (a3) }
% 0.20/0.42 a_45
% 0.20/0.42
% 0.20/0.42 Lemma 37: e_46 = e_44.
% 0.20/0.42 Proof:
% 0.20/0.42 e_46
% 0.20/0.42 = { by axiom 31 (a1) R->L }
% 0.20/0.42 select(store(a_43, i5, e_46), i5)
% 0.20/0.42 = { by axiom 25 (hyp9) R->L }
% 0.20/0.42 select(a_47, i5)
% 0.20/0.42 = { by lemma 36 }
% 0.20/0.42 select(a_45, i5)
% 0.20/0.42 = { by axiom 24 (hyp8) }
% 0.20/0.42 select(store(a_41, i5, e_44), i5)
% 0.20/0.42 = { by axiom 31 (a1) }
% 0.20/0.42 e_44
% 0.20/0.42
% 0.20/0.42 Lemma 38: a_43 = a_41.
% 0.20/0.42 Proof:
% 0.20/0.42 a_43
% 0.20/0.42 = { by axiom 30 (a3) R->L }
% 0.20/0.42 store(a_43, i5, select(a_43, i5))
% 0.20/0.42 = { by axiom 11 (hyp22) R->L }
% 0.20/0.42 store(a_43, i5, e_44)
% 0.20/0.42 = { by lemma 37 R->L }
% 0.20/0.42 store(a_43, i5, e_46)
% 0.20/0.42 = { by axiom 25 (hyp9) R->L }
% 0.20/0.42 a_47
% 0.20/0.42 = { by lemma 36 }
% 0.20/0.42 a_45
% 0.20/0.42 = { by axiom 24 (hyp8) }
% 0.20/0.42 store(a_41, i5, e_44)
% 0.20/0.42 = { by lemma 37 R->L }
% 0.20/0.42 store(a_41, i5, e_46)
% 0.20/0.42 = { by axiom 10 (hyp23) }
% 0.20/0.42 store(a_41, i5, select(a_41, i5))
% 0.20/0.42 = { by axiom 30 (a3) }
% 0.20/0.42 a_41
% 0.20/0.42
% 0.20/0.42 Lemma 39: e_42 = e_40.
% 0.20/0.42 Proof:
% 0.20/0.42 e_42
% 0.20/0.42 = { by axiom 31 (a1) R->L }
% 0.20/0.42 select(store(a_39, i4, e_42), i4)
% 0.20/0.42 = { by axiom 23 (hyp7) R->L }
% 0.20/0.42 select(a_43, i4)
% 0.20/0.43 = { by lemma 38 }
% 0.20/0.43 select(a_41, i4)
% 0.20/0.43 = { by axiom 22 (hyp6) }
% 0.20/0.43 select(store(a_37, i4, e_40), i4)
% 0.20/0.43 = { by axiom 31 (a1) }
% 0.20/0.43 e_40
% 0.20/0.43
% 0.20/0.43 Lemma 40: a_39 = a_37.
% 0.20/0.43 Proof:
% 0.20/0.43 a_39
% 0.20/0.43 = { by axiom 30 (a3) R->L }
% 0.20/0.43 store(a_39, i4, select(a_39, i4))
% 0.20/0.43 = { by axiom 9 (hyp20) R->L }
% 0.20/0.43 store(a_39, i4, e_40)
% 0.20/0.43 = { by lemma 39 R->L }
% 0.20/0.43 store(a_39, i4, e_42)
% 0.20/0.43 = { by axiom 23 (hyp7) R->L }
% 0.20/0.43 a_43
% 0.20/0.43 = { by lemma 38 }
% 0.20/0.43 a_41
% 0.20/0.43 = { by axiom 22 (hyp6) }
% 0.20/0.43 store(a_37, i4, e_40)
% 0.20/0.43 = { by lemma 39 R->L }
% 0.20/0.43 store(a_37, i4, e_42)
% 0.20/0.43 = { by axiom 8 (hyp21) }
% 0.20/0.43 store(a_37, i4, select(a_37, i4))
% 0.20/0.43 = { by axiom 30 (a3) }
% 0.20/0.43 a_37
% 0.20/0.43
% 0.20/0.43 Lemma 41: e_38 = e_36.
% 0.20/0.43 Proof:
% 0.20/0.43 e_38
% 0.20/0.43 = { by axiom 31 (a1) R->L }
% 0.20/0.43 select(store(a_35, i3, e_38), i3)
% 0.20/0.43 = { by axiom 21 (hyp5) R->L }
% 0.20/0.43 select(a_39, i3)
% 0.20/0.43 = { by lemma 40 }
% 0.20/0.43 select(a_37, i3)
% 0.20/0.43 = { by axiom 20 (hyp4) }
% 0.20/0.43 select(store(a_33, i3, e_36), i3)
% 0.20/0.43 = { by axiom 31 (a1) }
% 0.20/0.43 e_36
% 0.20/0.43
% 0.20/0.43 Lemma 42: a_35 = a_33.
% 0.20/0.43 Proof:
% 0.20/0.43 a_35
% 0.20/0.43 = { by axiom 30 (a3) R->L }
% 0.20/0.43 store(a_35, i3, select(a_35, i3))
% 0.20/0.43 = { by axiom 7 (hyp18) R->L }
% 0.20/0.43 store(a_35, i3, e_36)
% 0.20/0.43 = { by lemma 41 R->L }
% 0.20/0.43 store(a_35, i3, e_38)
% 0.20/0.43 = { by axiom 21 (hyp5) R->L }
% 0.20/0.43 a_39
% 0.20/0.43 = { by lemma 40 }
% 0.20/0.43 a_37
% 0.20/0.43 = { by axiom 20 (hyp4) }
% 0.20/0.43 store(a_33, i3, e_36)
% 0.20/0.43 = { by lemma 41 R->L }
% 0.20/0.43 store(a_33, i3, e_38)
% 0.20/0.43 = { by axiom 6 (hyp19) }
% 0.20/0.43 store(a_33, i3, select(a_33, i3))
% 0.20/0.43 = { by axiom 30 (a3) }
% 0.20/0.43 a_33
% 0.20/0.43
% 0.20/0.43 Lemma 43: e_34 = e_32.
% 0.20/0.43 Proof:
% 0.20/0.43 e_34
% 0.20/0.43 = { by axiom 31 (a1) R->L }
% 0.20/0.43 select(store(a_31, i2, e_34), i2)
% 0.20/0.43 = { by axiom 19 (hyp3) R->L }
% 0.20/0.43 select(a_35, i2)
% 0.20/0.43 = { by lemma 42 }
% 0.20/0.43 select(a_33, i2)
% 0.20/0.43 = { by axiom 18 (hyp2) }
% 0.20/0.43 select(store(a_29, i2, e_32), i2)
% 0.20/0.43 = { by axiom 31 (a1) }
% 0.20/0.43 e_32
% 0.20/0.43
% 0.20/0.43 Lemma 44: a_31 = a_29.
% 0.20/0.43 Proof:
% 0.20/0.43 a_31
% 0.20/0.43 = { by axiom 30 (a3) R->L }
% 0.20/0.43 store(a_31, i2, select(a_31, i2))
% 0.20/0.43 = { by axiom 5 (hyp16) R->L }
% 0.20/0.43 store(a_31, i2, e_32)
% 0.20/0.43 = { by lemma 43 R->L }
% 0.20/0.43 store(a_31, i2, e_34)
% 0.20/0.43 = { by axiom 19 (hyp3) R->L }
% 0.20/0.43 a_35
% 0.20/0.43 = { by lemma 42 }
% 0.20/0.43 a_33
% 0.20/0.43 = { by axiom 18 (hyp2) }
% 0.20/0.43 store(a_29, i2, e_32)
% 0.20/0.43 = { by lemma 43 R->L }
% 0.20/0.43 store(a_29, i2, e_34)
% 0.20/0.43 = { by axiom 4 (hyp17) }
% 0.20/0.43 store(a_29, i2, select(a_29, i2))
% 0.20/0.43 = { by axiom 30 (a3) }
% 0.20/0.43 a_29
% 0.20/0.43
% 0.20/0.43 Lemma 45: e_30 = e_28.
% 0.20/0.43 Proof:
% 0.20/0.43 e_30
% 0.20/0.43 = { by axiom 31 (a1) R->L }
% 0.20/0.43 select(store(a2, i1, e_30), i1)
% 0.20/0.43 = { by axiom 17 (hyp1) R->L }
% 0.20/0.43 select(a_31, i1)
% 0.20/0.43 = { by lemma 44 }
% 0.20/0.43 select(a_29, i1)
% 0.20/0.43 = { by axiom 16 (hyp0) }
% 0.20/0.43 select(store(a1, i1, e_28), i1)
% 0.20/0.43 = { by axiom 31 (a1) }
% 0.20/0.43 e_28
% 0.20/0.43
% 0.20/0.43 Goal 1 (goal): a1 = a2.
% 0.20/0.43 Proof:
% 0.20/0.43 a1
% 0.20/0.43 = { by axiom 30 (a3) R->L }
% 0.20/0.43 store(a1, i1, select(a1, i1))
% 0.20/0.43 = { by axiom 2 (hyp15) R->L }
% 0.20/0.43 store(a1, i1, e_30)
% 0.20/0.43 = { by lemma 45 }
% 0.20/0.43 store(a1, i1, e_28)
% 0.20/0.43 = { by axiom 16 (hyp0) R->L }
% 0.20/0.43 a_29
% 0.20/0.43 = { by lemma 44 R->L }
% 0.20/0.43 a_31
% 0.20/0.43 = { by axiom 17 (hyp1) }
% 0.20/0.43 store(a2, i1, e_30)
% 0.20/0.43 = { by lemma 45 }
% 0.20/0.43 store(a2, i1, e_28)
% 0.20/0.43 = { by axiom 3 (hyp14) }
% 0.20/0.43 store(a2, i1, select(a2, i1))
% 0.20/0.43 = { by axiom 30 (a3) }
% 0.20/0.43 a2
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43
% 0.20/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------