TSTP Solution File: SWV558-1.010 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV558-1.010 : 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 : n023.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 23:05:18 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
% 0.03/0.11 % Problem : SWV558-1.010 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 03:58:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 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(a4, axiom, ![F, A2, I2, E2]: store(store(A2, I2, E2), I2, F)=store(A2, I2, F)).
% 0.20/0.42 fof(goal, negated_conjecture, a1!=a2).
% 0.20/0.42 fof(hyp0, hypothesis, a_41=store(a1, i1, e_40)).
% 0.20/0.42 fof(hyp1, hypothesis, a_43=store(a2, i1, e_42)).
% 0.20/0.42 fof(hyp10, hypothesis, a_61=store(a_57, i6, e_60)).
% 0.20/0.42 fof(hyp11, hypothesis, a_63=store(a_59, i6, e_62)).
% 0.20/0.42 fof(hyp12, hypothesis, a_65=store(a_61, i7, e_64)).
% 0.20/0.42 fof(hyp13, hypothesis, a_67=store(a_63, i7, e_66)).
% 0.20/0.42 fof(hyp14, hypothesis, a_69=store(a_65, i8, e_68)).
% 0.20/0.42 fof(hyp15, hypothesis, a_71=store(a_67, i8, e_70)).
% 0.20/0.42 fof(hyp16, hypothesis, a_73=store(a_69, i9, e_72)).
% 0.20/0.42 fof(hyp17, hypothesis, a_75=store(a_71, i9, e_74)).
% 0.20/0.42 fof(hyp18, hypothesis, a_77=store(a_73, i10, e_76)).
% 0.20/0.42 fof(hyp19, hypothesis, a_79=store(a_75, i10, e_78)).
% 0.20/0.42 fof(hyp2, hypothesis, a_45=store(a_41, i2, e_44)).
% 0.20/0.42 fof(hyp20, hypothesis, e_40=select(a2, i1)).
% 0.20/0.42 fof(hyp21, hypothesis, e_42=select(a1, i1)).
% 0.20/0.42 fof(hyp22, hypothesis, e_44=select(a_43, i2)).
% 0.20/0.42 fof(hyp23, hypothesis, e_46=select(a_41, i2)).
% 0.20/0.42 fof(hyp24, hypothesis, e_48=select(a_47, i3)).
% 0.20/0.42 fof(hyp25, hypothesis, e_50=select(a_45, i3)).
% 0.20/0.42 fof(hyp26, hypothesis, e_52=select(a_51, i4)).
% 0.20/0.42 fof(hyp27, hypothesis, e_54=select(a_49, i4)).
% 0.20/0.42 fof(hyp28, hypothesis, e_56=select(a_55, i5)).
% 0.20/0.42 fof(hyp29, hypothesis, e_58=select(a_53, i5)).
% 0.20/0.42 fof(hyp3, hypothesis, a_47=store(a_43, i2, e_46)).
% 0.20/0.42 fof(hyp30, hypothesis, e_60=select(a_59, i6)).
% 0.20/0.42 fof(hyp31, hypothesis, e_62=select(a_57, i6)).
% 0.20/0.42 fof(hyp32, hypothesis, e_64=select(a_63, i7)).
% 0.20/0.42 fof(hyp33, hypothesis, e_66=select(a_61, i7)).
% 0.20/0.42 fof(hyp34, hypothesis, e_68=select(a_67, i8)).
% 0.20/0.42 fof(hyp35, hypothesis, e_70=select(a_65, i8)).
% 0.20/0.42 fof(hyp36, hypothesis, e_72=select(a_71, i9)).
% 0.20/0.42 fof(hyp37, hypothesis, e_74=select(a_69, i9)).
% 0.20/0.42 fof(hyp38, hypothesis, e_76=select(a_75, i10)).
% 0.20/0.42 fof(hyp39, hypothesis, e_78=select(a_73, i10)).
% 0.20/0.42 fof(hyp4, hypothesis, a_49=store(a_45, i3, e_48)).
% 0.20/0.42 fof(hyp40, hypothesis, a_77=a_79).
% 0.20/0.42 fof(hyp5, hypothesis, a_51=store(a_47, i3, e_50)).
% 0.20/0.42 fof(hyp6, hypothesis, a_53=store(a_49, i4, e_52)).
% 0.20/0.42 fof(hyp7, hypothesis, a_55=store(a_51, i4, e_54)).
% 0.20/0.42 fof(hyp8, hypothesis, a_57=store(a_53, i5, e_56)).
% 0.20/0.42 fof(hyp9, hypothesis, a_59=store(a_55, i5, e_58)).
% 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 (hyp40): a_77 = a_79.
% 0.20/0.42 Axiom 2 (hyp21): e_42 = select(a1, i1).
% 0.20/0.42 Axiom 3 (hyp20): e_40 = select(a2, i1).
% 0.20/0.42 Axiom 4 (hyp23): e_46 = select(a_41, i2).
% 0.20/0.42 Axiom 5 (hyp22): e_44 = select(a_43, i2).
% 0.20/0.42 Axiom 6 (hyp25): e_50 = select(a_45, i3).
% 0.20/0.42 Axiom 7 (hyp24): e_48 = select(a_47, i3).
% 0.20/0.42 Axiom 8 (hyp27): e_54 = select(a_49, i4).
% 0.20/0.42 Axiom 9 (hyp26): e_52 = select(a_51, i4).
% 0.20/0.42 Axiom 10 (hyp29): e_58 = select(a_53, i5).
% 0.20/0.42 Axiom 11 (hyp28): e_56 = select(a_55, i5).
% 0.20/0.42 Axiom 12 (hyp31): e_62 = select(a_57, i6).
% 0.20/0.42 Axiom 13 (hyp30): e_60 = select(a_59, i6).
% 0.20/0.42 Axiom 14 (hyp33): e_66 = select(a_61, i7).
% 0.20/0.42 Axiom 15 (hyp32): e_64 = select(a_63, i7).
% 0.20/0.42 Axiom 16 (hyp35): e_70 = select(a_65, i8).
% 0.20/0.42 Axiom 17 (hyp34): e_68 = select(a_67, i8).
% 0.20/0.42 Axiom 18 (hyp37): e_74 = select(a_69, i9).
% 0.20/0.42 Axiom 19 (hyp36): e_72 = select(a_71, i9).
% 0.20/0.42 Axiom 20 (hyp39): e_78 = select(a_73, i10).
% 0.20/0.42 Axiom 21 (hyp38): e_76 = select(a_75, i10).
% 0.20/0.42 Axiom 22 (hyp0): a_41 = store(a1, i1, e_40).
% 0.20/0.42 Axiom 23 (hyp1): a_43 = store(a2, i1, e_42).
% 0.20/0.42 Axiom 24 (hyp2): a_45 = store(a_41, i2, e_44).
% 0.20/0.42 Axiom 25 (hyp3): a_47 = store(a_43, i2, e_46).
% 0.20/0.42 Axiom 26 (hyp4): a_49 = store(a_45, i3, e_48).
% 0.20/0.42 Axiom 27 (hyp5): a_51 = store(a_47, i3, e_50).
% 0.20/0.42 Axiom 28 (hyp6): a_53 = store(a_49, i4, e_52).
% 0.20/0.42 Axiom 29 (hyp7): a_55 = store(a_51, i4, e_54).
% 0.20/0.42 Axiom 30 (hyp8): a_57 = store(a_53, i5, e_56).
% 0.20/0.42 Axiom 31 (hyp9): a_59 = store(a_55, i5, e_58).
% 0.20/0.42 Axiom 32 (hyp10): a_61 = store(a_57, i6, e_60).
% 0.20/0.42 Axiom 33 (hyp11): a_63 = store(a_59, i6, e_62).
% 0.20/0.42 Axiom 34 (hyp12): a_65 = store(a_61, i7, e_64).
% 0.20/0.42 Axiom 35 (hyp13): a_67 = store(a_63, i7, e_66).
% 0.20/0.42 Axiom 36 (hyp14): a_69 = store(a_65, i8, e_68).
% 0.20/0.42 Axiom 37 (hyp15): a_71 = store(a_67, i8, e_70).
% 0.20/0.42 Axiom 38 (hyp16): a_73 = store(a_69, i9, e_72).
% 0.20/0.42 Axiom 39 (hyp17): a_75 = store(a_71, i9, e_74).
% 0.20/0.42 Axiom 40 (hyp18): a_77 = store(a_73, i10, e_76).
% 0.20/0.42 Axiom 41 (hyp19): a_79 = store(a_75, i10, e_78).
% 0.20/0.42 Axiom 42 (a3): store(X, Y, select(X, Y)) = X.
% 0.20/0.42 Axiom 43 (a1): select(store(X, Y, Z), Y) = Z.
% 0.20/0.42 Axiom 44 (a4): store(store(X, Y, Z), Y, W) = store(X, Y, W).
% 0.20/0.42
% 0.20/0.42 Lemma 45: store(a_75, i10, e_78) = a_77.
% 0.20/0.42 Proof:
% 0.20/0.42 store(a_75, i10, e_78)
% 0.20/0.42 = { by axiom 41 (hyp19) R->L }
% 0.20/0.42 a_79
% 0.20/0.42 = { by axiom 1 (hyp40) R->L }
% 0.20/0.42 a_77
% 0.20/0.42
% 0.20/0.42 Lemma 46: a_77 = a_73.
% 0.20/0.42 Proof:
% 0.20/0.42 a_77
% 0.20/0.42 = { by axiom 40 (hyp18) }
% 0.20/0.42 store(a_73, i10, e_76)
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 store(a_73, i10, select(store(a_73, i10, e_76), i10))
% 0.20/0.42 = { by axiom 40 (hyp18) R->L }
% 0.20/0.42 store(a_73, i10, select(a_77, i10))
% 0.20/0.42 = { by lemma 45 R->L }
% 0.20/0.42 store(a_73, i10, select(store(a_75, i10, e_78), i10))
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 store(a_73, i10, e_78)
% 0.20/0.42 = { by axiom 20 (hyp39) }
% 0.20/0.42 store(a_73, i10, select(a_73, i10))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_73
% 0.20/0.42
% 0.20/0.42 Lemma 47: a_75 = a_73.
% 0.20/0.42 Proof:
% 0.20/0.42 a_75
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_75, i10, select(a_75, i10))
% 0.20/0.42 = { by axiom 44 (a4) R->L }
% 0.20/0.42 store(store(a_75, i10, e_78), i10, select(a_75, i10))
% 0.20/0.42 = { by lemma 45 }
% 0.20/0.42 store(a_77, i10, select(a_75, i10))
% 0.20/0.42 = { by lemma 46 }
% 0.20/0.42 store(a_73, i10, select(a_75, i10))
% 0.20/0.42 = { by axiom 21 (hyp38) R->L }
% 0.20/0.42 store(a_73, i10, e_76)
% 0.20/0.42 = { by axiom 40 (hyp18) R->L }
% 0.20/0.42 a_77
% 0.20/0.42 = { by lemma 46 }
% 0.20/0.42 a_73
% 0.20/0.42
% 0.20/0.42 Lemma 48: e_74 = e_72.
% 0.20/0.42 Proof:
% 0.20/0.42 e_74
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_71, i9, e_74), i9)
% 0.20/0.42 = { by axiom 39 (hyp17) R->L }
% 0.20/0.42 select(a_75, i9)
% 0.20/0.42 = { by lemma 47 }
% 0.20/0.42 select(a_73, i9)
% 0.20/0.42 = { by axiom 38 (hyp16) }
% 0.20/0.42 select(store(a_69, i9, e_72), i9)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_72
% 0.20/0.42
% 0.20/0.42 Lemma 49: a_71 = a_69.
% 0.20/0.42 Proof:
% 0.20/0.42 a_71
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_71, i9, select(a_71, i9))
% 0.20/0.42 = { by axiom 19 (hyp36) R->L }
% 0.20/0.42 store(a_71, i9, e_72)
% 0.20/0.42 = { by lemma 48 R->L }
% 0.20/0.42 store(a_71, i9, e_74)
% 0.20/0.42 = { by axiom 39 (hyp17) R->L }
% 0.20/0.42 a_75
% 0.20/0.42 = { by lemma 47 }
% 0.20/0.42 a_73
% 0.20/0.42 = { by axiom 38 (hyp16) }
% 0.20/0.42 store(a_69, i9, e_72)
% 0.20/0.42 = { by lemma 48 R->L }
% 0.20/0.42 store(a_69, i9, e_74)
% 0.20/0.42 = { by axiom 18 (hyp37) }
% 0.20/0.42 store(a_69, i9, select(a_69, i9))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_69
% 0.20/0.42
% 0.20/0.42 Lemma 50: e_70 = e_68.
% 0.20/0.42 Proof:
% 0.20/0.42 e_70
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_67, i8, e_70), i8)
% 0.20/0.42 = { by axiom 37 (hyp15) R->L }
% 0.20/0.42 select(a_71, i8)
% 0.20/0.42 = { by lemma 49 }
% 0.20/0.42 select(a_69, i8)
% 0.20/0.42 = { by axiom 36 (hyp14) }
% 0.20/0.42 select(store(a_65, i8, e_68), i8)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_68
% 0.20/0.42
% 0.20/0.42 Lemma 51: a_67 = a_65.
% 0.20/0.42 Proof:
% 0.20/0.42 a_67
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_67, i8, select(a_67, i8))
% 0.20/0.42 = { by axiom 17 (hyp34) R->L }
% 0.20/0.42 store(a_67, i8, e_68)
% 0.20/0.42 = { by lemma 50 R->L }
% 0.20/0.42 store(a_67, i8, e_70)
% 0.20/0.42 = { by axiom 37 (hyp15) R->L }
% 0.20/0.42 a_71
% 0.20/0.42 = { by lemma 49 }
% 0.20/0.42 a_69
% 0.20/0.42 = { by axiom 36 (hyp14) }
% 0.20/0.42 store(a_65, i8, e_68)
% 0.20/0.42 = { by lemma 50 R->L }
% 0.20/0.42 store(a_65, i8, e_70)
% 0.20/0.42 = { by axiom 16 (hyp35) }
% 0.20/0.42 store(a_65, i8, select(a_65, i8))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_65
% 0.20/0.42
% 0.20/0.42 Lemma 52: e_66 = e_64.
% 0.20/0.42 Proof:
% 0.20/0.42 e_66
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_63, i7, e_66), i7)
% 0.20/0.42 = { by axiom 35 (hyp13) R->L }
% 0.20/0.42 select(a_67, i7)
% 0.20/0.42 = { by lemma 51 }
% 0.20/0.42 select(a_65, i7)
% 0.20/0.42 = { by axiom 34 (hyp12) }
% 0.20/0.42 select(store(a_61, i7, e_64), i7)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_64
% 0.20/0.42
% 0.20/0.42 Lemma 53: a_63 = a_61.
% 0.20/0.42 Proof:
% 0.20/0.42 a_63
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_63, i7, select(a_63, i7))
% 0.20/0.42 = { by axiom 15 (hyp32) R->L }
% 0.20/0.42 store(a_63, i7, e_64)
% 0.20/0.42 = { by lemma 52 R->L }
% 0.20/0.42 store(a_63, i7, e_66)
% 0.20/0.42 = { by axiom 35 (hyp13) R->L }
% 0.20/0.42 a_67
% 0.20/0.42 = { by lemma 51 }
% 0.20/0.42 a_65
% 0.20/0.42 = { by axiom 34 (hyp12) }
% 0.20/0.42 store(a_61, i7, e_64)
% 0.20/0.42 = { by lemma 52 R->L }
% 0.20/0.42 store(a_61, i7, e_66)
% 0.20/0.42 = { by axiom 14 (hyp33) }
% 0.20/0.42 store(a_61, i7, select(a_61, i7))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_61
% 0.20/0.42
% 0.20/0.42 Lemma 54: e_62 = e_60.
% 0.20/0.42 Proof:
% 0.20/0.42 e_62
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_59, i6, e_62), i6)
% 0.20/0.42 = { by axiom 33 (hyp11) R->L }
% 0.20/0.42 select(a_63, i6)
% 0.20/0.42 = { by lemma 53 }
% 0.20/0.42 select(a_61, i6)
% 0.20/0.42 = { by axiom 32 (hyp10) }
% 0.20/0.42 select(store(a_57, i6, e_60), i6)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_60
% 0.20/0.42
% 0.20/0.42 Lemma 55: a_59 = a_57.
% 0.20/0.42 Proof:
% 0.20/0.42 a_59
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_59, i6, select(a_59, i6))
% 0.20/0.42 = { by axiom 13 (hyp30) R->L }
% 0.20/0.42 store(a_59, i6, e_60)
% 0.20/0.42 = { by lemma 54 R->L }
% 0.20/0.42 store(a_59, i6, e_62)
% 0.20/0.42 = { by axiom 33 (hyp11) R->L }
% 0.20/0.42 a_63
% 0.20/0.42 = { by lemma 53 }
% 0.20/0.42 a_61
% 0.20/0.42 = { by axiom 32 (hyp10) }
% 0.20/0.42 store(a_57, i6, e_60)
% 0.20/0.42 = { by lemma 54 R->L }
% 0.20/0.42 store(a_57, i6, e_62)
% 0.20/0.42 = { by axiom 12 (hyp31) }
% 0.20/0.42 store(a_57, i6, select(a_57, i6))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_57
% 0.20/0.42
% 0.20/0.42 Lemma 56: e_58 = e_56.
% 0.20/0.42 Proof:
% 0.20/0.42 e_58
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_55, i5, e_58), i5)
% 0.20/0.42 = { by axiom 31 (hyp9) R->L }
% 0.20/0.42 select(a_59, i5)
% 0.20/0.42 = { by lemma 55 }
% 0.20/0.42 select(a_57, i5)
% 0.20/0.42 = { by axiom 30 (hyp8) }
% 0.20/0.42 select(store(a_53, i5, e_56), i5)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_56
% 0.20/0.42
% 0.20/0.42 Lemma 57: a_55 = a_53.
% 0.20/0.42 Proof:
% 0.20/0.42 a_55
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_55, i5, select(a_55, i5))
% 0.20/0.42 = { by axiom 11 (hyp28) R->L }
% 0.20/0.42 store(a_55, i5, e_56)
% 0.20/0.42 = { by lemma 56 R->L }
% 0.20/0.42 store(a_55, i5, e_58)
% 0.20/0.42 = { by axiom 31 (hyp9) R->L }
% 0.20/0.42 a_59
% 0.20/0.42 = { by lemma 55 }
% 0.20/0.42 a_57
% 0.20/0.42 = { by axiom 30 (hyp8) }
% 0.20/0.42 store(a_53, i5, e_56)
% 0.20/0.42 = { by lemma 56 R->L }
% 0.20/0.42 store(a_53, i5, e_58)
% 0.20/0.42 = { by axiom 10 (hyp29) }
% 0.20/0.42 store(a_53, i5, select(a_53, i5))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_53
% 0.20/0.42
% 0.20/0.42 Lemma 58: e_54 = e_52.
% 0.20/0.42 Proof:
% 0.20/0.42 e_54
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_51, i4, e_54), i4)
% 0.20/0.42 = { by axiom 29 (hyp7) R->L }
% 0.20/0.42 select(a_55, i4)
% 0.20/0.42 = { by lemma 57 }
% 0.20/0.42 select(a_53, i4)
% 0.20/0.42 = { by axiom 28 (hyp6) }
% 0.20/0.42 select(store(a_49, i4, e_52), i4)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_52
% 0.20/0.42
% 0.20/0.42 Lemma 59: a_51 = a_49.
% 0.20/0.42 Proof:
% 0.20/0.42 a_51
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_51, i4, select(a_51, i4))
% 0.20/0.42 = { by axiom 9 (hyp26) R->L }
% 0.20/0.42 store(a_51, i4, e_52)
% 0.20/0.42 = { by lemma 58 R->L }
% 0.20/0.42 store(a_51, i4, e_54)
% 0.20/0.42 = { by axiom 29 (hyp7) R->L }
% 0.20/0.42 a_55
% 0.20/0.42 = { by lemma 57 }
% 0.20/0.42 a_53
% 0.20/0.42 = { by axiom 28 (hyp6) }
% 0.20/0.42 store(a_49, i4, e_52)
% 0.20/0.42 = { by lemma 58 R->L }
% 0.20/0.42 store(a_49, i4, e_54)
% 0.20/0.42 = { by axiom 8 (hyp27) }
% 0.20/0.42 store(a_49, i4, select(a_49, i4))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_49
% 0.20/0.42
% 0.20/0.42 Lemma 60: e_50 = e_48.
% 0.20/0.42 Proof:
% 0.20/0.42 e_50
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_47, i3, e_50), i3)
% 0.20/0.42 = { by axiom 27 (hyp5) R->L }
% 0.20/0.42 select(a_51, i3)
% 0.20/0.42 = { by lemma 59 }
% 0.20/0.42 select(a_49, i3)
% 0.20/0.42 = { by axiom 26 (hyp4) }
% 0.20/0.42 select(store(a_45, i3, e_48), i3)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_48
% 0.20/0.42
% 0.20/0.42 Lemma 61: a_47 = a_45.
% 0.20/0.42 Proof:
% 0.20/0.42 a_47
% 0.20/0.42 = { by axiom 42 (a3) R->L }
% 0.20/0.42 store(a_47, i3, select(a_47, i3))
% 0.20/0.42 = { by axiom 7 (hyp24) R->L }
% 0.20/0.42 store(a_47, i3, e_48)
% 0.20/0.42 = { by lemma 60 R->L }
% 0.20/0.42 store(a_47, i3, e_50)
% 0.20/0.42 = { by axiom 27 (hyp5) R->L }
% 0.20/0.42 a_51
% 0.20/0.42 = { by lemma 59 }
% 0.20/0.42 a_49
% 0.20/0.42 = { by axiom 26 (hyp4) }
% 0.20/0.42 store(a_45, i3, e_48)
% 0.20/0.42 = { by lemma 60 R->L }
% 0.20/0.42 store(a_45, i3, e_50)
% 0.20/0.42 = { by axiom 6 (hyp25) }
% 0.20/0.42 store(a_45, i3, select(a_45, i3))
% 0.20/0.42 = { by axiom 42 (a3) }
% 0.20/0.42 a_45
% 0.20/0.42
% 0.20/0.42 Lemma 62: e_46 = e_44.
% 0.20/0.42 Proof:
% 0.20/0.42 e_46
% 0.20/0.42 = { by axiom 43 (a1) R->L }
% 0.20/0.42 select(store(a_43, i2, e_46), i2)
% 0.20/0.42 = { by axiom 25 (hyp3) R->L }
% 0.20/0.42 select(a_47, i2)
% 0.20/0.42 = { by lemma 61 }
% 0.20/0.42 select(a_45, i2)
% 0.20/0.42 = { by axiom 24 (hyp2) }
% 0.20/0.42 select(store(a_41, i2, e_44), i2)
% 0.20/0.42 = { by axiom 43 (a1) }
% 0.20/0.42 e_44
% 0.20/0.42
% 0.20/0.43 Lemma 63: a_43 = a_41.
% 0.20/0.43 Proof:
% 0.20/0.43 a_43
% 0.20/0.43 = { by axiom 42 (a3) R->L }
% 0.20/0.43 store(a_43, i2, select(a_43, i2))
% 0.20/0.43 = { by axiom 5 (hyp22) R->L }
% 0.20/0.43 store(a_43, i2, e_44)
% 0.20/0.43 = { by lemma 62 R->L }
% 0.20/0.43 store(a_43, i2, e_46)
% 0.20/0.43 = { by axiom 25 (hyp3) R->L }
% 0.20/0.43 a_47
% 0.20/0.43 = { by lemma 61 }
% 0.20/0.43 a_45
% 0.20/0.43 = { by axiom 24 (hyp2) }
% 0.20/0.43 store(a_41, i2, e_44)
% 0.20/0.43 = { by lemma 62 R->L }
% 0.20/0.43 store(a_41, i2, e_46)
% 0.20/0.43 = { by axiom 4 (hyp23) }
% 0.20/0.43 store(a_41, i2, select(a_41, i2))
% 0.20/0.43 = { by axiom 42 (a3) }
% 0.20/0.43 a_41
% 0.20/0.43
% 0.20/0.43 Lemma 64: e_42 = e_40.
% 0.20/0.43 Proof:
% 0.20/0.43 e_42
% 0.20/0.43 = { by axiom 43 (a1) R->L }
% 0.20/0.43 select(store(a2, i1, e_42), i1)
% 0.20/0.43 = { by axiom 23 (hyp1) R->L }
% 0.20/0.43 select(a_43, i1)
% 0.20/0.43 = { by lemma 63 }
% 0.20/0.43 select(a_41, i1)
% 0.20/0.43 = { by axiom 22 (hyp0) }
% 0.20/0.43 select(store(a1, i1, e_40), i1)
% 0.20/0.43 = { by axiom 43 (a1) }
% 0.20/0.43 e_40
% 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 42 (a3) R->L }
% 0.20/0.43 store(a1, i1, select(a1, i1))
% 0.20/0.43 = { by axiom 2 (hyp21) R->L }
% 0.20/0.43 store(a1, i1, e_42)
% 0.20/0.43 = { by lemma 64 }
% 0.20/0.43 store(a1, i1, e_40)
% 0.20/0.43 = { by axiom 22 (hyp0) R->L }
% 0.20/0.43 a_41
% 0.20/0.43 = { by lemma 63 R->L }
% 0.20/0.43 a_43
% 0.20/0.43 = { by axiom 23 (hyp1) }
% 0.20/0.43 store(a2, i1, e_42)
% 0.20/0.43 = { by lemma 64 }
% 0.20/0.43 store(a2, i1, e_40)
% 0.20/0.43 = { by axiom 3 (hyp20) }
% 0.20/0.43 store(a2, i1, select(a2, i1))
% 0.20/0.43 = { by axiom 42 (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).
%------------------------------------------------------------------------------