TSTP Solution File: SWV558-1.004 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV558-1.004 : 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 : 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 23:05:17 EDT 2023
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV558-1.004 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 04:44:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.38 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
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% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 Take the following subset of the input axioms:
% 0.12/0.39 fof(a1, axiom, ![A, I, E]: select(store(A, I, E), I)=E).
% 0.12/0.39 fof(a3, axiom, ![A2, I2]: store(A2, I2, select(A2, I2))=A2).
% 0.12/0.39 fof(goal, negated_conjecture, a1!=a2).
% 0.12/0.39 fof(hyp0, hypothesis, a_17=store(a1, i1, e_16)).
% 0.12/0.39 fof(hyp1, hypothesis, a_19=store(a2, i1, e_18)).
% 0.12/0.39 fof(hyp10, hypothesis, e_20=select(a_19, i2)).
% 0.12/0.39 fof(hyp11, hypothesis, e_22=select(a_17, i2)).
% 0.12/0.39 fof(hyp12, hypothesis, e_24=select(a_23, i3)).
% 0.12/0.39 fof(hyp13, hypothesis, e_26=select(a_21, i3)).
% 0.12/0.39 fof(hyp14, hypothesis, e_28=select(a_27, i4)).
% 0.12/0.39 fof(hyp15, hypothesis, e_30=select(a_25, i4)).
% 0.12/0.39 fof(hyp16, hypothesis, a_29=a_31).
% 0.12/0.39 fof(hyp2, hypothesis, a_21=store(a_17, i2, e_20)).
% 0.12/0.39 fof(hyp3, hypothesis, a_23=store(a_19, i2, e_22)).
% 0.12/0.39 fof(hyp4, hypothesis, a_25=store(a_21, i3, e_24)).
% 0.12/0.39 fof(hyp5, hypothesis, a_27=store(a_23, i3, e_26)).
% 0.12/0.39 fof(hyp6, hypothesis, a_29=store(a_25, i4, e_28)).
% 0.12/0.39 fof(hyp7, hypothesis, a_31=store(a_27, i4, e_30)).
% 0.12/0.39 fof(hyp8, hypothesis, e_16=select(a2, i1)).
% 0.12/0.39 fof(hyp9, hypothesis, e_18=select(a1, i1)).
% 0.12/0.39
% 0.12/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.39 fresh(y, y, x1...xn) = u
% 0.12/0.39 C => fresh(s, t, x1...xn) = v
% 0.12/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.39 variables of u and v.
% 0.12/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.39 input problem has no model of domain size 1).
% 0.12/0.39
% 0.12/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.39
% 0.12/0.39 Axiom 1 (hyp16): a_29 = a_31.
% 0.12/0.39 Axiom 2 (hyp9): e_18 = select(a1, i1).
% 0.12/0.39 Axiom 3 (hyp8): e_16 = select(a2, i1).
% 0.12/0.39 Axiom 4 (hyp11): e_22 = select(a_17, i2).
% 0.12/0.39 Axiom 5 (hyp10): e_20 = select(a_19, i2).
% 0.12/0.39 Axiom 6 (hyp13): e_26 = select(a_21, i3).
% 0.12/0.39 Axiom 7 (hyp12): e_24 = select(a_23, i3).
% 0.12/0.39 Axiom 8 (hyp15): e_30 = select(a_25, i4).
% 0.12/0.39 Axiom 9 (hyp14): e_28 = select(a_27, i4).
% 0.12/0.39 Axiom 10 (hyp0): a_17 = store(a1, i1, e_16).
% 0.12/0.39 Axiom 11 (hyp1): a_19 = store(a2, i1, e_18).
% 0.12/0.39 Axiom 12 (hyp2): a_21 = store(a_17, i2, e_20).
% 0.12/0.39 Axiom 13 (hyp3): a_23 = store(a_19, i2, e_22).
% 0.12/0.39 Axiom 14 (hyp4): a_25 = store(a_21, i3, e_24).
% 0.12/0.39 Axiom 15 (hyp5): a_27 = store(a_23, i3, e_26).
% 0.12/0.39 Axiom 16 (hyp6): a_29 = store(a_25, i4, e_28).
% 0.12/0.39 Axiom 17 (hyp7): a_31 = store(a_27, i4, e_30).
% 0.12/0.39 Axiom 18 (a3): store(X, Y, select(X, Y)) = X.
% 0.12/0.39 Axiom 19 (a1): select(store(X, Y, Z), Y) = Z.
% 0.12/0.39
% 0.12/0.39 Lemma 20: store(a_27, i4, e_30) = a_29.
% 0.12/0.39 Proof:
% 0.12/0.39 store(a_27, i4, e_30)
% 0.12/0.39 = { by axiom 17 (hyp7) R->L }
% 0.12/0.39 a_31
% 0.12/0.39 = { by axiom 1 (hyp16) R->L }
% 0.12/0.39 a_29
% 0.12/0.39
% 0.12/0.39 Lemma 21: e_30 = e_28.
% 0.12/0.39 Proof:
% 0.12/0.39 e_30
% 0.12/0.39 = { by axiom 19 (a1) R->L }
% 0.12/0.39 select(store(a_27, i4, e_30), i4)
% 0.12/0.39 = { by lemma 20 }
% 0.12/0.39 select(a_29, i4)
% 0.12/0.39 = { by axiom 16 (hyp6) }
% 0.12/0.39 select(store(a_25, i4, e_28), i4)
% 0.12/0.39 = { by axiom 19 (a1) }
% 0.12/0.39 e_28
% 0.12/0.39
% 0.12/0.39 Lemma 22: a_27 = a_25.
% 0.12/0.39 Proof:
% 0.12/0.39 a_27
% 0.12/0.39 = { by axiom 18 (a3) R->L }
% 0.12/0.39 store(a_27, i4, select(a_27, i4))
% 0.12/0.39 = { by axiom 9 (hyp14) R->L }
% 0.12/0.39 store(a_27, i4, e_28)
% 0.12/0.39 = { by lemma 21 R->L }
% 0.12/0.39 store(a_27, i4, e_30)
% 0.12/0.39 = { by lemma 20 }
% 0.12/0.39 a_29
% 0.12/0.39 = { by axiom 16 (hyp6) }
% 0.12/0.39 store(a_25, i4, e_28)
% 0.12/0.39 = { by lemma 21 R->L }
% 0.12/0.39 store(a_25, i4, e_30)
% 0.12/0.39 = { by axiom 8 (hyp15) }
% 0.12/0.39 store(a_25, i4, select(a_25, i4))
% 0.12/0.39 = { by axiom 18 (a3) }
% 0.12/0.39 a_25
% 0.12/0.39
% 0.12/0.39 Lemma 23: e_26 = e_24.
% 0.12/0.39 Proof:
% 0.12/0.39 e_26
% 0.12/0.39 = { by axiom 19 (a1) R->L }
% 0.12/0.39 select(store(a_23, i3, e_26), i3)
% 0.12/0.39 = { by axiom 15 (hyp5) R->L }
% 0.12/0.39 select(a_27, i3)
% 0.12/0.39 = { by lemma 22 }
% 0.12/0.39 select(a_25, i3)
% 0.12/0.39 = { by axiom 14 (hyp4) }
% 0.12/0.39 select(store(a_21, i3, e_24), i3)
% 0.12/0.39 = { by axiom 19 (a1) }
% 0.12/0.39 e_24
% 0.12/0.39
% 0.12/0.39 Lemma 24: a_23 = a_21.
% 0.12/0.39 Proof:
% 0.12/0.39 a_23
% 0.12/0.39 = { by axiom 18 (a3) R->L }
% 0.12/0.39 store(a_23, i3, select(a_23, i3))
% 0.12/0.39 = { by axiom 7 (hyp12) R->L }
% 0.12/0.39 store(a_23, i3, e_24)
% 0.12/0.39 = { by lemma 23 R->L }
% 0.12/0.39 store(a_23, i3, e_26)
% 0.12/0.39 = { by axiom 15 (hyp5) R->L }
% 0.12/0.39 a_27
% 0.12/0.39 = { by lemma 22 }
% 0.12/0.39 a_25
% 0.12/0.39 = { by axiom 14 (hyp4) }
% 0.12/0.39 store(a_21, i3, e_24)
% 0.12/0.39 = { by lemma 23 R->L }
% 0.12/0.39 store(a_21, i3, e_26)
% 0.12/0.39 = { by axiom 6 (hyp13) }
% 0.12/0.39 store(a_21, i3, select(a_21, i3))
% 0.12/0.39 = { by axiom 18 (a3) }
% 0.12/0.39 a_21
% 0.12/0.39
% 0.12/0.39 Lemma 25: e_22 = e_20.
% 0.12/0.39 Proof:
% 0.12/0.39 e_22
% 0.12/0.39 = { by axiom 19 (a1) R->L }
% 0.12/0.39 select(store(a_19, i2, e_22), i2)
% 0.12/0.39 = { by axiom 13 (hyp3) R->L }
% 0.12/0.39 select(a_23, i2)
% 0.12/0.39 = { by lemma 24 }
% 0.12/0.39 select(a_21, i2)
% 0.12/0.39 = { by axiom 12 (hyp2) }
% 0.12/0.39 select(store(a_17, i2, e_20), i2)
% 0.12/0.39 = { by axiom 19 (a1) }
% 0.12/0.39 e_20
% 0.12/0.39
% 0.12/0.39 Lemma 26: a_19 = a_17.
% 0.12/0.39 Proof:
% 0.12/0.39 a_19
% 0.12/0.39 = { by axiom 18 (a3) R->L }
% 0.12/0.39 store(a_19, i2, select(a_19, i2))
% 0.12/0.39 = { by axiom 5 (hyp10) R->L }
% 0.12/0.39 store(a_19, i2, e_20)
% 0.12/0.39 = { by lemma 25 R->L }
% 0.12/0.39 store(a_19, i2, e_22)
% 0.12/0.39 = { by axiom 13 (hyp3) R->L }
% 0.12/0.39 a_23
% 0.12/0.39 = { by lemma 24 }
% 0.12/0.39 a_21
% 0.12/0.39 = { by axiom 12 (hyp2) }
% 0.12/0.39 store(a_17, i2, e_20)
% 0.12/0.39 = { by lemma 25 R->L }
% 0.12/0.39 store(a_17, i2, e_22)
% 0.12/0.39 = { by axiom 4 (hyp11) }
% 0.12/0.39 store(a_17, i2, select(a_17, i2))
% 0.12/0.39 = { by axiom 18 (a3) }
% 0.12/0.39 a_17
% 0.12/0.39
% 0.12/0.39 Lemma 27: e_18 = e_16.
% 0.12/0.39 Proof:
% 0.12/0.39 e_18
% 0.12/0.39 = { by axiom 19 (a1) R->L }
% 0.12/0.39 select(store(a2, i1, e_18), i1)
% 0.12/0.39 = { by axiom 11 (hyp1) R->L }
% 0.12/0.39 select(a_19, i1)
% 0.12/0.39 = { by lemma 26 }
% 0.12/0.39 select(a_17, i1)
% 0.12/0.39 = { by axiom 10 (hyp0) }
% 0.12/0.39 select(store(a1, i1, e_16), i1)
% 0.12/0.39 = { by axiom 19 (a1) }
% 0.12/0.39 e_16
% 0.12/0.39
% 0.12/0.39 Goal 1 (goal): a1 = a2.
% 0.12/0.39 Proof:
% 0.12/0.39 a1
% 0.12/0.39 = { by axiom 18 (a3) R->L }
% 0.12/0.39 store(a1, i1, select(a1, i1))
% 0.12/0.39 = { by axiom 2 (hyp9) R->L }
% 0.12/0.39 store(a1, i1, e_18)
% 0.12/0.39 = { by lemma 27 }
% 0.12/0.39 store(a1, i1, e_16)
% 0.12/0.39 = { by axiom 10 (hyp0) R->L }
% 0.12/0.39 a_17
% 0.12/0.39 = { by lemma 26 R->L }
% 0.12/0.39 a_19
% 0.12/0.39 = { by axiom 11 (hyp1) }
% 0.12/0.39 store(a2, i1, e_18)
% 0.12/0.39 = { by lemma 27 }
% 0.12/0.39 store(a2, i1, e_16)
% 0.12/0.39 = { by axiom 3 (hyp8) }
% 0.12/0.39 store(a2, i1, select(a2, i1))
% 0.12/0.39 = { by axiom 18 (a3) }
% 0.12/0.39 a2
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39
% 0.12/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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